opennurbs_mesh.cpp

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/* $NoKeywords: $ */
/*
//
// Copyright (c) 1993-2012 Robert McNeel & Associates. All rights reserved.
// OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert
// McNeel & Associates.
//
// THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY.
// ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF
// MERCHANTABILITY ARE HEREBY DISCLAIMED.
//                              
// For complete openNURBS copyright information see <http://www.opennurbs.org>.
//
*/

#include "pcl/surface/3rdparty/opennurbs/opennurbs.h"


// NEVER COPY OR MOVE THE NEXT 2 LINES
#define ON_BOZO_VACCINE_17F24E7521BE4a7b9F3D7F85225247E3
#define ON_BOZO_VACCINE_B5628CA982C44CAE9883487B3E4AB28B
// NEVER COPY OR MOVE THE PREVIOUS 2 LINES




//
// Double precision vertices user data
//

class /* DO NOT copy, move, or export this class */ ON_MeshDoubleVertices : public ON_UserData
{
  ON_OBJECT_DECLARE(ON_MeshDoubleVertices);

public:
  ON_MeshDoubleVertices();
  ~ON_MeshDoubleVertices();  

  // default copy constructor and operator= work fine.

  /*
    If the mesh has ON_MeshDoubleVertices user data, then return
    a pointer to it.
  */
  static ON_MeshDoubleVertices* Get(const ON_Mesh* mesh);

  /*
    Attach new ON_MeshDoubleVertices user data to the mesh.
    This will fail and return NULL if the mesh already has
    ON_MeshDoubleVertices user data.
  */
  static ON_MeshDoubleVertices* Attach(const ON_Mesh* mesh);

  // virtual ON_Object overrides
  ON_BOOL32 IsValid( ON_TextLog* = NULL ) const;
  void Dump( ON_TextLog& ) const;
  unsigned int SizeOf() const;
  ON__UINT32 DataCRC(ON__UINT32) const;
  ON_BOOL32 Write(ON_BinaryArchive&) const;
  ON_BOOL32 Read(ON_BinaryArchive&);

  // virtual ON_UserData overrides
  ON_BOOL32 GetDescription( ON_wString& );
  ON_BOOL32 Archive() const; 
  ON_BOOL32 Transform( const ON_Xform& ); 

#if !defined(ON_BOZO_VACCINE_17F24E7521BE4a7b9F3D7F85225247E3)
#error DO NOT copy, move or export the definition of ON_MeshDoubleVertices
#endif
#undef ON_BOZO_VACCINE_17F24E7521BE4a7b9F3D7F85225247E3

  ON__UINT32 DoubleCRC() const;
  static ON__UINT32 FloatCRC( const ON_3fPointArray& );

  // If m_dV.Count() != m_dcount or
  // m_dCRC != ON_CRC32(0,m_dV.Count()*sizeof(ON_3dPoint),m_dV.Array()),
  // then somebody has changed m_dV and not called
  // SetDoublePrecisionVerticesAsValid() to mark the
  // values as valid.
  //
  // If ON_Mesh.M_V.Count() != m_fcount or
  // m_fCRC != ON_CRC32(0,m_V.Count()*sizeof(ON_3fPoint),m_V.Array()),
  // then somebody has changed ON_Mesh.m_V and not called
  // SetSinglePrecisionVerticesAsValid() to mark the
  // values as valid.
  //
  // Whenever there is a question about which values are valid,
  // it is assumed the m_V array is valid and the double precision
  // informtion should be destroyed.
  int m_fcount;  // single precision vertex count
  int m_dcount;  // double precision vertex count
  ON__UINT32 m_fCRC; // crc of float vertex array
  ON__UINT32 m_dCRC; // crc of double vertex array

  ON_3dPointArray m_dV; // double precision mesh vertices
};

static const ON_3dPoint* Mesh_dV(const ON_Mesh& mesh)
{
  if ( mesh.HasDoublePrecisionVertices() && mesh.DoublePrecisionVerticesAreValid() )
  {
    const ON_3dPointArray& a = mesh.DoublePrecisionVertices();
    if ( a.Count() == mesh.m_V.Count() )
      return a.Array();
  }
  return 0;
}

ON_MeshCurveParameters::ON_MeshCurveParameters()
{
  memset(this,0,sizeof(*this));
}

ON_OBJECT_IMPLEMENT(ON_Mesh,ON_Geometry,"4ED7D4E4-E947-11d3-BFE5-0010830122F0");

/*
ON_MeshEdge& ON_MeshEdge::operator=( const ON_MeshEdge& src )
{
  int fc = src.m_fcount+(src.m_fcount%1);
  if ( fc <= 2 ) {
    if ( m_fi && m_fi != m_private_fi ) onfree((void*)m_fi);
    m_fi = m_private_fi;
    fc = 2;
  }
  else {
    if ( (m_fcount+(m_fcount%1)) != fc ) {
      if ( m_fi == m_private_fi )
        m_fi = 0;
      m_fi = (int*)onrealloc(m_fi,fc*sizeof(*m_fi));
    }
  }
  memcpy(m_fi,src.m_fi,fc*sizeof(*m_fi));
  m_fcount=src.m_fcount;
  return *this;
}

void ON_MeshEdge::AppendFaceIndex(int face_index)
{
  if ( m_fcount>0 && !(m_fcount%1) ) {
    if ( m_fi == m_private_fi ) {
      m_fi = (int*)onmalloc((m_fcount+2)*sizeof(*m_fi));
      m_fi[0] = m_private_fi[0];
      m_fi[1] = m_private_fi[1];
    }
    else {
      m_fi = (int*)onrealloc(m_fi,(m_fcount+2)*sizeof(*m_fi));
    }
  }
  m_fi[m_fcount++] = face_index;
}
*/

bool
ON_MeshFace::IsValid(int mesh_vertex_count) const
{
  return (    vi[0] >= 0 && vi[0] < mesh_vertex_count
           && vi[1] >= 0 && vi[1] < mesh_vertex_count
           && vi[2] >= 0 && vi[2] < mesh_vertex_count
           && vi[3] >= 0 && vi[3] < mesh_vertex_count
           && vi[0] != vi[1] && vi[1] != vi[2] && vi[2] != vi[0] 
           && (vi[2]==vi[3]||(vi[0] != vi[3] && vi[1] != vi[3])) );
}


bool
ON_MeshFace::IsValid(int mesh_vertex_count, const ON_3fPoint* V ) const
{
  if ( !IsValid(mesh_vertex_count) )
    return false;
  if ( !(V[vi[0]] != V[vi[1]]) )
    return false;
  if ( !(V[vi[0]] != V[vi[2]]) )
    return false;
  if ( !(V[vi[1]] != V[vi[2]]) )
    return false;
  if ( vi[2] != vi[3] )
  {
  if ( !(V[vi[0]] != V[vi[3]]) )
    return false;
  if ( !(V[vi[1]] != V[vi[3]]) )
    return false;
  if ( !(V[vi[2]] != V[vi[3]]) )
    return false;
  }
  return true;
}


bool
ON_MeshFace::IsValid(int mesh_vertex_count, const ON_3dPoint* V ) const
{
  if ( !IsValid(mesh_vertex_count) )
    return false;
  if ( !(V[vi[0]] != V[vi[1]]) )
    return false;
  if ( !(V[vi[0]] != V[vi[2]]) )
    return false;
  if ( !(V[vi[1]] != V[vi[2]]) )
    return false;
  if ( vi[2] != vi[3] )
  {
  if ( !(V[vi[0]] != V[vi[3]]) )
    return false;
  if ( !(V[vi[1]] != V[vi[3]]) )
    return false;
  if ( !(V[vi[2]] != V[vi[3]]) )
    return false;
  }
  return true;
}


bool ON_MeshFace::Repair(
  int mesh_vertex_count
  )
{
  ON_MeshFace f;
  int fvi_count = 0;
  f.vi[0] = f.vi[1] = f.vi[2] = f.vi[3] = -1;
  
  if ( vi[0] >= 0 && vi[0] < mesh_vertex_count )
    f.vi[fvi_count++] = vi[0];

  if ( vi[1] >= 0 && vi[1] < mesh_vertex_count && f.vi[0] != vi[1] )
    f.vi[fvi_count++] = vi[1];

  if ( vi[2] >= 0 && vi[2] < mesh_vertex_count && f.vi[0] != vi[2] && f.vi[1] != vi[2] )
    f.vi[fvi_count++] = vi[2];

  if ( vi[3] >= 0 && vi[3] < mesh_vertex_count && f.vi[0] != vi[3] && f.vi[1] != vi[3] && f.vi[2] != vi[3] )
    f.vi[fvi_count++] = vi[3];
  
  if ( fvi_count < 3 )
    return false;
 
  if ( 3 == fvi_count )
    f.vi[3] = f.vi[2];
  
  if ( !f.IsValid(mesh_vertex_count) )
    return false;

  vi[0] = f.vi[0];
  vi[1] = f.vi[1];
  vi[2] = f.vi[2];
  vi[3] = f.vi[3];

  return true;
}

bool ON_MeshFace::Repair(
  int mesh_vertex_count,
  const ON_3fPoint* V
  )
{
  ON_MeshFace f;
  int fvi_count = 0;
  f.vi[0] = f.vi[1] = f.vi[2] = f.vi[3] = -1;
  
  if ( vi[0] >= 0 && vi[0] < mesh_vertex_count )
    f.vi[fvi_count++] = vi[0];

  if ( vi[1] >= 0 && vi[1] < mesh_vertex_count && f.vi[0] != vi[1] )
  {
    if ( 0 == fvi_count || V[f.vi[0]] != V[vi[1]] )
      f.vi[fvi_count++] = vi[1];
  }

  if ( fvi_count < 1 )
    return false;

  if ( vi[2] >= 0 && vi[2] < mesh_vertex_count && f.vi[0] != vi[2] && f.vi[1] != vi[2] && V[f.vi[0]] != V[vi[2]] )
  {
    if ( 1 == fvi_count || V[f.vi[1]] != V[vi[2]] )
      f.vi[fvi_count++] = vi[2];
  }

  if ( fvi_count < 2 )
    return false;

  if ( vi[3] >= 0 && vi[3] < mesh_vertex_count && f.vi[0] != vi[3] && f.vi[1] != vi[3] && f.vi[2] != vi[3] && V[f.vi[0]] != V[vi[3]] && V[f.vi[1]] != V[vi[3]] )
  {
    if ( 2 == fvi_count || V[f.vi[2]] != V[vi[3]] )
      f.vi[fvi_count++] = vi[3];
  }
  
  if ( fvi_count < 3 )
    return false;
 
  if ( 3 == fvi_count )
    f.vi[3] = f.vi[2];
  
  if ( !f.IsValid(mesh_vertex_count) )
    return false;

  vi[0] = f.vi[0];
  vi[1] = f.vi[1];
  vi[2] = f.vi[2];
  vi[3] = f.vi[3];

  return true;
}


bool ON_MeshFace::Repair(
  int mesh_vertex_count,
  const ON_3dPoint* V
  )
{
  ON_MeshFace f;
  int fvi_count = 0;
  f.vi[0] = f.vi[1] = f.vi[2] = f.vi[3] = -1;
  
  if ( vi[0] >= 0 && vi[0] < mesh_vertex_count )
    f.vi[fvi_count++] = vi[0];

  if ( vi[1] >= 0 && vi[1] < mesh_vertex_count && f.vi[0] != vi[1] )
  {
    if ( 0 == fvi_count || V[f.vi[0]] != V[vi[1]] )
      f.vi[fvi_count++] = vi[1];
  }

  if ( fvi_count < 1 )
    return false;

  if ( vi[2] >= 0 && vi[2] < mesh_vertex_count && f.vi[0] != vi[2] && f.vi[1] != vi[2] && V[f.vi[0]] != V[vi[2]] )
  {
    if ( 1 == fvi_count || V[f.vi[1]] != V[vi[2]] )
      f.vi[fvi_count++] = vi[2];
  }

  if ( fvi_count < 2 )
    return false;

  if ( vi[3] >= 0 && vi[3] < mesh_vertex_count && f.vi[0] != vi[3] && f.vi[1] != vi[3] && f.vi[2] != vi[3] && V[f.vi[0]] != V[vi[3]] && V[f.vi[1]] != V[vi[3]] )
  {
    if ( 2 == fvi_count || V[f.vi[2]] != V[vi[3]] )
      f.vi[fvi_count++] = vi[3];
  }
  
  if ( fvi_count < 3 )
    return false;
 
  if ( 3 == fvi_count )
    f.vi[3] = f.vi[2];
  
  if ( !f.IsValid(mesh_vertex_count) )
    return false;

  vi[0] = f.vi[0];
  vi[1] = f.vi[1];
  vi[2] = f.vi[2];
  vi[3] = f.vi[3];

  return true;
}

ON_Mesh::ON_Mesh() 
: m_packed_tex_rotate(0)
, m_parent(0)
, m_mesh_parameters(0) 
, m_invalid_count(0) 
, m_quad_count(0) 
, m_triangle_count(0)
, m_mesh_is_closed(0)
, m_mesh_is_manifold(0)
, m_mesh_is_oriented(0)
, m_mesh_is_solid(0)
{
  m_top.m_mesh = this;
  m_srf_scale[0] = 0.0;
  m_srf_scale[1] = 0.0;
  m_kstat[0] = 0;
  m_kstat[1] = 0;
  m_kstat[2] = 0;
  m_kstat[3] = 0;
  InvalidateBoundingBoxes();
  m_partition = 0;
  m_hidden_count = 0;
}


ON_Mesh::ON_Mesh(
    int initial_facet_capacity,  // initial facet array capacity
    int initial_vertex_capacity,  // initial vertex array capacity
    bool bHasVertexNormals, // true if mesh has unit vertex normals
    bool bHasTextureCoordinates // true if mesh has texture coordinates
    )
: m_V(initial_vertex_capacity)
, m_F(initial_facet_capacity)
, m_N(bHasVertexNormals?initial_vertex_capacity:0)
, m_T(bHasTextureCoordinates?initial_vertex_capacity:0)
, m_packed_tex_rotate(0)
, m_parent(0) 
, m_mesh_parameters(0)
, m_invalid_count(0) 
, m_quad_count(0) 
, m_triangle_count(0)
, m_mesh_is_closed(0)
, m_mesh_is_manifold(0)
, m_mesh_is_oriented(0)
, m_mesh_is_solid(0)
{
  m_top.m_mesh = this;
  m_srf_scale[0] = 0.0;
  m_srf_scale[1] = 0.0;
  m_kstat[0] = 0;
  m_kstat[1] = 0;
  m_kstat[2] = 0;
  m_kstat[3] = 0;
  InvalidateBoundingBoxes();
  m_partition = 0;
  m_hidden_count = 0;
}

ON_Mesh::ON_Mesh( const ON_Mesh& src ) 
: m_packed_tex_rotate(0)
, m_parent(0) 
, m_mesh_parameters(0) 
, m_invalid_count(0) 
, m_quad_count(0) 
, m_triangle_count(0)
, m_mesh_is_closed(0)
, m_mesh_is_manifold(0)
, m_mesh_is_oriented(0)
, m_mesh_is_solid(0)
{
  // Do not copy m_mesh_cache. Cached information will
  // be recalculated if it is needed.
  m_top.m_mesh = this;
  m_srf_scale[0] = 0.0;
  m_srf_scale[1] = 0.0;

  m_kstat[0] = 0;
  m_kstat[1] = 0;
  m_kstat[2] = 0;
  m_kstat[3] = 0;
  InvalidateBoundingBoxes();
  m_partition = 0;
  m_hidden_count = 0;
  ON_Mesh::operator=(src);
}


unsigned int ON_Mesh::SizeOf() const
{
  unsigned int sz = ON_Geometry::SizeOf();
  sz += m_V.SizeOfArray();
  sz += m_F.SizeOfArray();
  sz += m_N.SizeOfArray();
  sz += m_FN.SizeOfArray();
  sz += m_T.SizeOfArray();
  sz += m_S.SizeOfArray();
  sz += m_K.SizeOfArray();
  sz += m_C.SizeOfArray();  
  sz += m_top.m_topv_map.SizeOfArray();
  sz += m_top.m_topv.SizeOfArray();
  sz += m_top.m_tope.SizeOfArray();
  sz += m_top.m_topf.SizeOfArray();
  return sz;
}

ON__UINT32 ON_Mesh::DataCRC(ON__UINT32 current_remainder) const
{
  const ON_3fPoint* p = m_V.Array();
  current_remainder = ON_CRC32(current_remainder,m_V.Count()*sizeof(p[0]),p);
  current_remainder = ON_CRC32(current_remainder,m_F.Count()*sizeof(ON_MeshFace),m_F.Array());
  const ON_3fVector* v = m_N.Array();
  current_remainder = ON_CRC32(current_remainder,m_N.Count()*sizeof(v[0]),v);
  return current_remainder;
}

ON_Mesh& ON_Mesh::operator=( const ON_Mesh& src )
{
  if ( this != &src ) 
  {
    Destroy();
    ON_Geometry::operator=(src);

    m_V  = src.m_V;
    m_F  = src.m_F;
    m_N  = src.m_N;
    m_FN = src.m_FN;
    m_T  = src.m_T;
    m_TC = src.m_TC;
    m_S  = src.m_S;
    m_H  = src.m_H;
    m_hidden_count = src.m_hidden_count;

    m_Ctag = src.m_Ctag;
    m_Ttag = src.m_Ttag;
    m_packed_tex_domain[0] = src.m_packed_tex_domain[0];
    m_packed_tex_domain[1] = src.m_packed_tex_domain[1];
    m_srf_domain[0] = src.m_srf_domain[0];
    m_srf_domain[1] = src.m_srf_domain[1];
    m_srf_scale[0] = src.m_srf_scale[0];
    m_srf_scale[1] = src.m_srf_scale[1];
    m_packed_tex_rotate = src.m_packed_tex_rotate;

    m_K = src.m_K;
    m_C = src.m_C;

    m_parent         = src.m_parent;
    //m_material_index = src.m_material_index;

    if ( m_mesh_parameters ) {
      delete m_mesh_parameters;
      m_mesh_parameters = 0;
    }
    if ( src.m_mesh_parameters )
      m_mesh_parameters = new ON_MeshParameters(*src.m_mesh_parameters);

    m_invalid_count = src.m_invalid_count;
    m_quad_count = src.m_quad_count;
    m_triangle_count = src.m_triangle_count;

    m_mesh_is_closed = src.m_mesh_is_closed;
    m_mesh_is_manifold = src.m_mesh_is_manifold;
    m_mesh_is_oriented = src.m_mesh_is_oriented;
    m_mesh_is_solid    = src.m_mesh_is_solid;

    memcpy(m_vbox,src.m_vbox,sizeof(m_vbox));
    memcpy(m_nbox,src.m_nbox,sizeof(m_nbox));
    memcpy(m_tbox,src.m_tbox,sizeof(m_tbox));

    int i;
    for ( i = 0; i < 4; i++ ) {
      if ( m_kstat[i] ) 
      {
        delete m_kstat[i];
        m_kstat[i] = 0;
      }
      if ( src.m_kstat[i] )
      {
        m_kstat[i] = new ON_MeshCurvatureStats(*src.m_kstat[i]);
      }
    }

    // do not copy m_top

    // Do not copy m_mesh_cache. Cached information will
    // be recalculated if it is needed.
  }
  return *this;
}

ON_Mesh::~ON_Mesh()
{
  Destroy();
  m_top.m_mesh = 0;
}

void ON_Mesh::MemoryRelocate()
{
  // the back pointer on m_top needs to be updated.
  m_top.m_mesh = this;
}

void ON_Mesh::Destroy()
{
  PurgeUserData();
  DestroyRuntimeCache( true );
  m_Ttag.Default();
  m_Ctag.Default();
  m_V.Destroy();
  m_F.Destroy();
  m_N.Destroy();
  m_FN.Destroy();
  m_T.Destroy();
  m_TC.Destroy();
  m_S.Destroy();
  m_K.Destroy();
  m_C.Destroy();
}

void ON_Mesh::EmergencyDestroy()
{
  DestroyRuntimeCache( false );
  m_V.EmergencyDestroy();
  m_F.EmergencyDestroy();
  m_N.EmergencyDestroy();
  m_FN.EmergencyDestroy();
  m_T.EmergencyDestroy();
  m_TC.EmergencyDestroy();
  m_S.EmergencyDestroy();
  m_K.EmergencyDestroy();
  m_C.EmergencyDestroy();
}

static bool ON_MeshIsNotValid(bool bSilentError)
{
  return bSilentError ? false : ON_IsNotValid(); // good place for a breakpoint;
}

ON_BOOL32 ON_Mesh::IsValid( ON_TextLog* text_logx ) const
{
  // If low bit of text_log pointer is 1, then ON_Error is not called when the
  // knot vector is invalid.
  const ON__INT_PTR lowbit = 1;
  const ON__INT_PTR hightbits = ~lowbit;
  bool bSilentError = ( 0 != (lowbit & ((ON__INT_PTR)text_logx)) );
  ON_TextLog* text_log = (ON_TextLog*)(((ON__INT_PTR)text_logx) & hightbits);

  const int facet_count = FaceCount();
  const int vertex_count = VertexCount();
  int fi, vi;

  if (facet_count < 1) 
  {
    if ( text_log )
    {
      text_log->Print("ON_Mesh.m_F.Count() < 1 (should be at least 1).\n");
    }
    return ON_MeshIsNotValid(bSilentError);
  }

  if ( vertex_count < 3 )
  {
    if ( text_log )
    {
      text_log->Print("ON_Mesh.m_V.Count() < 3 (should be at least 3).\n");
    }
    return ON_MeshIsNotValid(bSilentError);
  }

  if ( m_N.Count() > 0 && m_N.Count() != vertex_count )
  {
    if ( text_log )
    {
      text_log->Print("ON_Mesh.m_N.Count() = %d (should be 0 or %d=vertex_count).\n",
                      m_N.Count(),vertex_count);
    }
    return ON_MeshIsNotValid(bSilentError);
  }

  if ( m_T.Count() > 0 && m_T.Count() != vertex_count )
  {
    if ( text_log )
    {
      text_log->Print("ON_Mesh.m_T.Count() = %d (should be 0 or %d=vertex_count).\n",
                      m_T.Count(),vertex_count);
    }
    return ON_MeshIsNotValid(bSilentError);
  }

  if ( m_S.Count() > 0 && m_S.Count() != vertex_count )
  {
    if ( text_log )
    {
      text_log->Print("ON_Mesh.m_S.Count() = %d (should be 0 or %d=vertex_count).\n",
                      m_S.Count(),vertex_count);
    }
    return ON_MeshIsNotValid(bSilentError);
  }

  if ( HasVertexNormals() ) 
  {
    float x;
    for ( vi = 0; vi < vertex_count; vi++ ) {
      x = m_N[vi][0]*m_N[vi][0] + m_N[vi][1]*m_N[vi][1] + m_N[vi][2]*m_N[vi][2];
      if ( x < 0.985 || x > 1.015 )
      {
        if ( text_log )
        {
          text_log->Print("ON_Mesh.m_N[%d] is not a unit vector (length = %g).\n",vi,sqrt(x));
        }
        return ON_MeshIsNotValid(bSilentError);
      }
    }
  }

        // Greg Arden 9 May 2003. Fixes TRR#10604.  Attempt to detect meshes with non-finite vertices
        // by testing the bounding box.
  int i;
  for ( i = 0; i < 3; i++ )
  {
    if ( !ON_IsValid( m_vbox[0][i] ) || !ON_IsValid( m_vbox[1][i] ) )
    {
      if ( text_log )
      {
        text_log->Print("ON_Mesh.m_vbox is not finite.  Check for invalid vertices\n");
      }         
            return ON_MeshIsNotValid(bSilentError);
    }   
  }

  const ON_3dPoint* dV = 0;
  while ( HasDoublePrecisionVertices() )
  {
    bool bValidDoubles = DoublePrecisionVerticesAreValid();
    if ( bValidDoubles )
      dV = DoublePrecisionVertices().Array();
    bool bValidFloats  = SinglePrecisionVerticesAreValid();
    bool bSynchronized = HasSynchronizedDoubleAndSinglePrecisionVertices();
    if ( bSynchronized && bValidDoubles && bValidFloats )
      break;

    if ( !bSynchronized )
    {
      if ( text_log )
      {
        text_log->Print("Single and double precision vertices are not synchronized.\n");
      }         
            return ON_MeshIsNotValid(bSilentError);
    }

    if ( !bValidDoubles )
    {
      if ( text_log )
      {
        text_log->Print("Double precision vertices appear to be ok but are not marked as valid\n");
      }         
            return ON_MeshIsNotValid(bSilentError);
    }

    if ( !bValidFloats )
    {
      if ( text_log )
      {
        text_log->Print("Single precision vertices appear to be ok but are not marked as valid\n");
      }         
            return ON_MeshIsNotValid(bSilentError);
    }


    break;
  }

  if ( 0 != dV )
  {
    for ( fi = 0; fi < facet_count; fi++ ) 
    {
      if ( !m_F[fi].IsValid( vertex_count, dV ) ) 
      {
        if ( text_log )
        {
          if ( !m_F[fi].IsValid( vertex_count) )
            text_log->Print("ON_Mesh.m_F[%d].vi[] has invalid vertex indices.\n",fi);
          else
            text_log->Print("ON_Mesh.m_F[%d] has degenerate double precision vertex locations.\n",fi);
        }
        return ON_MeshIsNotValid(bSilentError);
      }
    }
  }
  else
  {
    //const ON_3fPoint* fV = m_V.Array();
    for ( fi = 0; fi < facet_count; fi++ ) 
    {
      // This test was too harsh for float precision meshes
      // with nearly degnerate faces after they are transformed
      // by a transform with a reasonable sized translation 
      // component.
      // See bug http://dev.mcneel.com/bugtrack/?q=87465

      //if ( !m_F[fi].IsValid( vertex_count, fV ) ) 
      //{
      //  if ( text_log )
      //  {
      //    if ( !m_F[fi].IsValid( vertex_count) )
      //      text_log->Print("ON_Mesh.m_F[%d].vi[] has invalid vertex indices.\n",fi);
      //    else
      //      text_log->Print("ON_Mesh.m_F[%d] has degenerate float precision vertex locations.\n",fi);
      //  }
      //  return ON_MeshIsNotValid(bSilentError);
      //}

      if ( !m_F[fi].IsValid( vertex_count ) ) 
      {
        if ( text_log )
          text_log->Print("ON_Mesh.m_F[%d].vi[] has invalid vertex indices.\n",fi);
        return ON_MeshIsNotValid(bSilentError);
      }
    }
  }


  return true;
}

void ON_Mesh::Dump( ON_TextLog& dump ) const
{
  const int half_max = 8;

  const int fcount = m_F.Count();
  int i;
  const int vcount = m_V.Count();
  ON_3dPoint p, q;

  bool bDoubles =    vcount > 0 
                  && HasDoublePrecisionVertices()
                  && HasSynchronizedDoubleAndSinglePrecisionVertices();

  dump.Print("ON_Mesh: vertex count = %d  facet count = %d\n", m_V.Count(), m_F.Count() );
  dump.Print("double precision: %s\n",bDoubles?"true":"false");
  dump.Print("vertex normals:   %s\n",HasVertexNormals()?"true":"false");
  dump.Print("face normals:     %s\n",HasFaceNormals()?"true":"false");
  dump.Print("srf parameters:   %s\n",HasSurfaceParameters()?"true":"false");
  dump.Print("tex coords:       %s\n",HasTextureCoordinates()?"true":"false");
  dump.Print("vertex kappa:     %s\n",HasPrincipalCurvatures()?"true":"false");
  dump.Print("vertex colors:    %s\n",HasVertexColors()?"true":"false");
  dump.Print("m_Ctag:\n"); dump.PushIndent(); m_Ctag.Dump(dump); dump.PopIndent();
  dump.Print("m_packed_tex_rotate: %s\n",m_packed_tex_rotate?"true":"false");
  dump.Print("m_packed_tex_domain: (%g,%g)x(%g,%g)\n",
             m_packed_tex_domain[0][0],m_packed_tex_domain[0][1],
             m_packed_tex_domain[1][0],m_packed_tex_domain[1][1]);
  dump.Print("m_srf_domain: (%g,%g)x(%g,%g)\n",m_srf_domain[0][0],m_srf_domain[0][1],m_srf_domain[1][0],m_srf_domain[1][1]);
  dump.Print("m_srf_scale: %g,%g\n",m_srf_scale[0],m_srf_scale[0]);
  dump.Print("m_Ttag:\n"); dump.PushIndent(); m_Ttag.Dump(dump); dump.PopIndent();

  dump.PushIndent();

  dump.Print("%d mesh vertices:\n",m_V.Count());
  {
    dump.PushIndent();
    const ON_3dPoint* D = 0;
    if ( bDoubles )
    {
      D = DoublePrecisionVertices().Array();
    }
    for (i = 0; i < vcount; i++)
    {
      if ( i == half_max && 2*half_max < vcount )
      {
        dump.Print("...\n");
        i = vcount-half_max;
      }
      else
      {
        p = m_V[i];
        if ( 0 != D )
        {
          q = D[i];
          dump.Print("m_V[%d] = (%.17g,%.17g,%.17g) D = (%.17g,%.17g,%.17g)\n",
                     i,
                     p.x,p.y,p.z,
                     q.x,q.y,q.z
                     );
        }
        else
        {
          dump.Print("m_V[%d] = (%g,%g,%g)\n",i,p.x,p.y,p.z);
        }
      }
    }
    dump.PopIndent();
  }

  if ( HasVertexNormals() )
  {
    dump.Print("%d mesh vertex normals:\n",m_N.Count());
    {
      dump.PushIndent();
      for (i = 0; i < vcount; i++)
      {
        if ( i == half_max && 2*half_max < vcount )
        {
          dump.Print("...\n");
          i = vcount-half_max;
        }
        else
        {
          p = m_N[i];
          dump.Print("m_N[%d] = (%g,%g,%g)\n",i,p.x,p.y,p.z);
        }
      }
      dump.PopIndent();
    }
  }

  if ( HasTextureCoordinates() )
  {
    dump.Print("%d mesh vertex texture coordinates:\n",m_T.Count());
    {
      dump.PushIndent();
      for (i = 0; i < vcount; i++)
      {
        if ( i == half_max && 2*half_max < vcount )
        {
          dump.Print("...\n");
          i = vcount-half_max;
        }
        else
        {
          ON_2fPoint tp = m_T[i];
          p.x = tp.x;
          p.y = tp.y;
          dump.Print("m_T[%d] = (%g,%g)\n",i,p.x,p.y);
        }
      }
      dump.PopIndent();
    }
  }


  if ( HasSurfaceParameters() )
  {
    dump.Print("%d mesh vertex surface parameters:\n",m_S.Count());
    {
      dump.PushIndent();
      for (i = 0; i < vcount; i++)
      {
        if ( i == half_max && 2*half_max < vcount )
        {
          dump.Print("...\n");
          i = vcount-half_max;
        }
        else
        {
          ON_2dPoint srfuv = m_S[i];
          dump.Print("m_S[%d] = (%g,%g)\n",i,srfuv.x,srfuv.y);
        }
      }
      dump.PopIndent();
    }
  }

  dump.Print("%d mesh faces:\n",m_F.Count());
  {
    dump.PushIndent();
    for (i = 0; i < fcount; i++)
    {
      if ( i == half_max && 2*half_max < fcount )
      {
        dump.Print("...\n");
        i = fcount-half_max;
      }
      else if ( m_F[i].vi[2] == m_F[i].vi[3] )
        dump.Print("m_F[%d].vi = (%d,%d,%d)\n",i,m_F[i].vi[0],m_F[i].vi[1],m_F[i].vi[2]);
      else
        dump.Print("m_F[%d].vi = (%d,%d,%d,%d)\n",i,m_F[i].vi[0],m_F[i].vi[1],m_F[i].vi[2],m_F[i].vi[3]);
    }
    dump.PopIndent();
  }

  if ( HasFaceNormals() )
  {
    dump.Print("%d mesh face normals:\n",m_FN.Count());
    {
      dump.PushIndent();
      for (i = 0; i < fcount; i++)
      {
        if ( i == half_max && 2*half_max < fcount )
        {
          dump.Print("...\n");
          i = fcount-half_max;
        }
        else
        {
          p = m_FN[i];
          dump.Print("m_FN[%d] = (%g,%g,%g)\n",i,p.x,p.y,p.z);
        }
      }
      dump.PopIndent();
    }
  }


  dump.PopIndent();
}


bool ON_Mesh::WriteFaceArray( int vcount, int fcount, ON_BinaryArchive& file ) const
{
  unsigned char  cvi[4];
  unsigned short svi[4];
  const int* vi;
  int i_size = 0;
  if ( vcount < 256 ) {
    i_size = 1; // unsigned chars
  }
  else if (vcount < 65536 ) {
    i_size = 2; // unsigned shorts
  }
  else {
    i_size = 4; // 4 byte ints
  }

  bool rc = file.WriteInt( i_size );
  int i;
  switch(i_size) {
  case 1:
    for ( i = 0; i < fcount && rc ; i++ ) {
      vi = m_F[i].vi;
      cvi[0] = (unsigned char)vi[0];
      cvi[1] = (unsigned char)vi[1];
      cvi[2] = (unsigned char)vi[2];
      cvi[3] = (unsigned char)vi[3];
      rc = file.WriteChar( 4, cvi );
    }
    break;
  case 2:
    for ( i = 0; i < fcount && rc ; i++ ) {
      vi = m_F[i].vi;
      svi[0] = (unsigned short)vi[0];
      svi[1] = (unsigned short)vi[1];
      svi[2] = (unsigned short)vi[2];
      svi[3] = (unsigned short)vi[3];
      rc = file.WriteShort( 4, svi );
    }
    break;
  case 4:
    for ( i = 0; i < fcount && rc ; i++ ) {
      rc = file.WriteInt( 4, m_F[i].vi );
    }
    break;
  }

  return rc;
}

bool ON_Mesh::ReadFaceArray( int vcount, int fcount, ON_BinaryArchive& file )
{
  unsigned char  cvi[4];
  unsigned short svi[4];
  unsigned int* vi;
  int i_size = 0;

  if ( m_F.Capacity() < fcount )
    m_F.SetCapacity(fcount);
  bool rc = file.ReadInt( &i_size );
  int i = 0;
  switch(i_size) {
  case 1:
    for ( i = 0; i < fcount && rc ; i++ ) {
      rc = file.ReadChar( 4, cvi );
      vi = (unsigned int*)m_F[i].vi;
      vi[0] = cvi[0];
      vi[1] = cvi[1];
      vi[2] = cvi[2];
      vi[3] = cvi[3];
    }
    break;
  case 2:
    for ( i = 0; i < fcount && rc ; i++ ) {
      rc = file.ReadShort( 4, svi );
      vi = (unsigned int*)m_F[i].vi;
      vi[0] = svi[0];
      vi[1] = svi[1];
      vi[2] = svi[2];
      vi[3] = svi[3];
    }
    break;
  case 4:
    for ( i = 0; i < fcount && rc ; i++ ) {
      rc = file.ReadInt( 4, m_F[i].vi );
    }
    break;
  }
  m_F.SetCount(i);

  return rc;
}


bool ON_Mesh::Write_1( ON_BinaryArchive& file ) const
{
  // ver 1.0 uncompressed format

  bool rc = file.WriteArray( m_V );
  if (rc) rc = file.WriteArray( m_N );
  if (rc) rc = file.WriteArray( m_T );
  if (rc) rc = file.WriteArray( m_K );
  if (rc) rc = file.WriteArray( m_C );

  return rc;
}

bool ON_Mesh::Read_1( ON_BinaryArchive& file )
{
  // common to all 1.x formats (uncompressed)

  bool rc = file.ReadArray( m_V );
  if (rc) rc = file.ReadArray( m_N );
  if (rc) rc = file.ReadArray( m_T );
  if (rc) rc = file.ReadArray( m_K );
  if (rc) rc = file.ReadArray( m_C );

  return rc;
}

bool ON_Mesh::Write_2( int Vcount, ON_BinaryArchive& file ) const
{
  // ver 2.0 compressed format
  const ON::endian e = file.Endian();

  bool rc = true;

  if ( Vcount > m_V.Count() )
    return false;

  if ( Vcount > 0 ) 
  {
    const int Ncount = (m_V.Count() == m_N.Count()) ? Vcount : 0;
    const int Tcount = (m_V.Count() == m_T.Count()) ? Vcount : 0;
    const int Kcount = (m_V.Count() == m_K.Count()) ? Vcount : 0;
    const int Ccount = (m_V.Count() == m_C.Count()) ? Vcount : 0;

    if ( e == ON::big_endian ) 
    {
      // These calls temporarily put the m_V[], m_N[], m_T[], m_K[]
      // and m_C[] arrays in little endian byte order because 3dm archives
      // are always in little endian byte order.
      //
      // This code assumes sizeof(ON_Color)=4, sizeof(float)=4 
      // and sizeof(double)=8.
      // If this is not the case, then changing the 4's and 8's below
      // will not work.  You will have to copy the mesh definition
      // into temporary arrays of 4 byte floats/8 byte doubles
      // and them compress the temporary arrays.  If you do this,
      // then remove the "restore" byte order calls below.
      file.ToggleByteOrder( Vcount*3, 4, m_V.Array(), (void*)m_V.Array() );
      file.ToggleByteOrder( Ncount*3, 4, m_N.Array(), (void*)m_N.Array() );
      file.ToggleByteOrder( Tcount*2, 4, m_T.Array(), (void*)m_T.Array() );
      file.ToggleByteOrder( Kcount*2, 8, m_K.Array(), (void*)m_K.Array() );
      file.ToggleByteOrder( Ccount,   4, m_C.Array(), (void*)m_C.Array() );
    }
    if (rc) rc = file.WriteCompressedBuffer( Vcount*sizeof(ON_3fPoint),         m_V.Array() );
    if (rc) rc = file.WriteCompressedBuffer( Ncount*sizeof(ON_3fVector),        m_N.Array() );
    if (rc) rc = file.WriteCompressedBuffer( Tcount*sizeof(ON_2fPoint),         m_T.Array() );
    if (rc) rc = file.WriteCompressedBuffer( Kcount*sizeof(ON_SurfaceCurvature),m_K.Array() );
    if (rc) rc = file.WriteCompressedBuffer( Ccount*sizeof(ON_Color),           m_C.Array() );
    if ( e == ON::big_endian ) 
    {
      // These calls restore the m_V[], m_N[], m_T[], m_K[] and m_C[] arrays
      // to the correct big endian runtime byte order.  This must be done even
      // if rc is false.
      file.ToggleByteOrder( Vcount*3, 4, m_V.Array(), (void*)m_V.Array() );
      file.ToggleByteOrder( Ncount*3, 4, m_N.Array(), (void*)m_N.Array() );
      file.ToggleByteOrder( Tcount*2, 4, m_T.Array(), (void*)m_T.Array() );
      file.ToggleByteOrder( Kcount*2, 8, m_K.Array(), (void*)m_K.Array() );
      file.ToggleByteOrder( Ccount,   4, m_C.Array(), (void*)m_C.Array() );
    }
  }

  return rc;
}

bool ON_Mesh::Read_2( int vcount, ON_BinaryArchive& file )
{
  // common to all 2.x formats (compressed)
  const ON::endian e = file.Endian();

  bool rc = true;


  if ( vcount > 0 ) 
  {
    size_t sz = 0;
    int bFailedCRC;

    sz = 0;
    if (rc) rc = file.ReadCompressedBufferSize( &sz );
    if (rc && sz) 
    {
      if ( sz == vcount*sizeof(m_V[0]) )
      {
        m_V.SetCapacity(vcount);
        if (rc) rc = file.ReadCompressedBuffer( sz,m_V.Array(),&bFailedCRC);
        if (rc) m_V.SetCount(vcount);
      }
      else
      {
        ON_ERROR("ON_Mesh::Read - compressed vertex point buffer size is wrong.");
        rc = false; // buffer is wrong size
      }
    }

    sz = 0;
    if (rc) rc = file.ReadCompressedBufferSize( &sz );
    if (rc && sz) 
    {
      if ( sz == vcount*sizeof(m_N[0]) )
      {
        m_N.SetCapacity(vcount);
        if (rc) rc = file.ReadCompressedBuffer( sz,m_N.Array(),&bFailedCRC );
        if (rc) m_N.SetCount(vcount);
      }
      else
      {
        ON_ERROR("ON_Mesh::Read - compressed vertex normal buffer size is wrong.");
        rc = false; // buffer is wrong size
      }
    }
    
    sz = 0;
    if (rc) rc = file.ReadCompressedBufferSize( &sz );
    if (rc && sz) 
    {
      if ( sz == vcount*sizeof(m_T[0]) )
      {
        m_T.SetCapacity(vcount);
        if (rc) rc = file.ReadCompressedBuffer( sz,m_T.Array(),&bFailedCRC );
        if (rc) m_T.SetCount(vcount);
      }
      else
      {
        ON_ERROR("ON_Mesh::Read - compressed texture coordinate buffer size is wrong.");
        rc = false; // buffer is wrong size
      }
    }
    
    sz = 0;
    if (rc) rc = file.ReadCompressedBufferSize( &sz );
    if (rc && sz) 
    {
      if ( sz == vcount*sizeof(m_K[0]) )
      {
        m_K.SetCapacity(vcount);
        if (rc) rc = file.ReadCompressedBuffer( sz,m_K.Array(),&bFailedCRC );
        if (rc) m_K.SetCount(vcount);
      }
      else
      {
        ON_ERROR("ON_Mesh::Read - compressed vertex curvature buffer size is wrong.");
        rc = false; // buffer is wrong size
      }
    }
    
    sz = 0;
    if (rc) rc = file.ReadCompressedBufferSize( &sz );
    if (rc && sz) 
    {
      if ( sz == vcount*sizeof(m_C[0]) )
      {
        m_C.SetCapacity(vcount);
        if (rc) rc = file.ReadCompressedBuffer( sz,m_C.Array(),&bFailedCRC );
        if (rc) m_C.SetCount(vcount);
      }
      else
      {
        ON_ERROR("ON_Mesh::Read - compressed vertex color buffer size is wrong.");
        rc = false; // buffer is wrong size
      }
    }
    
    if ( e == ON::big_endian ) 
    {
      // This code assumes sizeof(ON_Color)=4, sizeof(float)=4 
      // and sizeof(double)=8.
      // If this is not the case, then changing the 4's and 8's below
      // will not work.  You will have to read the compressed
      // information into temporary arrays of 4 byte floats/8 byte doubles
      // and then convert those numbers to whatever is stored in the
      // m_V[], m_N[], m_T[], m_K[] and m_C[] arrays/
      file.ToggleByteOrder( m_V.Count()*3, 4, m_V.Array(), (void*)m_V.Array() );
      file.ToggleByteOrder( m_N.Count()*3, 4, m_N.Array(), (void*)m_N.Array() );
      file.ToggleByteOrder( m_T.Count()*2, 4, m_T.Array(), (void*)m_T.Array() );
      file.ToggleByteOrder( m_K.Count()*2, 8, m_K.Array(), (void*)m_K.Array() );
      file.ToggleByteOrder( m_C.Count()*3, 4, m_C.Array(), (void*)m_C.Array() );
    }
  }

  return rc;
}


ON_BOOL32 ON_Mesh::Write( ON_BinaryArchive& file ) const
{
  int i;
  //const int major_version = 1; // uncompressed
  //const int major_version = 2; // beta format (never used)
  const int major_version = 3; // compressed
  bool rc = file.Write3dmChunkVersion(major_version,5);

  const int vcount = VertexCount();
  const int fcount = FaceCount();

  if (rc) rc = file.WriteInt( vcount );
  if (rc) rc = file.WriteInt( fcount );
  if (rc) rc = file.WriteInterval( m_packed_tex_domain[0] );
  if (rc) rc = file.WriteInterval( m_packed_tex_domain[1] );
  if (rc) rc = file.WriteInterval( m_srf_domain[0] );
  if (rc) rc = file.WriteInterval( m_srf_domain[1] );
  if (rc) rc = file.WriteDouble( 2, m_srf_scale );
  if (rc) rc = file.WriteFloat( 6, &m_vbox[0][0] );
  if (rc) rc = file.WriteFloat( 6, &m_nbox[0][0] );
  if (rc) rc = file.WriteFloat( 4, &m_tbox[0][0] );

  // archive int value meaning: -1 = unknown 0 = mesh is not closed, 1 = mesh is closed
  i = -1;
  switch( m_mesh_is_closed )
  {
  case 0: // unset
    i = -1;
    break;
  case 1: // closed
    i = 1;
    break;
  case 2: // not closed
    i = 0;
    break;
  }
  if (rc) rc = file.WriteInt( i );

  unsigned char b = m_mesh_parameters ? 1 : 0;
  if (rc) rc = file.WriteChar(b);
  if (rc && b) {
    if (rc) rc = file.BeginWrite3dmChunk( TCODE_ANONYMOUS_CHUNK, 0 );
    if (rc) {
      rc = m_mesh_parameters->Write(file);
      if ( !file.EndWrite3dmChunk() )
        rc = false;
    }
  }

  for ( i = 0; rc && i < 4; i++ ) {
    b = m_kstat[i] ? 1 : 0;
    rc = file.WriteChar(b);
    if (b) {
      rc = file.BeginWrite3dmChunk( TCODE_ANONYMOUS_CHUNK, 0 );
      if (rc) {
        rc = m_kstat[i]->Write(file);
        if ( !file.EndWrite3dmChunk() )
          rc = false;
      }
    }
  }

  if (rc) rc = WriteFaceArray( vcount, fcount, file );

  if (rc) {
    // major version is a hard coded 3

    //if ( major_version == 1 )
    //  rc = Write_1(file);
    //else if ( major_version == 3 )
      rc = Write_2(vcount,file);
    //else
    //  rc = false;
  }

  // added for minor version 1.2 and 3.2
  i = m_packed_tex_rotate ? 1 : 0;
  if (rc) rc = file.WriteInt( i );

  // added for minor version 3.3
  if (rc) rc = file.WriteUuid( m_Ttag.m_mapping_id );
 
  // compressed m_S[]
  if ( rc && vcount > 0 ) 
  {
    // Before 201011049 there was a bug that let m_S[] arrays
    // with the wrong size get saved in files. 
    const int Scount = (vcount == m_S.Count()) ? m_S.Count() : 0;
    const ON::endian e = file.Endian();
    if ( e == ON::big_endian ) 
    {
      file.ToggleByteOrder( Scount*2, 8, m_S.Array(), (void*)m_S.Array() );
    }
    if (rc) rc = file.WriteCompressedBuffer( Scount*sizeof(ON_2dPoint),m_S.Array() );
    if ( e == ON::big_endian ) 
    {
      file.ToggleByteOrder( Scount*2, 8, m_S.Array(), (void*)m_S.Array() );
    }
  }

  // added for minor version 3.4
  if (rc) rc = m_Ttag.Write(file);

  // added for minor version 3.5
  if (rc) rc = file.WriteChar( m_mesh_is_manifold );
  if (rc) rc = file.WriteChar( m_mesh_is_oriented );
  if (rc) rc = file.WriteChar( m_mesh_is_solid );


  return rc;
}

//
static const ON_UUID obsolete_default_srfp_mapping_id = { 0xb988a6c2, 0x61a6, 0x45a7, { 0xaa, 0xee, 0x9a, 0xed, 0x7e, 0xf4, 0xe3, 0x16 } };

// overrides virtual ON_Object::Write
ON_BOOL32 ON_TextureMapping::Write(
        ON_BinaryArchive& file
      ) const
{
  bool rc = file.BeginWrite3dmChunk(TCODE_ANONYMOUS_CHUNK,1,1);
  if (rc)
  {

    for(;;)
    {
      rc = file.WriteUuid( m_mapping_id);
      if (!rc) break;

      rc = file.WriteInt( m_type );
      if (!rc) break;

      rc = file.WriteInt( m_projection );
      if (!rc) break;

      rc = file.WriteXform( m_Pxyz );
      if (!rc) break;

      // Do not write m_Nxyz - it is calculated from m_Pxyz.
      rc = file.WriteXform( m_uvw );
      if (!rc) break;

      rc = file.WriteString(m_mapping_name);
      if (!rc) break;

      rc = file.WriteObject(m_mapping_primitive);
      if (!rc) break;

      // 13 October 2006 ver 1.1 fields
      rc = file.WriteInt(m_texture_space);
      if (!rc) break;

      rc = file.WriteBool(m_bCapped);
      if (!rc) break;

      break;
    }

    if ( !file.EndWrite3dmChunk() )
      rc = false;
  }

  return rc;
}

// overrides virtual ON_Object::Read
ON_BOOL32 ON_TextureMapping::Read(
        ON_BinaryArchive& file
      )
{
  Default();

  int major_version = 0;
  int minor_version = 0;
  int i;

  bool rc = file.BeginRead3dmChunk(TCODE_ANONYMOUS_CHUNK,&major_version,&minor_version);
  if (rc)
  {
    if ( 1 == major_version )
    {
      // DO NOT SAVE m_mapping_index in archive.
      // 1.0 fields
      for(;;)
      {
        rc = file.ReadUuid( m_mapping_id );
        if (!rc) break;
        if ( 0 == ON_UuidCompare(&obsolete_default_srfp_mapping_id,&m_mapping_id) )
          m_mapping_id = ON_nil_uuid;

        rc = file.ReadInt( &i );
        if (!rc) break;
        m_type = TypeFromInt(i);

        rc = file.ReadInt( &i );
        if (!rc) break;
        m_projection = ProjectionFromInt(i);

        rc = file.ReadXform( m_Pxyz );
        if (!rc) break;

        m_Pxyz.GetSurfaceNormalXform(m_Nxyz);

        rc = file.ReadXform( m_uvw );
        if (!rc) break;

        rc = file.ReadString(m_mapping_name);
        if (!rc) break;

        rc = (file.ReadObject(&m_mapping_primitive) >= 0);
        if (!rc) break;

        if ( minor_version >= 1 )
        {
          rc = file.ReadInt(&i);
          if (!rc) break;
          m_texture_space = TextureSpaceFromInt(i);

          rc = file.ReadBool(&m_bCapped);
          if (!rc) break;
        }

        break;
      }
    }

    if ( !file.EndRead3dmChunk() )
      rc = false;
  }

  return rc;
}

static
void GetSurfaceParametersHelper( const ON_Mesh& mesh,
                                 double tex_x, double tex_y, 
                                 double* srf_s, double* srf_t )
{
  // convert texture coordinates to surface parameters
  // Used to reconstruct m_S[] when old files are read.
  double tex_s, tex_t;

  if ( mesh.m_packed_tex_rotate ) 
  {
    // undo rotation and normalize
    tex_s =  mesh.m_packed_tex_domain[1].NormalizedParameterAt( tex_y );
    tex_t = 1.0 -  mesh.m_packed_tex_domain[0].NormalizedParameterAt( tex_x );
  }
  else 
  {
    // normalize
    tex_s =  mesh.m_packed_tex_domain[0].NormalizedParameterAt( tex_x );
    tex_t =  mesh.m_packed_tex_domain[1].NormalizedParameterAt( tex_y );
  }
  *srf_s =  mesh.m_srf_domain[0].ParameterAt(tex_s);
  *srf_t =  mesh.m_srf_domain[1].ParameterAt(tex_t);
}


ON_BOOL32 ON_Mesh::Read( ON_BinaryArchive& file )
{
  Destroy();

  int major_version = 0;
  int minor_version = 0;
  int i;
  bool rc = file.Read3dmChunkVersion(&major_version,&minor_version);
  
  if (rc && (1 == major_version || 3 == major_version) ) 
  {
    int vcount = 0;
    int fcount = 0;

    if (rc) rc = file.ReadInt( &vcount );
    if (rc) rc = file.ReadInt( &fcount );
    if (rc) rc = file.ReadInterval( m_packed_tex_domain[0] );
    if (rc) rc = file.ReadInterval( m_packed_tex_domain[1] );
    if (rc) rc = file.ReadInterval( m_srf_domain[0] );
    if (rc) rc = file.ReadInterval( m_srf_domain[1] );
    if (rc) rc = file.ReadDouble( 2, m_srf_scale );
    if (rc) rc = file.ReadFloat( 6, &m_vbox[0][0] );
    if (rc) rc = file.ReadFloat( 6, &m_nbox[0][0] );
    if (rc) rc = file.ReadFloat( 4, &m_tbox[0][0] );

    // int value meaning: -1 = unknown 0 = mesh is not closed, 1 = mesh is closed
    i = -1;
    if (rc) rc = file.ReadInt( &i );
    if (rc)
    {
      switch(i)
      {
      case 0: // not closed;
        SetClosed(0);
        break;
      case 1: // closed;
        SetClosed(1);
        break;
      case 2: // 13 April 2010 Dale Lear - "2" value is obsolete but appears in old files
        SetClosed(1);
        break;
      }
    }

    unsigned char b = 0;
    ON__UINT32 tcode=0;
    ON__INT64 big_value=0;
    if (rc) rc = file.ReadChar(&b);
    if (rc && b) 
    {
      // mesh parameters are in an anonymous chunk
      rc = file.BeginRead3dmBigChunk(&tcode,&big_value);
      if (rc) 
      {
        if ( TCODE_ANONYMOUS_CHUNK == tcode )
        {
          m_mesh_parameters = new ON_MeshParameters();
          rc = m_mesh_parameters->Read( file );
        }
        else
          rc = false;
        if (!file.EndRead3dmChunk())
          rc = false;
      }
    }

    for ( i = 0; rc && i < 4; i++ ) 
    {
      rc = file.ReadChar(&b);
      if (rc && b) 
      {
        // m_kstat[i] curvature stats are in an anonymous chunk
        tcode = 0;
        big_value = 0;
        rc = file.BeginRead3dmBigChunk( &tcode, &big_value );
        if (rc) 
        {
          if ( TCODE_ANONYMOUS_CHUNK == tcode )
          {
            m_kstat[i] = new ON_MeshCurvatureStats();
            rc = m_kstat[i]->Read(file);
          }
          else
            rc = false;
          if ( !file.EndRead3dmChunk() )
            rc = false;
        }
      }
    }

    if (rc) rc = ReadFaceArray( vcount, fcount, file );

    if (rc) {
      if ( major_version==1) {
        rc = Read_1(file);
      }
      else if ( major_version == 3 ) {
        rc = Read_2(vcount,file);
      }
      else
        rc = false;
    }

    if ( minor_version >= 2 ) 
    {
      int b = m_packed_tex_rotate;
      if (rc) rc = file.ReadInt( &b );
      m_packed_tex_rotate = b?true:false;
    }

    if ( 3 == major_version )
    {
      if ( minor_version >= 3 )
      {
        // added for minor version 3.3
        if (rc) rc = file.ReadUuid( m_Ttag.m_mapping_id );

        // compressed m_S[]
        if ( rc && vcount > 0 ) 
        {
          size_t sz = 0;
          ON_BOOL32 bFailedCRC=false;
          if (rc) rc = file.ReadCompressedBufferSize( &sz );
          if (rc && sz) 
          {
            if ( sz == vcount*sizeof(ON_2dPoint) )
            {
              m_S.SetCapacity(vcount);
              if (rc) rc = file.ReadCompressedBuffer( sz, m_S.Array(), &bFailedCRC );
              if (rc) m_S.SetCount(vcount);
              if ( ON::big_endian == file.Endian() ) 
              {
                file.ToggleByteOrder( m_S.Count()*2, 8, m_S.Array(), (void*)m_S.Array() );
              }
            }
            else
            {
              ON_ERROR("ON_Mesh::Read - surface parameter buffer size is wrong.");
              if (    rc
                   && file.ArchiveOpenNURBSVersion() <= 201011049 
                   && 0 == (sz % sizeof(ON_2dPoint))
                   && sz >= sizeof(ON_2dPoint)
                 )
              {
                // Before 201011049 there was a bug that let m_S[] arrays with
                // the wrong size get saved in files. There was also a bug in 
                // the Rhino .OBJ file reader that created meshes with m_S[] 
                // arrays that had the wrong size.  The next 4 lines of code
                // let us read the junk, discard it and then successfully read
                // the rest of the file.
                int Scount = (int)(sz / sizeof(ON_2dPoint));
                m_S.SetCapacity(Scount);
                rc = file.ReadCompressedBuffer( sz, m_S.Array(), &bFailedCRC );
                m_S.Destroy();
              }
              else
              {
                rc = false; // buffer is wrong size
              }
            }
          }
        }
        if ( minor_version >= 4 && file.ArchiveOpenNURBSVersion() >= 200606010 )
        {
          if (rc) rc = m_Ttag.Read(file);
          if ( minor_version >= 5 )
          {
            if (rc) rc = file.ReadChar( &m_mesh_is_manifold );
            if (rc) rc = file.ReadChar( &m_mesh_is_oriented );
            if (rc) rc = file.ReadChar( &m_mesh_is_solid );
          }
        }
      }
    }

    if (    0 == m_S.Count()
         && m_V.Count() > 0
         && HasTextureCoordinates()
         && m_srf_domain[0].IsIncreasing() 
         && m_srf_domain[1].IsIncreasing() 
         && m_packed_tex_domain[0].IsInterval()
         && m_packed_tex_domain[1].IsInterval()
         && 0 == m_Ttag.m_mapping_crc
         && ON_UuidIsNil(m_Ttag.m_mapping_id)
          ) 
    {
      // This is a mesh from an old file - but there is enough 
      // information to calculate the m_S[] values from the 
      // m_T[] values.
      m_S.SetCapacity(vcount);
      m_S.SetCount(0);
      ON_2dPoint sp;
      ON_2fPoint tc;
      for ( i = 0; i < vcount; i++)
      {
        tc = m_T[i];
        sp.x = tc.x;
        sp.y = tc.y;
        GetSurfaceParametersHelper(*this,sp.x,sp.y,&sp.x,&sp.y);
        m_S.Append(sp);
      }
      m_Ttag.SetDefaultSurfaceParameterMappingTag();
    }
  }

  return rc;
}

ON::object_type ON_Mesh::ObjectType() const
{
  return ON::mesh_object;
}

int ON_Mesh::Dimension() const
{
  return 3;
}

#if defined(ON_COMPILER_MSC)
// Disable the MSC /W4 warning
//   C4189: 'breakpoint_here_for_bad_vbox' : local variable is initialized but not referenced
// on the line
//   int breakpoint_here_for_bad_vbox = 0.  
// The warning disable is here because MS is ignoring it
// if I put it inside of the function.
#pragma warning( push )
#pragma warning( disable : 4189 ) 
#endif

float ON_FloatFloor(double x)
{
  // If x is a NaN, you get what you deserve.
  //
  // If x is a finite valid double in the range -3.402823466e+38
  // to +3.402823466e+38, then returned value of f is the largest
  // float value that is mathematically less than or equal to the
  // value of x.
  //
  // If x is not in the float range or x is a NaN, then you get
  // what you deserve.
  //
  // ON_FLOAT_EPSILON = 1.192092896e-07 is the smallest number such that
  // 1.0f + 1.192092896e-07f > 1.0f.  
  //
  // If x < 0, then (1.0 + 0.5*1.192092896e-07)*x rounds x down so
  // that converting the double precision mantissa cannot create a
  // float value that is mathematically larger than the value of x.  
  //
  // If x > 0, then (1.0 - 0.5*1.192092896e-07)*x rounds x down so
  // that converting the double precision mantissa cannot create a
  // float value that is mathematically larger than the value of x.  
  // 
  const double e = (x < 0.0) ? (1.0 + 0.5*ON_FLOAT_EPSILON) : (1.0 - 0.5*ON_FLOAT_EPSILON);
  float f;
  f = (float)(e*x);
  return f;
}

float ON_FloatCeil(double x)
{
  float f = (x != 0.0) ? (-ON_FloatFloor(-x)) : ((float)x);
  return f;
}

ON_BOOL32 ON_Mesh::GetBBox( // returns true if successful
       double* boxmin, // minimum
       double* boxmax, // maximum
       ON_BOOL32 bGrowBox
       ) const
{
  ON_BOOL32 rc = false;
  const int facet_count  = FaceCount();
  const int vertex_count = VertexCount();
  if ( facet_count >= 1 && vertex_count >= 3 ) 
  {
    ON_BoundingBox vbox;
    if ( m_vbox[0][0] > m_vbox[1][0] ) 
    {
      // const lie - cache mesh bounding box
      float* fbbox[2] = {const_cast<float*>(&m_vbox[0][0]),const_cast<float*>(&m_vbox[1][0])};
      while ( HasDoublePrecisionVertices() && DoublePrecisionVerticesAreValid() )
      {
        double dbbox[2][3];
        const ON_3dPointArray& dV = DoublePrecisionVertices();
        rc = ON_GetPointListBoundingBox(
                3, 0, vertex_count, 3, &dV[0].x,
                &dbbox[0][0], &dbbox[1][0], 
                false 
                );
        if (!rc)
          break;
        // make sure we round min doubles down to the nearest float
        // and max doubles up to the nearest float.
        fbbox[0][0] = ON_FloatFloor(dbbox[0][0]);
        fbbox[0][1] = ON_FloatFloor(dbbox[0][1]);
        fbbox[0][2] = ON_FloatFloor(dbbox[0][2]);
        fbbox[1][0] = ON_FloatCeil(dbbox[1][0]);
        fbbox[1][1] = ON_FloatCeil(dbbox[1][1]);
        fbbox[1][2] = ON_FloatCeil(dbbox[1][2]);

        // depending on how
        if ( SinglePrecisionVerticesAreValid() )
        {
          ON_GetPointListBoundingBox(
                3, 0, vertex_count, 3, &m_V[0].x,
                &fbbox[0][0], &fbbox[1][0], 
                true 
              );
        }
        break;
      }

      if (!rc)
      {
        rc = ON_GetPointListBoundingBox( 3, 0, 
                vertex_count, 3, &m_V[0].x,
                fbbox[0],fbbox[1],
                false 
                );
      }
    }
    else
    {
      rc = true;
    }

    if ( rc ) 
    {
      vbox.m_min.x = m_vbox[0][0];
      vbox.m_min.y = m_vbox[0][1];
      vbox.m_min.z = m_vbox[0][2];
      vbox.m_max.x = m_vbox[1][0];
      vbox.m_max.y = m_vbox[1][1];
      vbox.m_max.z = m_vbox[1][2];
      rc = vbox.IsValid();
      if (rc)
      {
        if ( bGrowBox )
        {
          vbox.Union( ON_BoundingBox(boxmin,boxmax) );
        }

        boxmin[0] = vbox.m_min.x;
        boxmin[1] = vbox.m_min.y;
        boxmin[2] = vbox.m_min.z;

        boxmax[0] = vbox.m_max.x;
        boxmax[1] = vbox.m_max.y;
        boxmax[2] = vbox.m_max.z;
      }
#if defined(ON_DEBUG) && !defined(ON_COMPILER_GNU)
      // generates gcc unused variable warning
      else
      {
        int breakpoint_here_for_bad_vbox=0;
      }
#endif
    }
  }
  return rc;
}

#if defined(ON_COMPILER_MSC)
#pragma warning( pop )
#endif

bool ON_Mesh::IsDeformable() const
{
  return true;
}

bool ON_Mesh::MakeDeformable()
{
  return true;
}

ON_BOOL32 ON_Mesh::Transform( 
       const ON_Xform& xform
       )
{
  const bool bIsValid_fV = SinglePrecisionVerticesAreValid();
  const bool bIsValid_dV = DoublePrecisionVerticesAreValid();
  const bool bSyncheddV = bIsValid_fV && bIsValid_dV && HasSynchronizedDoubleAndSinglePrecisionVertices();
  TransformUserData(xform);
        DestroyTree();

  double d = xform.Determinant();
  const int vertex_count = VertexCount();
  bool rc = false;
  if ( bSyncheddV )
  {
    // transforming the double precision vertices is the 
    // best way to set the floats.
    UpdateSinglePrecisionVertices();
    rc = true;
  }
  else
  {
    rc = ON_TransformPointList( 3, false, vertex_count, 3, &m_V[0][0], xform );
  }

  if ( rc )
  {
    m_Ctag.Transform(xform);
    m_Ttag.Transform(xform);
    int tci, tccnt = m_TC.Count();
    for ( tci = 0; tci < tccnt; tci++ )
    {
      m_TC[tci].m_tag.Transform(xform);
    }
  }

  if ( rc && 0.0 == d )
  {
    // mesh has been squashed to a plane (or worse)
    if ( HasVertexNormals() )
    {
      ComputeFaceNormals();
      ComputeVertexNormals();
    }
    else if ( HasFaceNormals() )
    {
      ComputeFaceNormals();
    }
  }
  else if ( rc )
  {
    if ( HasVertexNormals() ) 
    {
      // See http://www.gignews.com/realtime020100.htm or these
      // references.
      //
      // 1. Hanrahan, Pat, 
      //    "A Survey of Ray-Surface Intersection Algorithms", 
      //     chapter 3 in Andrew Glassner (editor), 
      //     An Introduction to Ray Tracing, 
      //     Academic Press Inc., London, 1989.
      //
      // 2. Turkowski, Ken, 
      //    "Properties of Surface-Normal Transformations", 
      //     in Andrew Glassner (editor), 
      //     Graphics Gems, Academic Press, Inc., 
      //     pp. 539-547, 1990. 
      ON_Xform N_xform;
      double d = xform.GetSurfaceNormalXform(N_xform);
      rc = ON_TransformVectorList( 3, vertex_count, 3, &m_N[0][0], N_xform )?true:false;
      if ( d < 0.0 )
      {
        FlipVertexNormals();
      }
      UnitizeVertexNormals();
    }

    if ( rc && HasFaceNormals() ) 
    {
      ComputeFaceNormals();
    }
  }

  if ( rc && HasPrincipalCurvatures() ) 
  {
    if ( fabs(fabs(d) - 1.0) > ON_SQRT_EPSILON ) 
    {
      // If it's a uniform scale, handle it, otherwise we can't do it.
      double scale = xform.m_xform[0][0];
      if ( 0.0 != scale && 0.0 != d
           && scale == xform.m_xform[1][1] 
           && scale == xform.m_xform[2][2] 
           && fabs(d - scale*scale*scale) <= d*ON_SQRT_EPSILON )
      {
        // uniform scale
        const double ks = 1.0/scale;
        ON_SurfaceCurvature* sc = m_K.Array();
        int ki = m_K.Count();
        while ( ki-- )
        {
          sc->k1 *= ks;
          sc->k2 *= ks;
          sc++;
        }

        // update curvature stats.
        for ( int j = 0; j < 4; j++ )
        {
          if ( m_kstat[j] )
            m_kstat[j]->Set( m_kstat[j]->m_style,m_K.Count(),m_K.Array(),m_N.Array() );
        }
      }
      else
      {
        ON_ERROR("ON_Mesh::Transform() cannot apply this transform to curvatures.\n");
        rc = false;
      }
    }
  }

  InvalidateVertexBoundingBox();
  InvalidateVertexNormalBoundingBox();
  if ( fabs(d) <= ON_ZERO_TOLERANCE )
    DestroyTopology(); // transform may not be one-to-one on vertices

  if ( bIsValid_fV )
    SetSinglePrecisionVerticesAsValid();
  if ( bIsValid_dV )
    SetDoublePrecisionVerticesAsValid();

  return rc;
}

void ON_Mesh::DestroyRuntimeCache( bool bDelete )
{
  int i;

  DestroyTree(bDelete);

  if (bDelete )
  {    
    DestroyPartition();
    m_top.Destroy();
    DeleteMeshParameters();
    InvalidateCurvatureStats();
  }
  else
  {
    // do not free any memory
    m_top.EmergencyDestroy();
  }

  InvalidateBoundingBoxes();
  m_partition = 0;
  m_mesh_parameters = 0;
  m_top.m_mesh = this;
  m_parent = 0;
  //m_material_index = -1;
  m_mesh_is_closed = 0;
  m_mesh_is_manifold = 0;
  m_mesh_is_oriented = 0;
  m_mesh_is_solid = 0;
  for ( i = 0; i < 4; i++ ) 
  {
    m_kstat[i] = 0;
  }
}

ON_BOOL32 ON_Mesh::SwapCoordinates(
      int i, int j        // indices of coords to swap
      )
{
  if ( i == j )
    return true;

  const bool bIsValid_fV = SinglePrecisionVerticesAreValid();
  const bool bIsValid_dV = DoublePrecisionVerticesAreValid();

  const int vertex_count = VertexCount();
  ON_BOOL32 rc = ON_SwapPointListCoordinates( vertex_count, 3, &m_V[0][0], i, j );
  if ( rc && HasVertexNormals() ) {
    rc = ON_SwapPointListCoordinates( vertex_count, 3, &m_N[0][0], i, j );
  }
  if ( rc )
  {
    float x;
    if ( m_vbox[0][0] <= m_vbox[1][0] ) {
      x = m_vbox[0][i]; m_vbox[0][i] = m_vbox[0][j]; m_vbox[0][j] = x;
      x = m_vbox[1][i]; m_vbox[1][i] = m_vbox[1][j]; m_vbox[1][j] = x;
    }
    if ( m_nbox[0][0] <= m_nbox[1][0] ) {
      x = m_nbox[0][i]; m_nbox[0][i] = m_nbox[0][j]; m_nbox[0][j] = x;
      x = m_nbox[1][i]; m_nbox[1][i] = m_nbox[1][j]; m_nbox[1][j] = x;
    }
  }

  if ( HasDoublePrecisionVertices() )
  {
    DoublePrecisionVertices().SwapCoordinates(i,j);
    if ( bIsValid_fV )
      SetSinglePrecisionVerticesAsValid();
    if ( bIsValid_dV )
      SetDoublePrecisionVerticesAsValid();
  }

  return rc;
}

void ON_Mesh::SetClosed(int b)
{
  // 6 Novermber 2003 Dale Lear - let expert user set m_mesh_is_closed
  char mesh_is_closed = 0;
  switch(b)
  {
  case 0: // not closed - at least one boundary edge
    mesh_is_closed = 2;
    SetSolidOrientation(0);
    break;
  case 1: // all edges are shared 
    // DO NOT SET m_mesh_is_solid here.
    // Meshes can be closed but not solid
    mesh_is_closed = 1; 
    break;
  case 2: // 31 April 2010 Dale Lear - 2 is obsolete - it's either 0 or 1 now.
    mesh_is_closed = 1; 
    // DO NOT SET m_mesh_is_solid here.
    // Meshes can be closed but not solid
    break;
  default:
    mesh_is_closed = 0; // unset
    break;
  }
  if ( 0 == mesh_is_closed || m_mesh_is_closed != mesh_is_closed )
  {
    m_mesh_is_closed = mesh_is_closed;
    m_mesh_is_manifold = 0; // unset - will be reevaluated when needed
    m_mesh_is_oriented = 0; // unset - will be reevaluated when needed
  }
}

void ON_Mesh::SetSolidOrientation(int solid_orientation)
{
  switch(solid_orientation)
  {
  case -1: // closed oriented manifold solid with inward face normals
    SetClosed(1);
    m_mesh_is_manifold = 1;
    m_mesh_is_oriented = 1;
    m_mesh_is_solid = 2;
    break;

  case  0: // not solid
    m_mesh_is_solid = 3;
    // DO NOT SET m_mesh_is_closed here.
    // Meshes can be closed but not solid
    break;

  case  1: // closed oriented manifold solid with outward face normals
    SetClosed(1);
    m_mesh_is_manifold = 1;
    m_mesh_is_oriented = 1;
    m_mesh_is_solid = 1;
    break;

  default:
    m_mesh_is_solid = 0;
    break;
  }
}


static 
int ON_MeshIsManifold_CompareV( const void* a, const void* b )
{
  return memcmp(a,b,sizeof(ON_3fPoint));
  /*
  float d;
  const float* fa = (const float*)a;
  const float* fb = (const float*)b;
  if ( 0.0f == (d = (*fa++ - *fb++)) )
  {
    if ( 0.0f == (d = (*fa++ - *fb++)) )
    {
      if ( 0.0f == (d = (*fa++ - *fb++)) )
        return 0;
    }
  }
  return ( d < 0.0f ) ? -1 : 1;
  */
}

static 
int ON_MeshGetVertexEdges_Compare2dex( const void* a, const void* b )
{
  return ON_Compare2dex((const ON_2dex*)a,(const ON_2dex*)b);
}

static 
int ON_MeshIsManifold_Compare3dex( const void* a, const void* b )
{
  return ON_Compare3dex((const ON_3dex*)a,(const ON_3dex*)b);
}

//static 
//int ON_MeshGetVertexEdges_CompareInt( const int* a, const int* b )
//{
//  return (*a-*b);
//}


int ON_Mesh::GetVertexEdges( 
  int vertex_index_count,
  const int* vertex_index, 
  bool bNoDuplicates,
  ON_SimpleArray<ON_2dex>& edges
  ) const
{
  // Get edges connected to vertices in vertex_index[] array.
  const int edges_count0 = edges.Count();

  const int mesh_vcount = m_V.Count();

  //03/12/2007 TimH. The line below appears to be a typo.  Using the following line works better.
  //const int mesh_fcount = m_V.Count();
  const int mesh_fcount = m_F.Count();

  if (   vertex_index_count <= 0 || 0 == vertex_index 
      || mesh_fcount <= 0 || mesh_vcount < 3 )
  {
    return 0;
  }

  int vei, efi, fvi, ei, fi, j, n, vi;
  const int* f_vi;
  ON_2dex edge_ends;
  const ON_MeshFace* f = m_F.Array();

  if (   TopologyExists()
       && mesh_vcount == m_top.m_topv_map.Count()
       && m_top.m_tope.Count() > 0 )
  {
    // Topology looks good; use it to speed up the search.
    const int* topv_map = m_top.m_topv_map;
    const int top_vcount = m_top.m_topv.Count();
    const int top_ecount = m_top.m_tope.Count();
    int top_vi;
    for ( n = 0; n < vertex_index_count; n++ )
    {
      vi = vertex_index[n];
      if ( vi < 0 || vi >= mesh_vcount )
        continue;
      top_vi = topv_map[vi];
      if ( top_vi < 0 || top_vi > top_vcount )
        continue;
      edge_ends.i = vi;
      const ON_MeshTopologyVertex& v = m_top.m_topv[top_vi];
      for ( vei = 0; vei < v.m_tope_count; vei++ )
      {
        ei = v.m_topei[vei];
        if ( ei < 0 || ei >= top_ecount )
          continue;
        const ON_MeshTopologyEdge& e = m_top.m_tope[ei];
        for ( efi = 0; efi < e.m_topf_count; efi++ )
        {
          fi = e.m_topfi[efi];
          if ( fi < 0 || fi >= mesh_fcount )
            continue;
          f_vi = f[fi].vi;
          for ( fvi = 0; fvi < 4; fvi++ )
          {
            if ( f_vi[fvi] == vi )
            {
              j = f_vi[(fvi+3)%4];
              if ( j >= 0 && j < mesh_vcount && vi != j )
              {
                edge_ends.i = j;
                edge_ends.j = vi;
                edges.Append(edge_ends);
              }
              j = f_vi[ (2==fvi && f_vi[2]==f_vi[3]) ? 0 : ((fvi+1)%4) ];
              if ( j >= 0 && j < mesh_vcount && vi != j )
              {
                edge_ends.i = vi;
                edge_ends.j = j;
                edges.Append(edge_ends);
              }
              break; // done with this face
            }
          }
        }
      }
    }
  }
  else
  {
    // slow-n-stupid search through all the faces

    // Sort vertex_index[] array so we can use a quick
    // binary search to see if a face is using one of 
    // the vertices in the list.
    ON_Workspace ws;
    for ( vi = 1; vi < vertex_index_count; vi++ )
    {
      if ( vertex_index[vi] < vertex_index[vi-1] )
      {
        // need to sort vertex_index[] array
        int* tmp = ws.GetIntMemory(vertex_index_count);
        memcpy(tmp,vertex_index,vertex_index_count*sizeof(tmp[0]));
        ON_SortIntArray(ON::quick_sort,tmp,vertex_index_count);
        vertex_index = tmp;
        break;
      }
    }

    // Find all the faces that use a vertex in the vertex_index[] array.
    for ( fi = 0; fi < mesh_fcount; fi++ )
    {
      f_vi = f[fi].vi;
      for ( fvi = 0; fvi < 4; fvi++ )
      {
        vi = f_vi[fvi];
        if ( ON_BinarySearchIntArray(vi,vertex_index,vertex_index_count) )
        {
          // vi is in the vertex_index[] array.  Add the edges
          // of this face that begin and end at this vertex.
          j = f_vi[(fvi+3)%4];
          if ( j >= 0 && j < mesh_vcount && vi != j )
          {
            edge_ends.i = j;
            edge_ends.j = vi;
            edges.Append(edge_ends);
          }
          j = f_vi[ (2==fvi && f_vi[2]==f_vi[3]) ? 0 : ((fvi+1)%4) ];
          if ( j >= 0 && j < mesh_vcount && vi != j )
          {
            edge_ends.i = vi;
            edge_ends.j = j;
            edges.Append(edge_ends);
          }
        }
      }
    }
  }

  if ( bNoDuplicates && edges.Count() > edges_count0 )
  {
    for ( ei = edges_count0; ei < edges.Count(); ei++ )
    {
      edge_ends = edges[ei];
      if ( edge_ends.i > edge_ends.j )
      {
        j = edge_ends.i; edge_ends.i = edge_ends.j; edge_ends.j = j;
      }
    }
    ON_qsort( edges.Array() + edges_count0,
              edges.Count() - edges_count0,
              sizeof(edge_ends), 
              ON_MeshGetVertexEdges_Compare2dex);
    edge_ends = edges[edges_count0];
    for ( ei = j = edges_count0+1; ei < edges.Count(); ei++ )
    {
      if ( ON_Compare2dex(&edge_ends,&edges[ei]) )
      {
        edge_ends = edges[ei];
        if ( j != ei )
          edges[j] = edge_ends;
        j++;
      }
    }
    edges.SetCount(j);
  }

  return (edges.Count() - edges_count0);
}

int ON_Mesh::GetMeshEdges( 
  ON_SimpleArray<ON_2dex>& edges
  ) const
{
  const int edges_count0 = edges.Count();
  int fi, ei, j, fvi;
  const int* f_vi;
  const ON_MeshFace* f = m_F.Array();
  const int mesh_vcount = m_V.Count();
  const int mesh_fcount = m_F.Count();
  edges.Reserve( edges_count0 + 4*mesh_fcount );
  ON_2dex e;

  // Find all the faces that use a vertex in the vertex_index[] array.
  for ( fi = 0; fi < mesh_fcount; fi++ )
  {
    f_vi = f[fi].vi;
    ei = f_vi[3];
    for ( fvi = 0; fvi < 4; fvi++ )
    {
      e.i = ei;
      ei = *f_vi++;
      e.j = ei;
      if ( e.i > e.j )
      {
        j = e.i; e.i = e.j; e.j = j;
      }
      if ( e.i != e.j && e.i >= 0 && e.j < mesh_vcount )
      {
        edges.Append(e);
      }
    }
  }
  

  if ( edges.Count() > edges_count0 )
  {
    ON_qsort( edges.Array() + edges_count0,
              edges.Count() - edges_count0,
              sizeof(e), 
              ON_MeshGetVertexEdges_Compare2dex);
    e = edges[edges_count0];
    for ( ei = j = edges_count0+1; ei < edges.Count(); ei++ )
    {
      if ( ON_Compare2dex(&e,&edges[ei]) )
      {
        e = edges[ei];
        if ( j != ei )
          edges[j] = e;
        j++;
      }
    }
    edges.SetCount(j);
  }

  return edges.Count() - edges_count0;
}


int ON_Mesh::SolidOrientation() const
{

  if ( m_mesh_is_solid <= 0 || m_mesh_is_solid > 3 )
  {
    // NOTE: calling IsSolid() will set m_mesh_is_solid
    //       to 3 if mes is non-manifold
    IsSolid();
  }

  switch(m_mesh_is_solid)
  {
  case 1:
    return 1;
    break;

  case 2:
    return -1;
    break;

  case 3:
    return 0;
    break;
  }

  return 0; // answer "no" if we don't know.
}


bool ON_Mesh::IsSolid() const
{
  return ( IsClosed() && IsManifold() && IsOriented() );
}


bool ON_Mesh::IsManifold(
  bool bTopologicalTest,
  bool* pbIsOriented,
  bool* pbHasBoundary
  ) const
{
  bool bIsManifold = false;
  if ( pbIsOriented )
    *pbIsOriented = false;
  if ( pbHasBoundary )
    *pbHasBoundary = false;
  const int vcount = m_V.Count();
  const int fcount = m_F.Count();
  if ( vcount > 0 && fcount > 0 )
  {
    ON_Workspace ws;
    ON_3dex e;
    int i, j, ecount;
    const int* fvi;
    ON_3fPoint v0;
    const ON_3fPoint* v;
    const ON_MeshFace* f;
    int* vid = ws.GetIntMemory(vcount);
    ON_3dex* edge = (ON_3dex*)ws.GetMemory(4*fcount*sizeof(*edge));

    if ( bTopologicalTest )
    {
      // coincident vertices are assigned the same vertex id
      ON_Sort(ON::quick_sort,vid,m_V.Array(),vcount,sizeof(m_V[0]),ON_MeshIsManifold_CompareV);
      ecount = 0;
      v = m_V.Array();
      ecount = 0;
      j = vcount;
      for ( i = 0; i < vcount; i = j)
      {
        v0 = v[vid[i]];
        vid[i] = ecount;
        for ( j = i+1; j < vcount; j++ )
        {
          if ( ON_MeshIsManifold_CompareV(&v,v+vid[j]) )
          {
            ecount++;
            break;
          }
          vid[j] = ecount;
        }
      }
    }
    else
    {
      // each vertex gets a unique id.
      for ( i = 0; i < vcount; i++ )
        vid[i] = i;
    }

    // build a list of edges
    f = m_F.Array();
    ecount = 0;
    for ( i = 0; i < fcount; i++ )
    {
      fvi = (f++)->vi;
      if (   fvi[0] >= 0 && fvi[0] < vcount 
          && fvi[1] >= 0 && fvi[1] < vcount
          && fvi[2] >= 0 && fvi[2] < vcount
          && fvi[3] >= 0 && fvi[3] < vcount )
      {
        // loop unrolled for speed
        j = ecount;
        e.i = vid[fvi[0]];  e.j = vid[fvi[1]];
        if ( 0 != (e.k = e.j - e.i) )
        {
          if ( e.k < 0 ) {e.k = e.i; e.i = e.j; e.j = e.k; e.k = 1;} else e.k = 0;
          edge[ecount++] = e;
        }
        e.i = vid[fvi[1]];  e.j = vid[fvi[2]];
        if ( 0 != (e.k = e.j - e.i) )
        {
          if ( e.k < 0 ) {e.k = e.i; e.i = e.j; e.j = e.k; e.k = 1;} else e.k = 0;
          edge[ecount++] = e;
        }
        e.i = vid[fvi[2]];  e.j = vid[fvi[3]];
        if ( 0 != (e.k = e.j - e.i) )
        {
          if ( e.k < 0 ) {e.k = e.i; e.i = e.j; e.j = e.k; e.k = 1;} else e.k = 0;
          edge[ecount++] = e;
        }
        e.i = vid[fvi[3]];  e.j = vid[fvi[0]];
        if ( 0 != (e.k = e.j - e.i) )
        {
          if ( e.k < 0 ) {e.k = e.i; e.i = e.j; e.j = e.k; e.k = 1;} else e.k = 0;
          edge[ecount++] = e;
        }
        if ( ecount < j+3 )
          ecount = j;
      }
    }

    if ( ecount >= 4 )
    {
      bIsManifold = true;
      bool bIsOriented  = (pbIsOriented)  ? true  : false;
      bool bHasBoundary = (pbHasBoundary) ? false : true;
      ON_qsort(edge,ecount,sizeof(edge[0]),ON_MeshIsManifold_Compare3dex);

      i = 0;
      e = *edge;
      while ( --ecount )
      {
        edge++;
        if ( memcmp(&e,edge,2*sizeof(int)) )
        {
          if (!i)
            bHasBoundary = true;
          e = *edge;
          i = 0;
        }
        else
        {
          if ( i++ )
          {
            bIsManifold = false;
            break;
          }
          if ( e.k == edge->k )
            bIsOriented = false;
        }
      }

      if ( bIsManifold )
      {
        if ( pbIsOriented )
          *pbIsOriented = bIsOriented;
        if ( pbHasBoundary )
          *pbHasBoundary = bHasBoundary;
      }
    }
  }

  return bIsManifold;
}

static void ON_hsort_3dex(ON_3dex *e, size_t nel)
{
  // dictionary sort e[]
  size_t i_end,k,i,j;
  ON_3dex e_tmp;

  if (nel < 2) return;
  k = nel >> 1;
  i_end = nel-1;
  for (;;)
  {
    if (k)
    {
      --k;
      e_tmp = e[k];
    }
    else 
    {
      e_tmp = e[i_end];
      e[i_end] = e[0];
      if (!(--i_end))
      {
        e[0] = e_tmp;
        break;
      }
    }
    i = k;
    j = (k<<1) + 1;
    while (j <= i_end) 
    {
      if ( j < i_end && ( e[j].i < e[j + 1].i || (e[j].i == e[j + 1].i && (e[j].j < e[j + 1].j || ( e[j].j == e[j + 1].j && e[j].k < e[j + 1].k)) ) ) ) 
        j++;

      if ( e_tmp.i < e[j].i || (e_tmp.i == e[j].i && (e_tmp.j < e[j].j || ( e_tmp.j == e[j].j && e_tmp.k < e[j].k) ) ) )
      {
        e[i] = e[j];
        i = j;
        j = (j<<1) + 1;
      }
      else
        j = i_end + 1;
    }
    e[i] = e_tmp;
  }
}

static void ON_Mesh_SetClosedHelper( 
          bool bClosedOnly,
          const ON_Mesh& mesh,
          const char& m_mesh_is_manifold,
          const char& m_mesh_is_oriented
          )
{
  // thread safe lazy evaluation for mesh's m_mesh_is_... flags
  // Sets: m_mesh_is_closed.
  //       If bClosedOnly is false, also sets m_mesh_is_manifold and m_mesh_is_oriented
  int is_closed = 0;
  char is_manifold = 2;
  char is_oriented = 2;
  for (;;)
  {
    const int Vcount = mesh.m_V.Count();
    const int Fcount = mesh.m_F.Count();
    if ( Vcount < 3 || Fcount < 1 )
    {
      ON_ERROR("Mesh is not valid.");
      break;
    }
    if ( bClosedOnly && (Vcount < 4 || Fcount < 4) )
    {
      // not closed - don't waste any more time.
      break;
    }

    int i, j;
    int Vidbuffer[256];
    int* Vid = mesh.GetVertexLocationIds( 
                     1,
                     (Vcount*sizeof(*Vid) <= sizeof(Vidbuffer) ? &Vidbuffer[0] : 0),
                     0
                    );
    if ( 0 == Vid )
    {
      ON_ERROR("Mesh has corrupt vertex information.");
      bClosedOnly = false;
      break;
    }

    // build an edge list where the "vertex" indices identify unique 3d locations
    ON_3dex* E_list = (ON_3dex*)onmalloc(4*Fcount*sizeof(E_list[0]));
    ON_3dex E;
    int Vid0;
    const int* fvi;
    int E_count = 0;
    const ON_MeshFace* F = mesh.m_F.Array();
    for ( j = 0; j < Fcount; j++ )
    {
      fvi = F[j].vi;
      E.i = Vid[fvi[0]];
      Vid0 = E.j = Vid[fvi[1]];
      if ( E.i == E.j )
        break;
      if ( E.i > E.j )
      {
        i = E.i; E.i = E.j; E.j = i;
        E.k = 1;
      }
      else
      {
        E.k = 0;
      }
      E_list[E_count++] = E;

      E.i = Vid0;
      Vid0 = E.j = Vid[fvi[2]];
      if ( E.i == E.j )
        break;
      if ( E.i > E.j )
      {
        i = E.i; E.i = E.j; E.j = i;
        E.k = 1;
      }
      else
      {
        E.k = 0;
      }
      E_list[E_count++] = E;

      if ( fvi[2] != fvi[3] )
      {
        // quad
        E.i = Vid0;
        Vid0 = E.j = Vid[fvi[3]];
        if ( E.i == E.j )
          break;
        if ( E.i > E.j )
        {
          i = E.i; E.i = E.j; E.j = i;
          E.k = 1;
        }
        else
        {
          E.k = 0;
        }
        E_list[E_count++] = E;
      }

      E.i = Vid0;
      E.j = Vid[fvi[0]];
      if ( E.i == E.j )
        break;
      if ( E.i > E.j )
      {
        i = E.i; E.i = E.j; E.j = i;
        E.k = 1;
      }
      else
      {
        E.k = 0;
      }
      E_list[E_count++] = E;
    }
    if ( Vid != &Vidbuffer[0] )
      onfree(Vid);

    if ( E_count < 3 || j != Fcount )
    {
      ON_ERROR("Mesh is corrupt or collapsed");
      bClosedOnly = false;
      break;
    }

    // sort the the edges
    ON_hsort_3dex(E_list,E_count);

    // Look for duplicate edges.  If we find an edge with no duplicate,
    // then the mesh is open.  It is possible that degenerate meshes,
    // like a flattened box, will be flagged as closed.
    is_closed = (Fcount >= 4 && E_count >= 6) ? 1 : 0;
    is_oriented = 1;
    is_manifold = 1;
    i = -1;
    if ( !bClosedOnly || 1 == is_closed ) for ( i = 0; i < E_count; /*empty iterator*/ )
    {
      E = E_list[i];
      if ( ++i >= E_count )
      {
        // boundary edge (and the last edge in our list)
        is_closed = 0;
        break;
      }

      if ( E.i != E_list[i].i || E.j != E_list[i].j )
      {
        // boundary edge
        is_closed = 0;
        if ( 2 == is_oriented && 2 == is_manifold )
        {
          bClosedOnly = false;
          break;
        }
        if ( bClosedOnly )
          break; // don't spend time with further testing
        continue;
      }

      if ( E.k == E_list[i].k )
      {
        // opposite face normals along this edge - mesh is not oriented
        is_oriented = 2; 
      }

      if ( ++i >= E_count || E.i != E_list[i].i || E.j != E_list[i].j )
      {
        // two faces share this edge
        continue;
      }

      // three or more faces share this edge - mesh is not oriented manifold
      is_oriented = 2; 
      is_manifold = 2; 
      if ( 0 == is_closed )
      {
        bClosedOnly = false;
        break;
      }

      // Check for more faces sharing this edge.
      for ( i++; i < E_count; i++ )
      {
        if ( E.i != E_list[i].i || E.j != E_list[i].j )
        {
          // the edges E and Eid_list[i] are in different locations
          break;
        }
      }
    }
    if ( i >= E_count )
    {
      // is_manifold and is_oriented are set correctly
      bClosedOnly = false;
    }

    onfree(E_list);

    break;
  }

  const_cast<ON_Mesh&>(mesh).SetClosed(is_closed);
  if ( !bClosedOnly )
  {
    // is_manifold and is_oriented are set correctly
    if ( 2 == is_manifold )
      is_oriented = 2;
    const_cast<char&>(m_mesh_is_manifold) = is_manifold;
    const_cast<char&>(m_mesh_is_oriented) = is_oriented;
  }
}

bool ON_Mesh::IsClosed() const
{
  if ( m_mesh_is_closed <= 0 || m_mesh_is_closed > 2) 
  {
    // thread safe lazy evaluation
    ON_Mesh_SetClosedHelper( true, *this, m_mesh_is_manifold, m_mesh_is_oriented );
  }

  return (1 == m_mesh_is_closed);
}

bool ON_Mesh::IsManifold() const
{
  if ( m_mesh_is_manifold <= 0 || m_mesh_is_manifold > 2 )
  {
    // thread safe lazy evaluation
    ON_Mesh_SetClosedHelper( false, *this, m_mesh_is_manifold, m_mesh_is_oriented );
  }
  return (1 == m_mesh_is_manifold);
}

bool ON_Mesh::IsOriented() const
{
  if ( m_mesh_is_oriented <= 0 || m_mesh_is_oriented > 2 )
  {
    // thread safe lazy evaluation
    ON_Mesh_SetClosedHelper( false, *this, m_mesh_is_manifold, m_mesh_is_oriented );
  }
  return (1 == m_mesh_is_oriented);
}


bool ON_Mesh::SetVertex(
       int vertex_index,
       const ON_3dPoint& vertex_location
       )
{
  bool rc = false;
  int vertex_count = m_V.Count();
  if ( vertex_index >= 0 && vertex_index <= vertex_count )
  {
    bool bIsValid_fV = false;
    if ( HasDoublePrecisionVertices() )
    {
      bIsValid_fV = SinglePrecisionVerticesAreValid();
      ON_3dPointArray& dV = DoublePrecisionVertices();
      if ( vertex_count == dV.Count() )
      {
        bool bIsValid_dV = DoublePrecisionVerticesAreValid();
        if ( vertex_index < vertex_count ) 
          dV[vertex_index] = vertex_location;
        else
          dV.Append(vertex_location);
        if ( bIsValid_dV )
          SetDoublePrecisionVerticesAsValid();
      }
    }
    if ( vertex_index < vertex_count ) 
      m_V[vertex_index] = vertex_location;
    else
      m_V.Append(vertex_location);
    if ( bIsValid_fV )
      SetSinglePrecisionVerticesAsValid();
    rc = true;
  }
  return rc;
}

bool ON_Mesh::SetVertex(
       int vertex_index,
       const ON_3fPoint& vertex_location
       )
{
  bool rc = false;
  int vertex_count = m_V.Count();
  if ( vertex_index >= 0 && vertex_index <= vertex_count )
  {
    bool bIsValid_fV = false;
    if ( HasDoublePrecisionVertices() )
    {
      bIsValid_fV = SinglePrecisionVerticesAreValid();
      ON_3dPointArray& dV = DoublePrecisionVertices();
      if ( vertex_count == dV.Count() )
      {
        bool bIsValid_dV = DoublePrecisionVerticesAreValid();
        if ( vertex_index < vertex_count ) 
          dV[vertex_index] = vertex_location;
        else
          dV.Append(vertex_location);
        if ( bIsValid_dV )
          SetDoublePrecisionVerticesAsValid();
      }
    }
    if ( vertex_index < vertex_count ) 
      m_V[vertex_index] = vertex_location;
    else
      m_V.Append(vertex_location);
    if ( bIsValid_fV )
      SetSinglePrecisionVerticesAsValid();
    rc = true;
  }
  return rc;
}

bool ON_Mesh::SetVertexNormal(
       int vertex_index,
       const ON_3dVector& normal
       )
{
  bool rc = false;
  // use double precision for unitizing normal
  ON_3dVector unit_vector = normal;
  const bool bUnitVector = unit_vector.Unitize();
  ON_3fVector v((float)unit_vector.x, (float)unit_vector.y, (float)unit_vector.z);
  int normal_count = m_N.Count();
  if ( vertex_index >= 0 ) {
    if ( vertex_index < normal_count ) {
      m_N[vertex_index] = v;
      rc = bUnitVector;
    }
    else if ( vertex_index == normal_count ) {
      m_N.Append(v);
      rc = bUnitVector;
    }
  }
  return rc;
}

bool ON_Mesh::SetVertexNormal(
       int vertex_index,
       const ON_3fVector& normal
       )
{
  ON_3dVector v(normal.x,normal.y,normal.z);
  return SetVertexNormal(vertex_index,v);
}

bool ON_Mesh::SetTextureCoord(
       int vertex_index,
       double s, double t    // texture coordinates
       )
{
  ON_2fPoint tc((float)s,(float)t);
  bool rc = false;
  int vertex_count = m_T.Count();
  if ( vertex_index >= 0 ) {
    if ( vertex_index < vertex_count ) {
      m_T[vertex_index] = tc;
      rc = true;
    }
    else if ( vertex_index == vertex_count ) {
      m_T.Append(tc);
      rc = true;
    }
  }
  return rc;
}


bool ON_Mesh::SetTriangle(
       int face_index,
       int a,int b ,int c // vertex indices
       )
{
  return SetQuad( face_index, a,b,c,c );
}

bool ON_Mesh::SetQuad(
       int face_index,
       int a, int b, int c, int d // vertex indices
       )
{
  bool rc = false;
  int face_count = m_F.Count();
  if ( face_index >= 0 ) {
    ON_MeshFace f;
    f.vi[0] = a;
    f.vi[1] = b;
    f.vi[2] = c;
    f.vi[3] = d;
    if ( face_index < face_count ) {
      m_F[face_index] = f;
      rc = true;
    }
    else if ( face_index == face_count ) {
      m_F.Append(f);
      rc = true;
    }
    if ( rc )
      rc = f.IsValid(m_V.Count());
  }
  return rc;
}



int ON_Mesh::FaceCount() const
{
  return m_F.Count();
}

int ON_Mesh::QuadCount() const
{
  // number of faces that are quads
  if (   m_quad_count     < 0
      || m_triangle_count < 0 
      || m_invalid_count  < 0 
      || m_quad_count + m_triangle_count + m_invalid_count != FaceCount() ) 
  {
    const_cast<ON_Mesh*>(this)->CountQuads();
  }
  return m_quad_count;
}

int ON_Mesh::TriangleCount() const
{
  // number of faces that are triangles
  QuadCount(); // makes sure counts are valid
  return m_triangle_count;
}

int ON_Mesh::InvalidFaceCount() const
{
  // number of faces that are invalid
  QuadCount(); // makes sure counts are valid
  return m_invalid_count;
}


int ON_Mesh::VertexCount() const
{
  return m_V.Count();
}

bool ON_Mesh::HasVertexNormals() const
{
  const int vertex_count = VertexCount();
  return ( vertex_count > 0 && m_N.Count() == vertex_count ) ? true : false;
}

bool ON_Mesh::HasFaceNormals() const
{
  const int face_count = FaceCount();
  return ( face_count > 0 && m_FN.Count() == face_count ) ? true : false;
}

bool ON_Mesh::HasTextureCoordinates() const
{
  const int vertex_count = VertexCount();
  return ( vertex_count > 0 && m_T.Count() == vertex_count ) ? true : false;
}

bool ON_Mesh::HasCachedTextureCoordinates() const
{
  const int vertex_count = VertexCount();
  if (vertex_count > 0 )
  {
    int tci, tccount = m_TC.Count();
    for ( tci = 0; tci < tccount; tci++ )
    {
      if ( vertex_count == m_TC[tci].m_T.Count() )
        return true;
    }
  }
  return false;
}

const ON_TextureCoordinates* 
ON_Mesh::CachedTextureCoordinates( const ON_UUID& mapping_id ) const
{
  const int vertex_count = VertexCount();
  if (vertex_count > 0 )
  {
    const ON_TextureCoordinates* TC = m_TC.Array();
    int tci, tccount = m_TC.Count();
    for ( tci = 0; tci < tccount; tci++ )
    {
      if (   vertex_count == TC->m_T.Count() 
          && mapping_id == TC->m_tag.m_mapping_id )
      {
        return TC;
      }
    }
  }
  return 0;
}

bool ON_Mesh::HasSurfaceParameters() const
{
  const int vertex_count = VertexCount();
  return ( vertex_count > 0 && m_S.Count() == vertex_count ) ? true : false;
}

bool ON_Mesh::HasPrincipalCurvatures() const
{
  const int vertex_count = VertexCount();
  return ( vertex_count > 0 && m_K.Count() == vertex_count ) ? true : false;
}

bool ON_Mesh::HasVertexColors() const
{
  const int vertex_count = VertexCount();
  return ( vertex_count > 0 && m_C.Count() == vertex_count ) ? true : false;
}

void ON_Mesh::InvalidateBoundingBoxes()
{
  InvalidateVertexBoundingBox();
  InvalidateVertexNormalBoundingBox();
  InvalidateTextureCoordinateBoundingBox();
  InvalidateCurvatureStats();
}

void ON_Mesh::InvalidateVertexBoundingBox()
{
  m_vbox[0][0] = m_vbox[0][1] = m_vbox[0][2] =  1.0;
  m_vbox[1][0] = m_vbox[1][1] = m_vbox[1][2] = -1.0;
}

void ON_Mesh::InvalidateVertexNormalBoundingBox()
{
  m_nbox[0][0] = m_nbox[0][1] = m_nbox[0][2] =  1.0;
  m_nbox[1][0] = m_nbox[1][1] = m_nbox[1][2] = -1.0;
}

void ON_Mesh::InvalidateTextureCoordinateBoundingBox()
{
  m_tbox[0][0] = m_tbox[0][1] =  1.0;
  m_tbox[1][0] = m_tbox[1][1] = -1.0;
}

void ON_Mesh::InvalidateCurvatureStats()
{
  int i;
  for ( i = 0; i < 4; i++ ) {
    if ( m_kstat[i] ) {
      delete m_kstat[i];
      m_kstat[i] = 0;
    }
  }
}

bool ON_Mesh::UnitizeVertexNormals()
{
  bool rc = HasVertexNormals();
  if ( rc ) {
    const int vertex_count = VertexCount();
    float* n = &m_N[0][0];
    int i;
    ON_3dVector N;
    for ( i = 0; i < vertex_count; i++ ) {
      N.x = n[0];
      N.y = n[1];
      N.z = n[2];
      if ( !N.Unitize() )
        rc = false;
      *n++ = (float)N.x;
      *n++ = (float)N.y;
      *n++ = (float)N.z;
    }
  }
  return rc;
}

bool ON_Mesh::UnitizeFaceNormals()
{
  bool rc = HasFaceNormals();
  if ( rc ) {
    const int face_count = FaceCount();
    float* n = &m_FN[0][0];
    int i;
    ON_3dVector N;
    for ( i = 0; i < face_count; i++ ) {
      N.x = n[0];
      N.y = n[1];
      N.z = n[2];
      if ( !N.Unitize() )
        rc = false;
      *n++ = (float)N.x;
      *n++ = (float)N.y;
      *n++ = (float)N.z;
    }
  }
  return rc;
}


bool ON_Mesh::GetCurvatureStats( // returns true if successful
       ON::curvature_style kappa_style,
       ON_MeshCurvatureStats& stats
       ) const
{
  bool rc = false;
  stats.Destroy();
  int ksi;
  switch ( kappa_style ) {
    case ON::gaussian_curvature:
      ksi = 0;
      break;
    case ON::mean_curvature:
      ksi = 1;
      break;
    case ON::min_curvature: // minimum unsigned radius of curvature
      ksi = 2;
      break;
    case ON::max_curvature: // maximum unsigned radius of curvature
      ksi = 3;
      break;
    //case ON::section_curvature_x:
    //  ksi = 4;
    //  break;
    //case ON::section_curvature_y:
    //  ksi = 5;
    //  break;
    //case ON::section_curvature_z:
    //  ksi = 6;
    //  break;
    default:
      ksi = -1;
      break;
  }
  if ( ksi >= 0 && ksi <= 3 && HasPrincipalCurvatures() ) {
    ON_Mesh* p = (ON_Mesh*)this; // const lie 
    if ( !m_kstat[ksi] ) {
      p->m_kstat[ksi] = new ON_MeshCurvatureStats();
      p->m_kstat[ksi]->Set( kappa_style, m_K.Count(), m_K.Array(), m_N.Array() );
    }
    if ( p->m_kstat[ksi] ) {
      stats = *p->m_kstat[ksi];
      rc = true;
    }
  }
  return rc;
}

int ON_MeshTopology::WaitUntilReady(int sleep_value) const
{
  return m_b32IsValid;
}


bool ON_Mesh::TopologyExists() const
{
  return (1 == m_top.WaitUntilReady(0));
}

const ON_MeshTopology& ON_Mesh::Topology() const
{
  int top_b32IsValid =  m_top.WaitUntilReady(-1);

  if ( 0 == top_b32IsValid ) 
  {
    ON_MeshTopology& top = const_cast<ON_MeshTopology&>(m_top);
    top.m_mesh = this;
    top_b32IsValid = top.Create() ? 1 : 0;
    top.m_b32IsValid = top_b32IsValid;
  }

  return m_top;
}

void ON_Mesh::DestroyTopology()
{
  m_top.Destroy();
}

bool
ON_MeshFace::IsTriangle() const 
{
  return vi[2]==vi[3];
}

bool
ON_MeshFace::IsQuad() const 
{
  return vi[2]!=vi[3];
}

void
ON_MeshFace::Flip()
{
  int i;
  if ( vi[2] == vi[3] ) {
    i = vi[1];
    vi[1] = vi[2];
    vi[2] = i;
    vi[3] = i;
  }
  else {
    i = vi[1];
    vi[1] = vi[3];
    vi[3] = i;
  }
}

/*
ON_MeshEdge::ON_MeshEdge() : m_fcount(0)
{
  m_fi = m_private_fi;
  m_private_fi[0] = 0;
  m_private_fi[0] = 0;
}

ON_MeshEdge::~ON_MeshEdge()
{
  if ( m_fi && m_fi != m_private_fi ) onfree((void*)m_fi);
}

ON_MeshEdge::ON_MeshEdge( const ON_MeshEdge& src ) : m_fcount(0), m_fi(0)
{
  *this = src;
}

int ON_MeshEdge::FaceIndexCount() const
{
  return m_fcount;
}

const int* ON_MeshEdge::FaceIndexArray() const
{
  return m_fi;
}

int& ON_MeshEdge::operator[](int i)
{
  return (i>=0&&i<m_fcount) ? m_fi[i] : m_private_fi[0];
}

int ON_MeshEdge::operator[](int i) const
{
  return (i>=0&&i<m_fcount) ? m_fi[i] : m_private_fi[0];
}
*/

void 
ON_Mesh::Flip()
{
  FlipFaceOrientation();
  FlipFaceNormals();
  FlipVertexNormals();

  // Do not modify m_S[] or m_T[]
  // values here.
}

void 
ON_Mesh::FlipVertexNormals()
{
  int i;
  const int vcount = VertexCount();
  if ( HasVertexNormals() ) {
    for ( i = 0; i < vcount; i++ ) {
      m_N[i].Reverse();
    }
  }
}

void 
ON_Mesh::FlipFaceNormals()
{
  int i;
  const int fcount = FaceCount();
  if ( HasFaceNormals() ) {
    for( i = 0; i < fcount; i++ ) {
      m_FN[i].Reverse();
    }
  }
}

void 
ON_Mesh::FlipFaceOrientation()
{
  int i;
  const int fcount = FaceCount();
  for( i = 0; i < fcount; i++ ) {
    m_F[i].Flip();
  }
  if ( fcount > 0 )
    DestroyTopology(); // flipping changes order of face corners
}

bool ON_MeshFace::ComputeFaceNormal( const ON_3dPoint* dV, ON_3dVector& FN ) const
{
  if ( 0 != dV )
  {
    ON_3dVector a = dV[vi[2]] - dV[vi[0]];
    ON_3dVector b = dV[vi[3]] - dV[vi[1]];
    FN = ON_CrossProduct( a, b ); // works for triangles, quads, and nonplanar quads
    if ( FN.Unitize() )
      return true;
  }

  FN.Zero();
  return false;
}

bool ON_MeshFace::ComputeFaceNormal( const ON_3fPoint* fV, ON_3dVector& FN ) const
{
  if ( 0 != fV )
  {
    ON_3dVector a = fV[vi[2]] - fV[vi[0]];
    ON_3dVector b = fV[vi[3]] - fV[vi[1]];
    FN = ON_CrossProduct( a, b ); // works for triangles, quads, and nonplanar quads
    if ( FN.Unitize() )
      return true;
  }

  FN.Zero();
  return false;
}

bool
ON_Mesh::ComputeFaceNormal( int fi )
{
  if ( fi < 0 )
    return false;
  if ( fi >= m_F.Count() )
    return false;
  if ( m_FN.Count() != m_F.Count() )
    return false;
  
  ON_3dVector FN;
  bool rc = ( HasDoublePrecisionVertices() )
          ? m_F[fi].ComputeFaceNormal(DoublePrecisionVertices().Array(),FN)
          : m_F[fi].ComputeFaceNormal(m_V.Array(),FN);
  
  m_FN[fi] = FN;

  return rc;
}

bool
ON_Mesh::ComputeFaceNormals()
{
  bool rc = false;
  const int fcount = FaceCount();
  if ( fcount > 0 )
  {
    ON_3dVector a, b, n;
    int fi;
    const int* vi;
    if ( m_FN.Capacity() < fcount )
      m_FN.SetCapacity(fcount);
    m_FN.SetCount(0);
    rc = true;
    if ( HasDoublePrecisionVertices() && DoublePrecisionVerticesAreValid() )
    {      
      const ON_3dPointArray& dV = DoublePrecisionVertices();
      for ( fi = 0; fi < fcount; fi++ ) {
        vi = m_F[fi].vi;
        a = dV[vi[2]] - dV[vi[0]];
        b = dV[vi[3]] - dV[vi[1]];
        n = ON_CrossProduct( a, b ); // works for triangles, quads, and nonplanar quads
        n.Unitize();
        m_FN.Append(n);
      }
    }
    else
    {
      for ( fi = 0; fi < fcount; fi++ ) {
        vi = m_F[fi].vi;
        a = m_V[vi[2]] - m_V[vi[0]];
        b = m_V[vi[3]] - m_V[vi[1]];
        n = ON_CrossProduct( a, b ); // works for triangles, quads, and nonplanar quads
        n.Unitize();
        m_FN.Append(n);
      }
    }
  }
  else 
  {
    m_FN.Destroy();
  }
  return rc;
}


//static int compareRadial3fPoint( const ON_3fPoint* a, const ON_3fPoint* b )
//{
//  double ar = a->x+a->y+a->z;
//  double br = b->x+b->y+b->z;
//  if ( ar < br )
//    return -1;
//  if ( ar > br )
//    return 1;
//  return 0;
//}

bool ON_Mesh::CombineCoincidentVertices( 
        const ON_3fVector tolerance,
        double cos_normal_angle // = -1.0  // cosine(break angle) -1.0 will merge all coincident vertices
        )
{
  // TODO - If you need this function, please ask Dale Lear to finish it.
  //bool rc = false;
  //const int vcount = VertexCount();
  //if ( vcount > 0 && rc ) {
  //  ON_Workspace ws;
  //  int* index = ws.GetIntMemory(vcount);
  //  rc = m_V.Sort( ON::quick_sort, index, compareRadial3fPoint );
  //  int i, j;
  //  ON_3fPoint p0, p1, pmin, pmax;
  //  for ( i = 0; i < vcount; i++ ) {
  //    p0 = m_V[i];
  //    pmin = p0 - tolerance;
  //    pmax = p0 + tolerance;
  //    for ( j = i+1; j < vcount; j++ ) {
  //      p1 = m_V[j];
  //      // TODO        
  //    }
  //  }
  //}
  return false;
}


struct tagMESHPOINTS
{
  // p0 = bogus pointer - never dereferenced - that is used
  //      to calculate vertex index in CompareMeshPoint().
  const char* p0;
  ON_3fPoint*  V;
  ON_2fPoint*  T;
  ON_3fVector* N;
  ON_SurfaceCurvature* K;
  ON_Color* C;
};

static int CompareMeshPoint(const void* a,const void* b,void* ptr)
{
  float d;
  const struct tagMESHPOINTS * mp = (const struct tagMESHPOINTS *)ptr;

  // use bogus pointer to convert a,b into vertex indices
  int i = (int)(((const char*)a) - mp->p0); // the (int) is for 64 bit size_t conversion
  int j = (int)(((const char*)b) - mp->p0);

  d = mp->V[j].x - mp->V[i].x;
  if ( d == 0.0f )
  {
    d = mp->V[j].y - mp->V[i].y;
    if ( d == 0.0f )
    {
      d = mp->V[j].z - mp->V[i].z;

      //if ( d == 0.0f )
      //  return 0;

      if ( d == 0.0f && 0 != mp->N)
      {
        d = mp->N[j].x - mp->N[i].x;
        if ( d == 0.0f )
        {
          d = mp->N[j].y - mp->N[i].y;
          if ( d == 0.0f )
          {
            d = mp->N[j].z - mp->N[i].z;
          }
        }
      }

      if ( d == 0.0f && 0 != mp->T)
      {
        d = mp->T[j].x - mp->T[i].x;
        if ( d == 0.0f )
        {
          d = mp->T[j].y - mp->T[i].y;
        }
      }

      if ( d == 0.0f && 0 != mp->C )
      {
        int u = ((int)mp->C[j])-((int)mp->C[i]);
        if ( u < 0 )
          d = -1.0f;
        else if ( u > 0 )
          d = 1.0f;
      }

      if ( d == 0.0f && 0 != mp->K )
      {
        double dk = mp->K[j].k1 - mp->K[i].k1;
        if ( dk < 0.0 )
          d = -1.0;
        else if ( dk > 0.0 )
          d = 1.0;
        else
        {
          dk = mp->K[j].k2 - mp->K[i].k2;
          if ( dk < 0.0 )
            d = -1.0;
          else if ( dk > 0.0 )
            d = 1.0;
        }
      }
    }
  }
  
  if ( d < 0.0f )
    return -1;
  if ( d > 0.0f )
    return 1;
  return 0;
}

bool ON_Mesh::CombineIdenticalVertices(
                                bool bIgnoreVertexNormals,
                                bool bIgnoreTextureCoordinates
                                )
{
  // 11 June 2003 - added and tested.
  bool rc = false;
  ON_Mesh& mesh = *this;

  int vertex_count = mesh.VertexCount();
  if ( vertex_count > 0 )
  {
    ON_SimpleArray<int> index_array(vertex_count);
    ON_SimpleArray<int> remap_array(vertex_count);

    int remap_vertex_count = 0;
    int merge_count = 0;
    int i0, i1, k;

    struct tagMESHPOINTS mp;
    memset(&mp,0,sizeof(mp));
    mp.p0 = (const char*)&mp; // bogus pointer - never dereferenced
    mp.V = mesh.m_V.Array();
    mp.N = mesh.HasVertexNormals()       ? mesh.m_N.Array() : 0;
    mp.T = mesh.HasTextureCoordinates()  ? mesh.m_T.Array() : 0;
    mp.C = mesh.HasVertexColors()        ? mesh.m_C.Array() : 0;
    mp.K = mesh.HasPrincipalCurvatures() ? mesh.m_K.Array() : 0;

    if ( bIgnoreVertexNormals )
    {
      mp.N = 0;
    }

    if ( bIgnoreTextureCoordinates )
    {
      mp.T = 0;
      mp.C = 0;
      mp.K = 0;
    }

    index_array.SetCount(vertex_count);
    index_array.Zero();
    int* index = index_array.Array();

    remap_array.SetCount(vertex_count);
    int* remap = remap_array.Array();
    for ( k = 0; k < vertex_count; k++ )
      remap[k] = -1;

    ON_Sort( 
          ON::quick_sort,
          index,
          mp.p0,                 // data buffer
          vertex_count,
          sizeof(*mp.p0),
          CompareMeshPoint,
          &mp
         );

    for ( i0 = 0; i0 < vertex_count; i0 = i1 )
    {
      for ( i1 = i0+1; i1 < vertex_count; i1++ )
      {
        if ( CompareMeshPoint( mp.p0+index[i0], mp.p0+index[i1], &mp ) )
          break;
        else
          merge_count++;
      }
      for ( /*empty*/; i0 < i1; i0++ )
      {
        remap[index[i0]] = remap_vertex_count;
      }
      remap_vertex_count++;
    }

    if ( bIgnoreVertexNormals )
    {
      mp.N = mesh.HasVertexNormals() ? mesh.m_N.Array() : 0;
    }

    if ( bIgnoreTextureCoordinates )
    {
      mp.T = mesh.HasTextureCoordinates()  ? mesh.m_T.Array() : 0;
      mp.C = mesh.HasVertexColors()        ? mesh.m_C.Array() : 0;
      mp.K = mesh.HasPrincipalCurvatures() ? mesh.m_K.Array() : 0;
    }

    if ( remap_vertex_count > 0 && remap_vertex_count < vertex_count )
    {
      ON_SimpleArray<ON_3fPoint> p_array(remap_vertex_count);
      p_array.SetCount(remap_vertex_count);
      ON_3fPoint* p = p_array.Array();
      ON_3fVector* v = (ON_3fVector*)p;

      for ( k = 0; k < vertex_count; k++ )
      {
        p[remap[k]] = mp.V[k];
      }
      for ( k = 0; k < remap_vertex_count; k++ )
        mp.V[k] = p[k];
      mesh.m_V.SetCount(remap_vertex_count);

      if ( 0 != mp.N )
      {
        if ( bIgnoreVertexNormals )
        {
          // average vertex normals of combined vertices
          p_array.Zero();
          for ( k = 0; k < vertex_count; k++ )
          {
            v[remap[k]] += mp.N[k];
          }
          for ( k = 0; k < remap_vertex_count; k++ )
          {
            v[k].Unitize();
          }
        }
        else
        {
          for ( k = 0; k < vertex_count; k++ )
          {
            v[remap[k]] = mp.N[k];
          }
        }
        for ( k = 0; k < remap_vertex_count; k++ )
          mp.N[k] = v[k];
        mesh.m_N.SetCount(remap_vertex_count);
      }
      else
        mesh.m_N.SetCount(0);

      if ( 0 != mp.T && !bIgnoreTextureCoordinates )
      {
        for ( k = 0; k < vertex_count; k++ )
        {
          p[remap[k]] = mp.T[k];
        }
        for ( k = 0; k < remap_vertex_count; k++ )
          mp.T[k] = p[k];
        mesh.m_T.SetCount(remap_vertex_count);
      }
      else
        mesh.m_T.SetCount(0);

      if ( 0 != mp.C && !bIgnoreTextureCoordinates )
      {
        ON_SimpleArray<ON_Color> c_array(remap_vertex_count);
        c_array.SetCount(remap_vertex_count);
        ON_Color* c = c_array.Array();
        for ( k = 0; k < vertex_count; k++ )
        {
          c[remap[k]] = mp.C[k];
        }
        for ( k = 0; k < remap_vertex_count; k++ )
          mp.C[k] = c[k];
        mesh.m_C.SetCount(remap_vertex_count);
      }
      else
        mesh.m_C.SetCount(0);

      if ( 0 != mp.K && !bIgnoreTextureCoordinates )
      {
        ON_SimpleArray<ON_SurfaceCurvature> s_array(remap_vertex_count);
        s_array.SetCount(remap_vertex_count);
        ON_SurfaceCurvature* s = s_array.Array();
        for ( k = 0; k < vertex_count; k++ )
        {
          s[remap[k]] = mp.K[k];
        }
        for ( k = 0; k < remap_vertex_count; k++ )
          mp.K[k] = s[k];
        mesh.m_K.SetCount(remap_vertex_count);
      }
      else
        mesh.m_K.SetCount(0);

      const int face_count = mesh.m_F.Count();
      ON_MeshFace* f = mesh.m_F.Array();
      int* fvi;
      for ( k = 0; k < face_count; k++ )
      {
        fvi = f[k].vi;
        fvi[0] = remap[fvi[0]];
        fvi[1] = remap[fvi[1]];
        fvi[2] = remap[fvi[2]];
        fvi[3] = remap[fvi[3]];
      }

      if (0 != NgonList())
      {
        //This mesh has an ngon list.
        //Modify the vertex indexes in the ngons as 
        //we did the faces above
        ON_MeshNgonList* ngonlist = ModifyNgonList();
        int kk, kkct = ngonlist->NgonCount();
        for (kk = 0; kk < kkct; kk++)
        {
          ON_MeshNgon* ngon = ngonlist->Ngon(kk);
          if (0 == ngon)
            continue;
          for ( k = 0; k < ngon->N; k++ )
            ngon->vi[k] = remap[ngon->vi[k]];
        }
      }

      mesh.DestroyPartition();
      mesh.DestroyTopology();

      if ( mesh.m_V.Capacity() > 4*mesh.m_V.Count() && mesh.m_V.Capacity() > 50 )
      {
        // There is lots of unused memory in the dynamic arrays.
        // Release what we can.
        mesh.Compact();
      }
      rc = true;
    }
  }
  return rc;
}

void ON_Mesh::Append( int mesh_count, const ON_Mesh* const* meshes )
{
  if ( mesh_count <= 0 || 0 == meshes )
    return;

  int mi;
  int vcount0 = VertexCount();
  if ( vcount0 <= 0 )
    m_F.SetCount(0);
  int fcount0 = FaceCount();
  int* vi;
  int j;
  const ON_Mesh* m;

  // The calls to Has*() must happen before the m_V[] and m_F[] arrays get enlarged
  // Allow the appendage of VertexNormals, TextureCoordinates, PrincipalCurvatures to empty meshes
  // by checking for 0 == vcount0 && 0 == fcount0
  bool bHasVertexNormals       = (0 == vcount0 || HasVertexNormals());
  bool bHasFaceNormals         = (0 == vcount0 || 0 == fcount0 || HasFaceNormals());
  bool bHasTextureCoordinates  = (0 == vcount0 || HasTextureCoordinates());
  bool bHasPrincipalCurvatures = (0 == vcount0 || HasPrincipalCurvatures());
  bool bHasVertexColors        = (0 == vcount0 || HasVertexColors());
  bool bHasSurfaceParameters   = (0 == vcount0 || HasSurfaceParameters());
  bool bHasDoubles             = (0 == vcount0 || HasSynchronizedDoubleAndSinglePrecisionVertices());

  int fcount = fcount0;
  int vcount = vcount0;
  for ( mi = 0; mi < mesh_count; mi++ )
  {
    m = meshes[mi];
    if ( 0 == m )
      continue;
    int vcount1 = m->m_V.Count();
    if ( vcount1 <= 0 )
      continue;
    int fcount1 = m->m_F.Count();
    if ( fcount1 > 0 )
      fcount += fcount1;
    vcount += vcount1;
    if ( bHasVertexNormals && !m->HasVertexNormals() )
      bHasVertexNormals = false;
    if ( bHasTextureCoordinates && !m->HasTextureCoordinates())
      bHasTextureCoordinates = false;
    if ( bHasPrincipalCurvatures && !m->HasPrincipalCurvatures())
      bHasPrincipalCurvatures = false;
    if ( bHasVertexColors && !m->HasVertexColors())
      bHasVertexColors = false;
    if ( bHasSurfaceParameters && !m->HasSurfaceParameters())
      bHasSurfaceParameters = false;
    if ( bHasDoubles && !m->HasSynchronizedDoubleAndSinglePrecisionVertices())
      bHasDoubles = false;
    if ( bHasFaceNormals && fcount1 > 0 && !m->HasFaceNormals() )
      bHasFaceNormals = false;
  }

  if ( vcount <= vcount0 && fcount <= fcount0 )
    return;

  m_top.Destroy();

  // It is critical to call DoublePrecisionVertices() before 
  // we modify m_V[] because DoublePrecisionVertices() will
  // attempt to update the double precision information
  // when it notices that m_V has new vertices added.
  ON_MeshDoubleVertices* dv = 0;
  if ( bHasDoubles )
  {
    dv = ON_MeshDoubleVertices::Get(this);
    if ( 0 == dv && 0 == m_V.Count() )
    {
      DoublePrecisionVertices(); // creates ON_MeshDoubleVertices info on "this"
      dv = ON_MeshDoubleVertices::Get(this);
    }
    if ( 0 == dv )
      bHasDoubles = false;
  }

  m_V.Reserve(vcount);
  m_F.Reserve(fcount);
  for (mi = 0; mi < mesh_count; mi++ )
  {
    m = meshes[mi];
    if ( 0 == m )
      continue;
    int vcount1 = m->m_V.Count();
    if ( vcount1 <= 0 )
      continue;
    int fcount1 = m->m_F.Count();
    if ( fcount1 > 0 )
    {
      int vc0 = m_V.Count();
      j = m_F.Count();
      m_F.Append(fcount1,m->m_F.Array());
      fcount1 += j;
      while (j < fcount1)
      {
        vi = m_F[j].vi;
        vi[0] += vc0;
        vi[1] += vc0;
        vi[2] += vc0;
        vi[3] += vc0;
        j++;
      }
    }
    m_V.Append(vcount1,m->m_V.Array());
  }

  if ( bHasDoubles)
  {
    // Now update the double precision vertex locations.
    dv->m_dV.Reserve(vcount);
    for (mi = 0; mi < mesh_count; mi++ )
    {
      m = meshes[mi];
      if ( 0 == m || m->m_V.Count() <= 0 )
        continue;
      ON_MeshDoubleVertices* dv1 = ON_MeshDoubleVertices::Get(m);
      if ( 0 == dv1 )
        break;
      dv->m_dV.Append(dv1->m_dV.Count(),dv1->m_dV.Array());
    }
    if ( dv->m_dV.Count() == vcount )
    {
      // The calculation of the CRCs in the following calls
      // is what slows down appending meshes one-by-one
      // when thousands of meshes are being appended.
      // That's why the code is structured to do the calculation
      // a single time here.
      SetSinglePrecisionVerticesAsValid();
      SetDoublePrecisionVerticesAsValid();
    }
    else
    {
      DestroyDoublePrecisionVertices();
    }
  }
  else
  {
    DestroyDoublePrecisionVertices();
  }


  if ( bHasVertexNormals ) 
  {
    m_N.Reserve(vcount);
    for (mi = 0; mi < mesh_count; mi++ )
    {
      m = meshes[mi];
      if ( 0 == m )
        continue;
      m_N.Append(m->m_N.Count(), m->m_N.Array());
    }
  }
  else
  {
    m_N.Destroy();
  }


  if ( bHasFaceNormals ) 
  {
    m_FN.Reserve(fcount);
    for (mi = 0; mi < mesh_count; mi++ )
    {
      m = meshes[mi];
      if ( 0 == m || m->m_V.Count() <= 0 )
        continue;
      m_FN.Append(m->m_FN.Count(), m->m_FN.Array());
    }
  }
  else
  {
    m_FN.Destroy();
  }

  if ( bHasTextureCoordinates ) 
  {
    m_T.Reserve(vcount);
    for (mi = 0; mi < mesh_count; mi++ )
    {
      m = meshes[mi];
      if ( 0 == m )
        continue;
      m_T.Append(m->m_T.Count(), m->m_T.Array());
    }
  }
  else 
  {
    m_T.Destroy();
  }


  if ( bHasSurfaceParameters )
  {
    m_S.Reserve(vcount);
    for (mi = 0; mi < mesh_count; mi++ )
    {
      m = meshes[mi];
      if ( 0 == m )
        continue;
      m_S.Append(m->m_S.Count(), m->m_S.Array());
    }
  }
  else 
  {
    m_S.Destroy();
  }

  if ( bHasPrincipalCurvatures )
  {
    m_K.Reserve(vcount);
    for (mi = 0; mi < mesh_count; mi++ )
    {
      m = meshes[mi];
      if ( 0 == m )
        continue;
      m_K.Append(m->m_K.Count(), m->m_K.Array());
    }
  }
  else
  {
    m_K.Destroy();
  }

  if ( bHasVertexColors ) 
  {
    m_C.Reserve(vcount);
    for (mi = 0; mi < mesh_count; mi++ )
    {
      m = meshes[mi];
      if ( 0 == m )
        continue;
      m_C.Append(m->m_C.Count(), m->m_C.Array());
    }
  }
  else 
  {
    m_C.Destroy();
  }

  if ( 0 !=  m_mesh_parameters )
  {
    for (mi = 0; mi < mesh_count; mi++ )
    {
      m = meshes[mi];
      if ( 0 == m )
        continue;
      if ( 0 == m->m_mesh_parameters || *m_mesh_parameters != *m->m_mesh_parameters )
      {
        delete m_mesh_parameters;
        m_mesh_parameters = 0;
        break;
      }
    }
  }

  for ( j = 0; j < 4; j++ ) 
  {
    if ( m_kstat[j] ) 
    {
      // will be recomputed if required
      delete m_kstat[j];
      m_kstat[j] = 0;
    }
  }

  SetClosed(-99);
  SetSolidOrientation(-99);
  InvalidateBoundingBoxes();
}

void ON_Mesh::Append( const ON_Mesh& m )
{ 
  const ON_Mesh* meshes[1];
  meshes[0] = &m;
  Append(1,meshes);
}

ON_MeshParameters::ON_MeshParameters()
{
  Default();
}

ON_MeshParameters::~ON_MeshParameters()
{
}

double ON_MeshParameters::MinEdgeLength( double max_edge_length, double tolerance )
{
  // The 1.0e-4 is a guess.  1.0e-12 was too small to help with objects
  // like the one in 67885.
  double min_edge_length = 1.0e-4;
  if ( max_edge_length > 0.0 && min_edge_length > 1.0e-3*max_edge_length )
    min_edge_length =  1.0e-3*max_edge_length;
  if ( tolerance > 0.0 && min_edge_length > 1.0e-2*tolerance )
    min_edge_length =  1.0e-2*tolerance;
  return min_edge_length;
}

double ON_MeshParameters::Tolerance( double density, double actual_size )
{
  // min_rel_tol creates the most facets
  //const double min_rel_tol = 5.0e-5;

  //max rel tol creates the fewest facets
  //const double max_rel_tol = 0.1;
  //m_relative_tolerance = 0.0;
  //if ( density <= 0.0 )
  //  m_relative_tolerance = max_rel_tol;
  //else if ( density >= 1.0 )
  //  m_relative_tolerance = min_rel_tol;
  //else
  //{
  //  ON_Interval e(log10(max_rel_tol),log10(min_rel_tol));
  //  m_relative_tolerance = pow(10.0,e.ParameterAt(density));
  //}

  double tol = 0.0;
  double x, e;
  if ( ON_IsValid(density) && ON_IsValid(actual_size)
       && density > 0.0 && actual_size > 0.0 )
  {
    if ( density > 1.0 )
      density = 1.0;

    //e = (density*(12.0 + density*(2.0*density - 9.0)));
    //e = (1.0 + density*(8.0 - 4.0*density));
    //e = 1.0 + density*4.0;
    //x = 5.0*pow(10.0,-e);

    e = (density < 0.5) 
      ? 1.0 + density*(6.0 - 4.0*density) // 1.0 + 4.0*density
      : 2.0 + 2.0*density;
    x = pow(10.0,-e);

    tol = actual_size*x;
  }
  return tol;
}

static ON_MeshParameters FastRenderMeshParameters()
{
  // If you change these, put your name, the date, and the reasons for
  // the change in this comment so we can keep track of what we are
  // trying to accomplish;
  ON_MeshParameters mp;

  // Added 27 April 2006 for the Meshkateers
  //   Attempting to make jagged and faster render meshes a little
  //   more dense.
  //
  // Turn off everything ...
  mp.m_bComputeCurvature = false;
  mp.m_tolerance = 0.0;
  mp.m_bJaggedSeams  = false;
  mp.m_max_edge_length = 0.0;
  mp.m_grid_aspect_ratio = 0.0;
  mp.m_grid_max_count = 0;
  mp.m_grid_angle = 0.0;
  mp.m_grid_amplification = 0.0;
  mp.m_refine_angle = 0.0;

  // ... except ...
  // The m_relative_tolerance setting must be set so that
  // 0.0005 = ON_MeshParameters::Tolerance(m_relative_tolerance,1.0).
  mp.m_relative_tolerance = 0.65;
  //double x = Tolerance(m_relative_tolerance,1.0);

  mp.m_grid_min_count     = 16;
  mp.m_min_edge_length    = 0.0001;
  mp.m_bRefine            = true;
  mp.m_bSimplePlanes      = true;

  mp.m_texture_range = 2; // Don't change this without speaking to Dale Lear

  //{
  //  // 16 July, 2002 - copied V2 hard coded "jagged and faster" render mesh settings
  //  //
  //  // Settings used in V2, V3 and early V4 beta
  //  mp.m_refine_angle       = 20.0*ON_PI/180.0;
  //  mp.m_grid_angle         = 20.0*ON_PI/180.0;
  //  mp.m_grid_aspect_ratio  = 0.0;
  //  mp.m_min_edge_length    = 0.0001;
  //  mp.m_max_edge_length    = 0.0;
  //  mp.m_tolerance          = 0.0;
  //  mp.m_grid_min_count     = 16;
  //  mp.m_bRefine            = 1;
  //  mp.m_bJaggedSeams       = 0;
  //  mp.m_bSimplePlanes      = 0;
  //}

  return mp;
}

static ON_MeshParameters QualityRenderMeshParameters()
{
  // If you change these, put your name, the date, and the reasons for
  // the change in this comment so we can keep track of what we are
  // trying to accomplish;
  ON_MeshParameters mp;

  // Added 27 April 2006 for the Meshkateers
  //   Attempting to make smooth and slower render meshing a little
  //   faster.
  //
  // Turn off everything ...
  mp.m_bComputeCurvature = false;
  mp.m_tolerance = 0.0;
  mp.m_bJaggedSeams  = false;
  mp.m_max_edge_length = 0.0;
  mp.m_grid_aspect_ratio = 0.0;
  mp.m_grid_max_count = 0;
  mp.m_grid_angle = 0.0;
  mp.m_grid_amplification = 0.0;

  // ... except ...
  // The m_relative_tolerance setting must be set so that
  // 0.00025 = ON_MeshParameters::Tolerance(m_relative_tolerance,1.0).
  mp.m_relative_tolerance = 0.8;
  //double x = Tolerance(m_relative_tolerance,1.0);

  mp.m_grid_min_count     = 16;
  mp.m_min_edge_length    = 0.0001;
  mp.m_bRefine            = true;
  mp.m_bSimplePlanes      = true;
  mp.m_refine_angle       = 20.0*ON_PI/180.0;

  mp.m_texture_range = 2; // Don't change this without speaking to Dale Lear


  //mp.m_refine_angle       = 15.0*ON_PI/180.0;
  //mp.m_grid_angle         = 15.0*ON_PI/180.0;
  //mp.m_grid_aspect_ratio  = 6.0;
  //mp.m_min_edge_length    = 0.0001;
  //mp.m_max_edge_length    = 0.0;
  //mp.m_tolerance          = 0.0;
  //mp.m_grid_min_count     = 16;
  //mp.m_bRefine            = 1;
  //mp.m_bJaggedSeams       = 0;
  //mp.m_bSimplePlanes      = 0;

  return mp;
}

const ON_MeshParameters ON_MeshParameters::FastRenderMesh(FastRenderMeshParameters());

const ON_MeshParameters ON_MeshParameters::QualityRenderMesh(QualityRenderMeshParameters());

void ON_MeshParameters::JaggedAndFasterMeshParameters()
{
  *this = ON_MeshParameters::FastRenderMesh;
}

void ON_MeshParameters::SmoothAndSlowerMeshParameters()
{
  *this = ON_MeshParameters::QualityRenderMesh;
}

void ON_MeshParameters::DefaultAnalysisMeshParameters()
{
  Default();

  // 7 July 2006 Dale Lear
  //    I added this line for RR 10330
  Set( 0.5, m_min_edge_length );

  m_texture_range = 1; // THIS IS REQUIRED - DO NOT CHANGE IT

  // Meshkateers 
  //   Add your stuff below this line.
  //   Do not change m_texture_range.
}

bool ON_MeshParameters::operator==(const ON_MeshParameters& m2) const
{
  return (Compare(m2)==0) ? true : false;
}

bool ON_MeshParameters::operator!=(const ON_MeshParameters& m2) const
{
  return (Compare(m2)) ? true : false;
}

bool ON_MeshParameters::operator==(const ON_Mesh& mesh) const
{
  const ON_MeshParameters* mp1 = mesh.MeshParameters();
  return mp1 ? (*this == *mp1) : false;
}

bool ON_MeshParameters::operator!=(const ON_Mesh& mesh) const
{
  const ON_MeshParameters* mp1 = mesh.MeshParameters();
  return mp1 ? (*this != *mp1) : true;
}

void ON_MeshParameters::Dump( ON_TextLog& text_log ) const
{
  text_log.Print("Gridding:\n");
  text_log.PushIndent();
  text_log.Print("Min grid count = %d\n",m_grid_min_count);
  text_log.Print("Max grid count = %d\n",m_grid_max_count);
  text_log.Print("Gridding angle = %g radians (%g degrees)\n",m_grid_angle,180.0*m_grid_angle/ON_PI);
  text_log.Print("Aspect ratio = %g\n",m_grid_aspect_ratio);
  text_log.Print("Amplification = %g\n",m_grid_amplification);
  text_log.PopIndent();

  text_log.Print("Refining:\n");
  text_log.PushIndent();
  text_log.Print("Refine = %s\n",m_bRefine?"true":"false");
  text_log.Print("Refine angle = %g radians (%g degrees)\n",m_refine_angle,180.0*m_refine_angle/ON_PI);
  text_log.PopIndent();

  text_log.Print("Metrics:\n");
  text_log.PushIndent();
  text_log.Print("Density = %g (relative tolerance = %g)\n",m_relative_tolerance,ON_MeshParameters::Tolerance(m_relative_tolerance,1.0));
  text_log.Print("Minimum tolerance = %g\n",m_min_tolerance);
  text_log.Print("Tolerance = %g\n",m_tolerance);
  text_log.Print("Min edge length = %g\n",m_min_edge_length);
  text_log.Print("Max edge length = %g\n",m_max_edge_length);
  text_log.PopIndent();

  text_log.Print("Misceleanous:\n");
  text_log.PushIndent();
  text_log.Print("Face type = %d\n",m_face_type );
  text_log.Print("Compute curvature = %s\n",m_bComputeCurvature?"true":"false");
  text_log.Print("Texture range = %d\n",m_texture_range);
  text_log.Print("Simple planes = %s\n",m_bSimplePlanes?"true":"false");
  text_log.Print("Jagged Seams = %s\n",m_bJaggedSeams?"true":"false");
  text_log.Print("Double Precision = %s\n",m_bDoublePrecision?"true":"false");
  text_log.Print("Custom settings = %s\n",m_bCustomSettings?"true":"false");
  text_log.PopIndent();
}

void ON_MeshParameters::Default()
{
  memset(this,0,sizeof(*this));

  m_bCustomSettings = false;
  m_bComputeCurvature = false;
  m_bSimplePlanes = false;
  m_bRefine = true;
  m_bJaggedSeams = false;
  m_bDoublePrecision = false;
  m_bCustomSettingsEnabled = true;
  m_mesher = 0;
  m_texture_range = 2; // packed normalized textures
  m_reserved2 = 0;
  m_tolerance = 0.0;
  m_relative_tolerance = 0.0;
  m_min_tolerance = 0.0;
  m_min_edge_length = 0.0001;
  m_max_edge_length = 0.0;
  m_grid_aspect_ratio = 6.0;
  m_grid_min_count = 0;
  m_grid_max_count = 0;
  m_grid_angle = 20.0*ON_PI/180.0;
  m_grid_amplification = 1.0;
  m_refine_angle = 20.0*ON_PI/180.0;
  m_face_type = 0;
  m_reserved3 = 0;
}

void ON_MeshParameters::Set( double density, double min_edge_length )
{
  bool bRelTolTest = true;

  Default();

  // These 4 settings should not be changed
  m_bComputeCurvature = false;
  m_min_edge_length = min_edge_length;
  m_texture_range = 0;
  m_tolerance = 0.0;

  if ( bRelTolTest )
  {
    // Added 27 April 2005
    m_relative_tolerance = density;

    // The other meshing parameters are disabled.
    //
    //   Dale Lear's remark:
    //     I think it is a mistake to leave m_grid_aspect_ratio = 0
    //     at all settings.  This will result in long skinny triangles
    //     in areas where the principal curvatures are dramatically
    //     different.  
    //
    m_bRefine = (density < 0.65);
    m_bSimplePlanes = (density <= 0.0);
    m_bJaggedSeams  = false;
    m_max_edge_length = 0.0;
    m_grid_aspect_ratio = 0.0;
    m_grid_min_count = 0;
    m_grid_max_count = 0;
    m_grid_angle = 0.0;
    m_grid_amplification = 0.0;
    m_refine_angle = 0.0;
  }
  else
  {
    // Used in V3 and prior to 27 April 2005
    double t0, t1;

    m_bRefine = true;
    m_bSimplePlanes = false;
    m_bJaggedSeams  = false;
    m_max_edge_length = 0.0;
    m_grid_aspect_ratio = 0.0;
    m_grid_min_count = 16;
    m_grid_max_count = 0;
    m_grid_angle = 20.0*ON_PI/180.0;
    m_grid_amplification = 1.0;
    m_refine_angle = 20.0*ON_PI/180.0;
 
    if ( density <= 0.0) 
    {
      m_bSimplePlanes = true;
      m_bRefine       = false;

      m_grid_min_count     = 0;
      m_grid_aspect_ratio  = 0.0;
      m_grid_angle         = 0.0;
      m_grid_amplification = 1.0;

      m_refine_angle       = m_grid_angle;
    }
    else if ( density < 0.5)
    {
      t1 = 2.0*density;
      t0 = 1.0-t1;
      
      m_bRefine = density < 0.10 ? false : true;

      m_grid_min_count = 0;
      m_grid_aspect_ratio  = 6.0;
      m_grid_angle         = 20.0*ON_PI/180.0;
      m_grid_amplification = (t1 > 0.0 ) ? t1 : 1.0;

      m_refine_angle = (t0*65.0 + t1*20.0)*ON_PI/180.0;
    }
    else if ( density == 0.5 ) 
    {
      m_bRefine       = true;

      m_grid_min_count     = 0;
      m_grid_aspect_ratio  = 6.0;
      m_grid_angle         = 20.0*ON_PI/180.0;
      m_grid_amplification = 1.0;

      m_refine_angle        = m_grid_angle;
    }
    else
    {
      t1 = 2.0*(density - 0.5);
      if ( t1 > 1.0 )
        t1 = 1.0;
      t0 = 1.0-t1;
      
      m_bRefine = true;

      m_grid_min_count     = 0;
      m_grid_aspect_ratio  = t0*6.0 + t1;
      m_grid_angle         = (t0*20.0 + t1*5.0)*ON_PI/180.0;
      m_grid_amplification = 1.0 + t1;

      m_refine_angle       = m_grid_angle;
    }
  }
}


int ON_MeshParameters::Compare( const ON_MeshParameters& src ) const
{
  // Discuss any changes with Dale Lear.
  if ( !m_bCustomSettings && src.m_bCustomSettings )
    return -1;
  if ( m_bCustomSettings && !src.m_bCustomSettings )
    return 1;
  if ( m_texture_range < src.m_texture_range )
    return -1;
  if ( m_texture_range > src.m_texture_range )
    return 1;
  return CompareGeometrySettings(src);
}

static int ON_MeshParameters_CompareDouble(double t0, double t1, double default_value)
{
  if ( !ON_IsValid(t0) || t0 <= 0.0 )
    t0 = default_value;
  if ( !ON_IsValid(t1) || t1 <= 0.0 )
    t1 = default_value;
  if ( t0 < t1 )
    return 1;
  if ( t1 < t0 )
    return -1;
  return 0;
}

static int ON_MeshParameters_CompareInt(int i0, int i1)
{
  if ( i0 <= 0 )
    i0 = 0;
  if ( i1 <= 0 )
    i1 = 0;
  return i1-i0;
}

static int ON_MeshParameters_CompareBool(bool b0, bool b1)
{
  const int i0 = b0 ? 1 : 0; 
  const int i1 = b1 ? 1 : 0;
  return i1-i0;
}

int ON_MeshParameters::CompareGeometrySettings( const ON_MeshParameters& src ) const
{
  int rc;

  // Discuss any changes with Dale Lear.
  rc = ON_MeshParameters_CompareBool(m_bSimplePlanes,src.m_bSimplePlanes);
  if (rc)
    return rc;
  rc = ON_MeshParameters_CompareBool(m_bRefine,src.m_bRefine);
  if (rc)
    return rc;
  rc = ON_MeshParameters_CompareBool(m_bJaggedSeams,src.m_bJaggedSeams);
  if (rc)
    return rc;
  if ( m_mesher < src.m_mesher )
    return -1;
  if ( m_mesher > src.m_mesher )
    return 1;

  rc = ON_MeshParameters_CompareDouble(m_tolerance,src.m_tolerance,0.0);
  if (rc)
    return rc;

  rc = ON_MeshParameters_CompareDouble(m_relative_tolerance,src.m_relative_tolerance,0.0);
  if (rc)
    return rc;

  // DO NOT COMPARE m_min_tolerance - it is a runtime lower bound clamp.
  //                If it is included here, Rhino will remesh everytime
  //                model tolerance changes.

  rc = ON_MeshParameters_CompareDouble(m_min_edge_length,src.m_min_edge_length,0.0);
  if (rc)
    return rc;

  rc = ON_MeshParameters_CompareDouble(m_max_edge_length,src.m_max_edge_length,0.0);
  if (rc)
    return rc;

  rc = ON_MeshParameters_CompareDouble(m_grid_aspect_ratio,src.m_grid_aspect_ratio,0.0);
  if (rc)
    return rc;

  rc = ON_MeshParameters_CompareInt(m_grid_min_count,src.m_grid_min_count);
  if (rc)
    return rc;

  rc = ON_MeshParameters_CompareInt(m_grid_max_count,src.m_grid_max_count);
  if (rc)
    return rc;

  rc = ON_MeshParameters_CompareDouble(m_grid_angle,src.m_grid_angle,ON_PI);
  if (rc)
    return rc;

  rc = ON_MeshParameters_CompareDouble(m_refine_angle,src.m_refine_angle,0.0);
  if (rc)
    return rc;

  rc = ON_MeshParameters_CompareDouble(m_grid_amplification,src.m_grid_amplification,1.0);
  if (rc)
    return rc;

  if ( m_face_type < src.m_face_type )
    return -1;
  if ( m_face_type > src.m_face_type )
    return 1;

  return 0;
}

ON__UINT32 ON_MeshParameters::DataCRC(ON__UINT32 current_remainder) const
{
  ON__UINT32 crc = ON_CRC32(current_remainder,sizeof(m_bComputeCurvature),&m_bComputeCurvature);
  crc = ON_CRC32(crc,sizeof(m_bSimplePlanes),&m_bSimplePlanes);
  crc = ON_CRC32(crc,sizeof(m_bRefine),&m_bRefine);
  crc = ON_CRC32(crc,sizeof(m_bJaggedSeams),&m_bJaggedSeams);
  crc = ON_CRC32(crc,sizeof(m_tolerance),&m_tolerance);
  crc = ON_CRC32(crc,sizeof(m_min_edge_length),&m_min_edge_length);
  crc = ON_CRC32(crc,sizeof(m_max_edge_length),&m_max_edge_length);
  crc = ON_CRC32(crc,sizeof(m_grid_aspect_ratio),&m_grid_aspect_ratio);
  crc = ON_CRC32(crc,sizeof(m_grid_min_count),&m_grid_min_count);
  crc = ON_CRC32(crc,sizeof(m_grid_max_count),&m_grid_max_count);
  crc = ON_CRC32(crc,sizeof(m_grid_angle),&m_grid_angle);
  crc = ON_CRC32(crc,sizeof(m_grid_amplification),&m_grid_amplification);
  crc = ON_CRC32(crc,sizeof(m_refine_angle),&m_refine_angle);
  crc = ON_CRC32(crc,sizeof(m_face_type),&m_face_type);
  crc = ON_CRC32(crc,sizeof(m_texture_range),&m_texture_range);
  crc = ON_CRC32(crc,sizeof(m_bCustomSettings),&m_bCustomSettings);
  crc = ON_CRC32(crc,sizeof(m_relative_tolerance),&m_relative_tolerance);
  crc = ON_CRC32(crc,sizeof(m_mesher),&m_mesher);
  return crc;
}

bool ON_MeshParameters::Write( ON_BinaryArchive& file ) const
{
  bool rc = file.Write3dmChunkVersion(1,4);
  if (rc) {
    if (rc) rc = file.WriteInt(m_bComputeCurvature);
    if (rc) rc = file.WriteInt(m_bSimplePlanes);
    if (rc) rc = file.WriteInt(m_bRefine);
    if (rc) rc = file.WriteInt(m_bJaggedSeams);
    if (rc) rc = file.WriteInt(0); // obsolete m_bWeld field
    if (rc) rc = file.WriteDouble(m_tolerance);
    if (rc) rc = file.WriteDouble(m_min_edge_length);
    if (rc) rc = file.WriteDouble(m_max_edge_length);
    if (rc) rc = file.WriteDouble(m_grid_aspect_ratio);
    if (rc) rc = file.WriteInt(m_grid_min_count);
    if (rc) rc = file.WriteInt(m_grid_max_count);
    if (rc) rc = file.WriteDouble(m_grid_angle);
    if (rc) rc = file.WriteDouble(m_grid_amplification);
    if (rc) rc = file.WriteDouble(m_refine_angle);
    if (rc) rc = file.WriteDouble(5.0*ON_PI/180.0); // obsolete m_combine_angle field
    int mft = m_face_type;
    if ( mft < 0 || mft > 2 ) 
    {
      ON_ERROR("ON_MeshParameters::Read() - m_face_type out of bounds.");
      mft = 0;
    }
    if (rc) rc = file.WriteInt(mft);

    // added for chunk version 1.1
    if (rc) rc = file.WriteInt( m_texture_range );

    // added for chunk version 1.2 - 14 October 2005
    if (rc) rc = file.WriteBool( m_bCustomSettings );
    if (rc) rc = file.WriteDouble( m_relative_tolerance );
    // DO NOT SAVE m_min_tolerance - yet ??

    // added for chunk version 1.3 - 20 February 2006
    if (rc) rc = file.WriteChar(m_mesher);

    // added for chunk version 1.4 - 3 March 2011
    if (rc) rc = file.WriteBool( m_bCustomSettingsEnabled );
  }
  return rc;
}

bool ON_MeshParameters::Read( ON_BinaryArchive& file )
{
  Default();
  int major_version = 0;
  int minor_version = 0;
  bool rc = file.Read3dmChunkVersion(&major_version,&minor_version);
  if ( rc && major_version == 1 ) 
  {
    int i;

    i = m_bComputeCurvature;
    if (rc) rc = file.ReadInt(&i);
    m_bComputeCurvature = i?true:false;

    i = m_bSimplePlanes;
    if (rc) rc = file.ReadInt(&i);
    m_bSimplePlanes = i?true:false;

    i = m_bRefine;
    if (rc) rc = file.ReadInt(&i);
    m_bRefine = i?true:false;

    i = m_bJaggedSeams;
    if (rc) rc = file.ReadInt(&i);
    m_bJaggedSeams = i?true:false;

    int obsolete_m_bWeld;
    if (rc) rc = file.ReadInt(&obsolete_m_bWeld);

    if (rc) rc = file.ReadDouble(&m_tolerance);
    if (rc) rc = file.ReadDouble(&m_min_edge_length);
    if (rc) rc = file.ReadDouble(&m_max_edge_length);
    if (rc) rc = file.ReadDouble(&m_grid_aspect_ratio);
    if (rc) rc = file.ReadInt(&m_grid_min_count);
    if (rc) rc = file.ReadInt(&m_grid_max_count);
    if (rc) rc = file.ReadDouble(&m_grid_angle);
    if (rc) rc = file.ReadDouble(&m_grid_amplification);
    if (rc) rc = file.ReadDouble(&m_refine_angle);
    double obsolete_m_combine_angle;
    if (rc) rc = file.ReadDouble(&obsolete_m_combine_angle);
    if (rc) rc = file.ReadInt(&m_face_type);
    if ( m_face_type < 0 || m_face_type > 2 ) 
    {
      ON_ERROR("ON_MeshParameters::Read() - m_face_type out of bounds.");
      m_face_type = 0;
    }

    if ( rc && minor_version >= 1 ) 
    {
      rc = file.ReadInt( &m_texture_range );
      if ( rc && minor_version >= 2 )
      {
        rc = file.ReadBool(&m_bCustomSettings);
        if (rc) rc = file.ReadDouble(&m_relative_tolerance);
        if ( rc && minor_version >= 3 )
        {
          rc = file.ReadChar(&m_mesher);
          if ( rc && minor_version >= 4 )
          {
            rc = file.ReadBool(&m_bCustomSettingsEnabled);
          }
        }
      }
    }
  }
  return rc;
}



ON_MeshCurvatureStats::ON_MeshCurvatureStats()
{
  Destroy(); // initializes defaults
}

ON_MeshCurvatureStats::~ON_MeshCurvatureStats()
{}

void ON_MeshCurvatureStats::Destroy()
{
  m_style = ON::unknown_curvature_style;
  m_infinity = 0.0;
  m_count_infinite = 0;
  m_count = 0;
  m_mode = 0.0;
  m_average = 0.0;
  m_adev = 0.0;
  m_range.Set(0.0,0.0);
}

void ON_MeshCurvatureStats::EmergencyDestroy()
{
  Destroy(); // - no memory is freed so Destroy() will work
}

ON_MeshCurvatureStats::ON_MeshCurvatureStats(const ON_MeshCurvatureStats& src)
{
  *this = src;
}

ON_MeshCurvatureStats& ON_MeshCurvatureStats::operator=(const ON_MeshCurvatureStats& src)
{
  if ( this != &src ) {
    m_style          = src.m_style;
    m_infinity       = src.m_infinity;
    m_count_infinite = src.m_count_infinite;
    m_count          = src.m_count;
    m_mode           = src.m_mode;
    m_average        = src.m_average;
    m_adev           = src.m_adev;
    m_range          = src.m_range;
  }
  return *this;
}

bool ON_MeshCurvatureStats::Write( ON_BinaryArchive& file ) const
{
  int i;
  bool rc = file.Write3dmChunkVersion(1,1);
  if (rc) {
    i = m_style;
    if (rc) rc = file.WriteInt(i);
    if (rc) rc = file.WriteDouble(m_infinity);
    if (rc) rc = file.WriteInt(m_count_infinite);
    if (rc) rc = file.WriteInt(m_count);
    if (rc) rc = file.WriteDouble(m_mode);
    if (rc) rc = file.WriteDouble(m_average);
    if (rc) rc = file.WriteDouble(m_adev);
    if (rc) rc = file.WriteInterval(m_range);
  }
  return rc;
}


bool ON_MeshCurvatureStats::Read( ON_BinaryArchive& file )
{
  int major_version = 0;
  int minor_version = 0;
  Destroy();
  bool rc = file.Read3dmChunkVersion(&major_version,&minor_version);
  if (rc && major_version == 1) {
    int i=0;
    if (rc) rc = file.ReadInt(&i);
    if (rc) m_style = ON::CurvatureStyle(i);
    if (rc) rc = file.ReadDouble(&m_infinity);
    if (rc) rc = file.ReadInt(&m_count_infinite);
    if (rc) rc = file.ReadInt(&m_count);
    if (rc) rc = file.ReadDouble(&m_mode);
    if (rc) rc = file.ReadDouble(&m_average);
    if (rc) rc = file.ReadDouble(&m_adev);
    if (rc) rc = file.ReadInterval(m_range);
  }
  return rc;
}

bool ON_MeshCurvatureStats::Set( ON::curvature_style kappa_style,
                                 int Kcount,
                                 const ON_SurfaceCurvature* K,
                                 const ON_3fVector* N, // needed for normal sectional curvatures
                                 double infinity
                                 )
{
  bool rc = (Kcount > 0 && K != NULL);

  Destroy();

  if (rc) {
    ON_Workspace ws;
    //ON_3dVector tangent;
    double k;
    double* kappa = ws.GetDoubleMemory(Kcount);
    int i;

    switch( kappa_style ) {
    case ON::gaussian_curvature:
      m_style = kappa_style;
      m_infinity = ( infinity > 0.0 ) ? infinity : 1.0e20;
      break;
    case ON::mean_curvature: // unsigned mean
      m_style = kappa_style;
      m_infinity = ( infinity > 0.0 ) ? infinity : 1.0e10;
      break;
    case ON::min_curvature: // minimum unsigned radius of curvature
      m_style = kappa_style;
      m_infinity = ( infinity > 0.0 ) ? infinity : 1.0e10;
      break;
    case ON::max_curvature: // maximum unsigned radius of curvature
      m_style = kappa_style;
      m_infinity = ( infinity > 0.0 ) ? infinity : 1.0e10;
      break;
    //case ON::section_curvature_x:
    //  if ( !N )
    //    kappa_style = ON::unknown_curvature_style;
    //  m_style = kappa_style;
    //  m_infinity = ( infinity > 0.0 ) ? infinity : 1.0e10;
    //  break;
    //case ON::section_curvature_y:
    //  if ( !N )
    //    kappa_style = ON::unknown_curvature_style;
    //  m_style = kappa_style;
    //  m_infinity = ( infinity > 0.0 ) ? infinity : 1.0e10;
    //  break;
    //case ON::section_curvature_z:
    //  if ( !N )
    //    kappa_style = ON::unknown_curvature_style;
    //  m_style = kappa_style;
    //  m_infinity = ( infinity > 0.0 ) ? infinity : 1.0e10;
    //  break;
    default:
      rc = false;
      break;
    }

    for ( i = 0; i < Kcount; i++ ) {
      switch( kappa_style ) {
      case ON::gaussian_curvature:
        k = K[i].GaussianCurvature();
        break;
      case ON::mean_curvature: // unsigned mean
        k = fabs(K[i].MeanCurvature());
        break;
      case ON::min_curvature: // minimum unsigned radius of curvature
        k = fabs(K[i].MinimumRadius());
        break;
      case ON::max_curvature: // maximum unsigned radius of curvature
        k = fabs(K[i].MaximumRadius());
        break;
      //case ON::section_curvature_x:
      //  tangent.x = 0.0; tangent.y = -N[i].z; tangent.z = N[i].y;
      //  if ( fabs(tangent.y) <= ON_SQRT_EPSILON && fabs(tangent.z) <= ON_SQRT_EPSILON )
      //    tangent.Zero();
      //  else
      //    tangent.Unitize();
      //  k = fabs(K[i].NormalCurvature(tangent));
      //  break;
      //case ON::section_curvature_y:
      //  tangent.x = N[i].z; tangent.y = 0.0; tangent.z = -N[i].x;
      //  if ( fabs(tangent.x) <= ON_SQRT_EPSILON && fabs(tangent.z) <= ON_SQRT_EPSILON )
      //    tangent.Zero();
      //  else
      //    tangent.Unitize();
      //  k = fabs(K[i].NormalCurvature(tangent));
      //  break;
      //case ON::section_curvature_z:
      //  tangent.x = -N[i].y; tangent.y = N[i].x; tangent.z = 0.0;
      //  if ( fabs(tangent.x) <= ON_SQRT_EPSILON && fabs(tangent.y) <= ON_SQRT_EPSILON )
      //    tangent.Zero();
      //  else
      //    tangent.Unitize();
      //  k = fabs(K[i].NormalCurvature(tangent));
      //  break;
      default:
        k=0.0;
        break;
      }
      if ( fabs(k) >= m_infinity ) {
        m_count_infinite++;
        continue;
      }
      if ( m_count ) {
        if ( k < m_range.m_t[0] )
          m_range.m_t[0] = k;
        else if ( k > m_range.m_t[1] )
          m_range.m_t[1] = k;
      }
      else {
        m_range.m_t[0] = m_range.m_t[1] = k;
      }
      kappa[m_count++] = k;
    }


    if ( m_count == 0 )
      rc = false;
    else {
      // sum curvatures
      ON_SortDoubleArray( ON::quick_sort, kappa, m_count );

      // mode
      m_mode = kappa[m_count/2];
      if ( 0 == (m_count % 2) ) {
        m_mode += kappa[(m_count/2)-1];
        m_mode *= 0.5;
      }

      // average
      for ( i = 0; i < m_count; i++ ) {
        m_average += kappa[i];
      }
      m_average = m_average/m_count;
      
      // average deviation
      for ( i = 0; i < m_count; i++ ) {
        m_adev += fabs(kappa[i] - m_average);
      }
      m_adev = m_adev/m_count;
    }  
  }
  
  return rc;  
}

struct EDGEINFO
{
  int fi[2]; // m_F[] triangles on either side of the edge
  int vi[4]; // potential m_V[] quad indices
  int flag; // 0 = available, 
            // 1 = side of quad, 
            // 2 = bndry or nonmanifold edge,
            // 3 = edge crease angle > angle_tol_radians
            // 4 = edge is not longest side of triangle
            // 5 = edge length is zero
            // 6 = edge would be a boundary if mesh were exploded
            // 16 = edge will be removed to make a quad
  double length;
};

bool ON_Mesh::ConvertTrianglesToQuads( 
              double angle_tol_radians,
              double min_diagonal_length_ratio
              )
{
  ON_Workspace ws;

  double d;

  int i, ii, jj;
  int diagonal_count;
  const int* f0vi;
  const int* f1vi;
  const int* fei;

  diagonal_count = 0;

  if ( angle_tol_radians < 0.0 || !ON_IsValid(angle_tol_radians) )
  {
    // 2.5 degrees
    angle_tol_radians = 0.043633231299858239423092269212215;
  }
  else if ( angle_tol_radians < ON_ZERO_TOLERANCE )
  {
    angle_tol_radians = ON_ZERO_TOLERANCE;
  }

  angle_tol_radians = cos(angle_tol_radians);
  if ( angle_tol_radians < 0.5 )
    angle_tol_radians = 0.5;
  else if ( angle_tol_radians > 1.0-ON_SQRT_EPSILON )
    angle_tol_radians = 1.0-ON_SQRT_EPSILON;

  const ON_MeshTopology& top = Topology();

  if ( !HasFaceNormals() )
    ComputeFaceNormals();

  if ( min_diagonal_length_ratio < ON_ZERO_TOLERANCE )
    min_diagonal_length_ratio = ON_ZERO_TOLERANCE;

  double max_diagonal_length_ratio = 1.0/min_diagonal_length_ratio;

  if( min_diagonal_length_ratio > max_diagonal_length_ratio )
  {
    d = min_diagonal_length_ratio;
    min_diagonal_length_ratio = max_diagonal_length_ratio;
    max_diagonal_length_ratio = d;
  }

  //double rel_tol = ON_SQRT_EPSILON;
  double rel_tol = 8.0*ON_SQRT_EPSILON; // to fix RR 51543
  if ( min_diagonal_length_ratio > 1.0-rel_tol )
    min_diagonal_length_ratio = 1.0-rel_tol;
  if ( max_diagonal_length_ratio < 1.0+rel_tol )
    max_diagonal_length_ratio = 1.0+rel_tol;


  const int face_count = m_F.Count();
  int* face_flag = ws.GetIntMemory(face_count);  
  for ( i = 0; i < face_count; i++ )
  {
    f0vi = m_F[i].vi;
    face_flag[i] = ( f0vi[2] == f0vi[3] ) ? 0 : 1;
  }

  const int edge_count = top.m_tope.Count();
  struct EDGEINFO* EI = (struct EDGEINFO*)ws.GetMemory(edge_count*sizeof(*EI));
  for ( i = 0; i < edge_count; i++ )
  {
    struct EDGEINFO& ei = EI[i];
    const ON_MeshTopologyEdge& tope = top.m_tope[i];
    ei.flag = 0;
    ei.vi[0] = top.m_topv[tope.m_topvi[0]].m_vi[0];
    ei.vi[2] = top.m_topv[tope.m_topvi[1]].m_vi[0];
    ei.length = m_V[ei.vi[0]].DistanceTo(m_V[ei.vi[2]]);
    if ( ei.length <= 0.0 || !ON_IsValid(ei.length) )
    {
      ei.flag = 5;
    }
    else if ( tope.m_topf_count != 2 )
    {
      ei.flag = 2;
    }
    else
    {
      ei.fi[0] = tope.m_topfi[0];
      ei.fi[1] = tope.m_topfi[1];
      if (face_flag[ei.fi[0]] || face_flag[ei.fi[1]] )
      {
        ei.flag = 1;
      }
      else if ( m_FN[ei.fi[0]] * m_FN[ei.fi[1]] < angle_tol_radians )
      {
        ei.flag = 3;
      }
      else 
      {
        f0vi = m_F[ei.fi[0]].vi;
        f1vi = m_F[ei.fi[1]].vi;
        ei.flag = 6;
        for ( ii = 0; ii < 3 && ei.flag; ii++ )
        {
          for (jj = 0; jj < 3; jj++)
          {
            if (    f0vi[ii] == f1vi[jj] 
                 && f0vi[(ii+1)%3] == f1vi[(jj+2)%3]
                 && f0vi[(ii+2)%3] != f1vi[(jj+1)%3] )
            {
              if ( ei.fi[0] > ei.fi[1] )
              {
                jj = ei.fi[0]; ei.fi[0] = ei.fi[1]; ei.fi[1] = jj;
              }
              ei.vi[0] = f0vi[ii];
              ei.vi[1] = f1vi[(jj+1)%3];
              ei.vi[2] = f0vi[(ii+1)%3];
              ei.vi[3] = f0vi[(ii+2)%3];
              ei.flag = 0;
              break;
            }
          }
        }
      }
    }
  }

  for ( i = 0; i < edge_count; i++ )
  {
    struct EDGEINFO& ei = EI[i];
    if ( ei.flag )
      continue;

    ei.flag = 16;

    // It is CRITICAL that the length compare use >=.
    // Otherwise tesselations of equailateral triangles
    // will not work right in this fuction.
    fei = top.m_topf[ei.fi[0]].m_topei;
    if (    ( i != fei[0] && EI[fei[0]].length >= ei.length )
         || ( i != fei[1] && EI[fei[1]].length >= ei.length )
         || ( i != fei[2] && EI[fei[2]].length >= ei.length )
         )
    {
      // diagonal is not strictly longest in this triangle
      continue;
    }

    // It is CRITICAL that the length compare use >=.
    // Otherwise tesselations of equailateral triangles
    // will not work right in this fuction.
    fei = top.m_topf[ei.fi[1]].m_topei;
    if (    ( i != fei[0] && EI[fei[0]].length >= ei.length )
         || ( i != fei[1] && EI[fei[1]].length >= ei.length )
         || ( i != fei[2] && EI[fei[2]].length >= ei.length )
         )
    {
      // diagonal is not strictly longest in this triangle
      continue;
    }

    d = m_V[ei.vi[1]].DistanceTo(m_V[ei.vi[3]]);
    d /= ei.length;
    if ( d < min_diagonal_length_ratio || d > max_diagonal_length_ratio )
    {
      // quad wouldn't be square enough
      continue;
    }

    ei.flag = 0;

    diagonal_count++;
  }

  if ( diagonal_count > 0 )
  {
    DestroyTree();
    DestroyPartition();
    m_top.Destroy();
    for ( i = 0; i < edge_count; i++ )
    {
      struct EDGEINFO& ei = EI[i];
      if ( ei.flag )
        continue;
      memcpy( m_F[ei.fi[0]].vi, ei.vi, 4*sizeof(ei.vi[0]) );
      memset( m_F[ei.fi[1]].vi, 0xFF,  4*sizeof(ei.vi[0]) );
      m_triangle_count--;
      m_quad_count++;
    }    
    CullDegenerateFaces();
  }

  return (diagonal_count > 0 );
}

bool ON_Mesh::ConvertQuadsToTriangles()
{
  const bool bHasFaceNormals = HasFaceNormals();
  const int fcount = FaceCount();
  const int vcount = VertexCount();
  int fi, idmin;;
  double d0, d1, dmin, d;
  if ( fcount > 0 && QuadCount() > 0 ) 
  {
    // use SetCapacity() instead of Reserve() because it's unlikely
    // this mesh will have anything else added and we don't want to
    // waste memory.
    if ( m_F.Capacity() < fcount + m_quad_count )
      m_F.SetCapacity( fcount + m_quad_count );
    if ( bHasFaceNormals && m_FN.Capacity() < fcount + m_quad_count )
      m_FN.SetCapacity( fcount + m_quad_count );

    const ON_3dPoint* dV = ( vcount > 0 && HasDoublePrecisionVertices() 
                             && ( HasSynchronizedDoubleAndSinglePrecisionVertices() || DoublePrecisionVerticesAreValid() ) 
                           )
                   ? DoublePrecisionVertices().Array()
                   : 0;

    const ON_3fPoint* fV = m_V.Array();

    const double rel_tol = 8.0*( (0 != dV) ? ON_EPSILON : ON_FLOAT_EPSILON );

    ON_3dVector FN;

    for ( fi = 0; fi < fcount; fi++ ) 
    {
      ON_MeshFace& f0 = m_F[fi];
      if ( f0.IsValid(vcount) && f0.IsQuad() )
      {
        if ( 0 != dV )
        {
          d0 = dV[f0.vi[0]].DistanceTo(dV[f0.vi[2]]);
          d1 = dV[f0.vi[1]].DistanceTo(dV[f0.vi[3]]);

          // if quad is degenerate, just turn it into a triangle
          idmin = -1;
          dmin = ((d0<=d1)?d0:d1)*rel_tol;
          if ( dmin > ON_ZERO_TOLERANCE )
            dmin = ON_ZERO_TOLERANCE;
          d = dV[f0.vi[0]].DistanceTo(dV[f0.vi[1]]);
          if ( d < dmin )
          {
            idmin = 0;
            dmin = d;
          }
          d = dV[f0.vi[1]].DistanceTo(dV[f0.vi[2]]);
          if ( d < dmin )
          {
            idmin = 1;
            dmin = d;
          }
          d = dV[f0.vi[2]].DistanceTo(dV[f0.vi[3]]);
          if ( d < dmin )
          {
            idmin = 2;
            dmin = d;
          }
          d = dV[f0.vi[3]].DistanceTo(dV[f0.vi[0]]);
          if ( d < dmin )
          {
            idmin = 3;
            dmin = d;
          }
        }
        else
        {
          d0 = m_V[f0.vi[0]].DistanceTo(m_V[f0.vi[2]]);
          d1 = m_V[f0.vi[1]].DistanceTo(m_V[f0.vi[3]]);

          // if quad is degenerate, just turn it into a triangle
          idmin = -1;
          dmin = ((d0<=d1)?d0:d1)*rel_tol;
          if ( dmin > ON_ZERO_TOLERANCE )
            dmin = ON_ZERO_TOLERANCE;
          d = m_V[f0.vi[0]].DistanceTo(m_V[f0.vi[1]]);
          if ( d < dmin )
          {
            idmin = 0;
            dmin = d;
          }
          d = m_V[f0.vi[1]].DistanceTo(m_V[f0.vi[2]]);
          if ( d < dmin )
          {
            idmin = 1;
            dmin = d;
          }
          d = m_V[f0.vi[2]].DistanceTo(m_V[f0.vi[3]]);
          if ( d < dmin )
          {
            idmin = 2;
            dmin = d;
          }
          d = m_V[f0.vi[3]].DistanceTo(m_V[f0.vi[0]]);
          if ( d < dmin )
          {
            idmin = 3;
            dmin = d;
          }
        }

        if ( !(d0 > 0.0) )
        {
          if ( !(d1 > 0.0) )
            continue;
          // d0 = 0 or is invalid and d1 > 0
          // force split along v[1],v[3]
          idmin = -1;
          d0 = 1.0;
          d1 = 0.0;
        }
        else if ( !(d1 > 0.0) )
        {
          // d1 = 0 or is invalid and d0 > 0
          // force split along v[0],v[1]
          idmin = -1;
          d1 = 1.0;
          d0 = 0.0;
        }

        m_quad_count--;
        m_triangle_count++;
        if ( 0 == idmin ) // m_V[f0.vi[0]] == m_V[f0.vi[1]] (nearly)
        {
          // degenerate quad - remove duplicate vertex
          f0.vi[0] = f0.vi[1];
          f0.vi[1] = f0.vi[2];
          f0.vi[2] = f0.vi[3];
        }
        else if ( 1 == idmin ) // m_V[f0.vi[1]] == m_V[f0.vi[2]] (nearly)
        {
          // degenerate quad - remove duplicate vertex
          int vi0 = f0.vi[0]; 
          f0.vi[0] = f0.vi[2];
          f0.vi[1] = f0.vi[3];
          f0.vi[2] = vi0;
          f0.vi[3] = vi0;
        }
        else if ( 2 == idmin ) // m_V[f0.vi[2]] == m_V[f0.vi[3]] (nearly)
        {
          // degenerate quad - remove duplicate vertex
          f0.vi[2] = f0.vi[1];
          f0.vi[1] = f0.vi[0];
          f0.vi[0] = f0.vi[3];
          f0.vi[3] = f0.vi[2];
        }
        else if ( 3 == idmin ) // m_V[f0.vi[3]] == m_V[f0.vi[0]] (nearly)
        {
          // degenerate quad - remove duplicate vertex
          f0.vi[3] = f0.vi[2];
        }
        else
        {
          // split non-degenerate quad into two triangles
          ON_MeshFace& f1 = m_F.AppendNew();
          if  ( d0 <= d1 ) 
          {
            f1.vi[0] = f0.vi[0];
            f1.vi[1] = f0.vi[2];
            f1.vi[2] = f0.vi[3];
            f1.vi[3] = f1.vi[2];
            f0.vi[3] = f0.vi[2];
          }
          else 
          {
            f1.vi[0] = f0.vi[1];
            f1.vi[1] = f0.vi[2];
            f1.vi[2] = f0.vi[3];
            f1.vi[3] = f1.vi[2];
            f0.vi[2] = f0.vi[3];
          }
          if ( bHasFaceNormals ) 
          {
            if ( 0 != dV )
            {
              m_F[fi].ComputeFaceNormal(dV,FN);
              m_FN[fi] = FN;
              m_F[m_F.Count()-1].ComputeFaceNormal(dV,FN);
            }
            else
            {
              m_F[fi].ComputeFaceNormal(fV,FN);
              m_FN[fi] = FN;
              m_F[m_F.Count()-1].ComputeFaceNormal(fV,FN);
            }
            m_FN.AppendNew() = FN;
          }
        }
      }
    }
    if ( fcount != m_F.Count() )
      DestroyTopology(); // we added some triangles
  }
  return ( QuadCount() == 0 && TriangleCount() == FaceCount() ) ? true : false;
}

bool ON_Mesh::CountQuads()
{
  const int fcount = FaceCount();
  const int vcount = VertexCount();
  int fi;
  m_quad_count = 0;
  m_triangle_count = 0;
  m_invalid_count = 0;
  for ( fi = 0; fi < fcount; fi++ ) {
    const ON_MeshFace& f = m_F[fi];
    if ( f.IsValid(vcount) ) {
      if ( f.IsTriangle() )
        m_triangle_count++;
      else
        m_quad_count++;
    }
    else
      m_invalid_count++;
  }
  return true;
}

bool ON_Mesh::ComputeVertexNormals()
{
  bool rc = false;
  const int fcount = FaceCount();
  const int vcount = VertexCount();
  int vi, fi, j;
  ON_3fVector n;

  if ( fcount > 0 && vcount > 0 ) {
    rc = HasFaceNormals();
    if ( !rc )
      rc = ComputeFaceNormals();
    if ( rc ) {
      ON_Workspace ws;
      //double* face_area = ws.GetDoubleMemory(fcount);
      int* vfcount = ws.GetIntMemory( vcount );
      memset ( vfcount, 0, vcount*sizeof(*vfcount) );

      // count number of faces that use each vertex
      for ( fi = 0; fi < fcount; fi++ ) {
        ON_MeshFace& f = m_F[fi];
        if ( f.IsValid(vcount) ) {
          vfcount[f.vi[0]]++;
          vfcount[f.vi[1]]++;
          vfcount[f.vi[2]]++;
          if ( f.IsQuad() )
            vfcount[f.vi[3]]++;
        }
      }

      // set vfi[vi][] = array of face indices that use vertex vi
      int** vfi = (int**)ws.GetMemory( vcount*sizeof(vfi[0] ) );
      {
        int scratch_sz = 0;
        for ( vi = 0; vi < vcount; vi++ ) {
          scratch_sz += vfcount[vi];
        }
        int* scratch = ws.GetIntMemory(scratch_sz);
        for ( vi = 0; vi < vcount; vi++ ) {
          if ( vfcount[vi] ) {
            vfi[vi] = scratch;
            scratch += vfcount[vi];
          }
          vfcount[vi] = 0;
        }
      }
      for ( fi = 0; fi < fcount; fi++ ) {
        ON_MeshFace& f = m_F[fi];
        if ( f.IsValid(vcount) ) {
          vi = f.vi[0]; vfi[vi][vfcount[vi]++] = fi;
          vi = f.vi[1]; vfi[vi][vfcount[vi]++] = fi;
          vi = f.vi[2]; vfi[vi][vfcount[vi]++] = fi;
          if ( f.IsQuad() ) {
            vi = f.vi[3]; vfi[vi][vfcount[vi]++] = fi;
          }
        }
      }

      // average face normals to get an estimate for a vertex normal
      m_N.SetCapacity(vcount);
      m_N.SetCount(0);
      for ( vi = 0; vi < vcount; vi++ ) {
        n.Zero();
        for ( j = vfcount[vi]-1; j >= 0; j-- ) {
          n += m_FN[vfi[vi][j]];
        }
        if ( !n.Unitize() )
        {
          // this vertex is not used by a face or the face normals cancel out.
          // set a unit z normal and press on.
          n.Set(0,0,1);
        }
        m_N.Append(n);
      }
    }
  }
  return rc;
}

bool ON_Mesh::NormalizeTextureCoordinates()
{
  ON_2fPoint t0;//, t1;
  int ti;
  const int vertex_count = m_V.Count();
  bool rc = HasSurfaceParameters();
  if ( rc )
  {
    const ON_2dPoint* S = m_S.Array();
    ON_Interval udom = m_srf_domain[0];
    ON_Interval vdom = m_srf_domain[1];
    rc = udom.IsIncreasing() && vdom.IsIncreasing();
    if ( !rc )
    {
      udom.Set(S[0].x,S[0].x);
      vdom.Set(S[0].y,S[0].y);
      for ( ti = 1; ti < vertex_count; ti++ )
      {
        if      ( S[ti].x < udom.m_t[0] ) udom.m_t[0] = S[ti].x;
        else if ( S[ti].x > udom.m_t[1] ) udom.m_t[1] = S[ti].x;
        if      ( S[ti].y < vdom.m_t[0] ) vdom.m_t[0] = S[ti].y;
        else if ( S[ti].y > vdom.m_t[1] ) vdom.m_t[1] = S[ti].y;
      }
      rc = udom.IsIncreasing() && vdom.IsIncreasing();
    }

    if (rc)
    {
      m_T.Reserve(vertex_count);
      m_T.SetCount(0);
      for (ti = 0; ti < vertex_count; ti++ )
      {
        t0.x = (float)udom.NormalizedParameterAt(S[ti].x);
        t0.y = (float)vdom.NormalizedParameterAt(S[ti].y);
        m_T.Append(t0);
      }
      m_packed_tex_domain[0].Set(0.0,1.0);
      m_packed_tex_domain[1].Set(0.0,1.0);
      m_packed_tex_rotate = false;
      m_Ttag.SetDefaultSurfaceParameterMappingTag();
      if ( m_mesh_parameters )
        m_mesh_parameters->m_texture_range = 1;
    }
  }

  return rc;
}

bool ON_Mesh::TransposeSurfaceParameters()
{
        // swap m_srf_domain 
        ON_Interval temp = m_srf_domain[0];
        m_srf_domain[0]  = m_srf_domain[1];
        m_srf_domain[1]  = temp;

        double t = m_srf_scale[0];
        m_srf_scale[0] = m_srf_scale[1];
  m_srf_scale[1] = t;

  int S_count = m_S.Count();
  ON_2dPoint* S_array = m_S.Array();
  for (int i = 0; i < S_count; i++ )
  {
    ON_2dPoint& S = S_array[i];
    t = S.x; S.x = S.y; S.y = t;
  }
  return true;
}

bool ON_Mesh::HasPackedTextureRegion() const
{
  return (    ON_IsValid(m_srf_scale[0])
           && m_srf_scale[0] > 0.0
           && ON_IsValid(m_srf_scale[1])
           && m_srf_scale[1] > 0.0
           && m_packed_tex_domain[0].IsInterval()
           && m_packed_tex_domain[1].IsInterval()
           && 0.0 <= m_packed_tex_domain[0].Min()
           && m_packed_tex_domain[0].Max() <= 1.0
           && 0.0 <= m_packed_tex_domain[1].Min()
           && m_packed_tex_domain[1].Max() <= 1.0
           && (   fabs(m_packed_tex_domain[0].Length()) < 1.0
               || fabs(m_packed_tex_domain[1].Length()) < 1.0)
         );
}


bool ON_Mesh::TransposeTextureCoordinates()
{
  if ( !HasTextureCoordinates() )
    return false;

  const int vcnt = m_T.Count();
  int i;

  bool bPackedRegion =  HasPackedTextureRegion();

  bool bSrfParamTag = (!m_Ttag.IsSet() || m_Ttag.IsDefaultSurfaceParameterMapping());

  if ( bPackedRegion && bSrfParamTag )
  {
    // The region of the bitmap the texture uses 
    // cannot change.  The texture coordinates 
    // themselves get reflected in the subrectangle
    // about either the lowerleft to upperright
    // diagonal (llur = true) or the lowerright
    // to upperleft diagonal (llur = false).
    bool bRevU = m_packed_tex_domain[0].IsDecreasing();
    bool bRevV = m_packed_tex_domain[1].IsDecreasing();
    bool llur = (bRevU == bRevV) ? true : false;
    if ( m_packed_tex_rotate )
      llur = !llur;

    ON_Interval TD[2];
        TD[0] = m_packed_tex_domain[0];
          TD[1] = m_packed_tex_domain[1];
          TD[0].MakeIncreasing(); 
          TD[1].MakeIncreasing(); 
    for( i=0; i<vcnt; i++)
    {
            ON_2fPoint tc = m_T[i];
            double x = TD[0].NormalizedParameterAt(tc[0]);
            double y = TD[1].NormalizedParameterAt(tc[1]);
            if(!llur)
      {
                    x = 1.0-x;
                    y = 1.0-y;
            }   
            double s = TD[0].ParameterAt(y);
            double t = TD[1].ParameterAt(x);
            m_T[i].Set((float)s,(float)t);
    }
  }
  else
  {
    float f;
          for(i=0; i<vcnt; i++)
    {
                  ON_2fPoint& tc = m_T[i];
      f = tc.x; tc.x = tc.y; tc.y = f;
          }
  }
        return true;
}

bool ON_Mesh::ReverseTextureCoordinates( int dir )
{
  if ( dir < 0 || dir > 1 || !HasTextureCoordinates() )
    return false;

  bool bPackedRegion =  HasPackedTextureRegion();

  bool bSrfParamTag = (!m_Ttag.IsSet() || m_Ttag.IsDefaultSurfaceParameterMapping());

  const int vcount = m_T.Count();
  int i;
  if ( bPackedRegion && bSrfParamTag )
  {
    // The region of the bitmap the texture uses 
    // cannot change.  The texture coordinates 
    // themselves get reflected in the subrectangle
    // about either the lowerleft to upperright
    // diagonal (llur = true) or the lowerright
    // to upperleft diagonal (llur = false).
    if ( m_packed_tex_rotate )
      dir = 1-dir;
    const ON_Interval tex_dom = m_packed_tex_domain[dir];
    double s;
    m_packed_tex_domain[dir].Swap(); // Swap() is correct - Reverse() is wrong.
    for (i = 0; i < vcount; i++ )
    {
      ON_2fPoint& tc = m_T[i];
      s = 1.0 - tex_dom.NormalizedParameterAt(tc[dir]);
      if ( dir )
        tc.y = (float)tex_dom.ParameterAt(s);
      else
        tc.x = (float)tex_dom.ParameterAt(s);
    }
  }
  else
  {
    for (i = 0; i < vcount; i++ )
    {
      ON_2fPoint& tc = m_T[i];
      if ( dir )
        tc.y = 1.0f-tc.y;
      else
        tc.x = 1.0f-tc.x;
    }
  }
        return true;
}

bool ON_Mesh::ReverseSurfaceParameters( int dir )
{
  if ( dir < 0 || dir > 1 || !HasSurfaceParameters() )
    return false;
  if ( m_srf_domain[dir].IsIncreasing() )
    m_srf_domain[dir].Reverse();
  int i, vcount = m_S.Count();
  for (i = 0; i < vcount; i++)
  {
    ON_2dPoint& S = m_S[i];
    if ( dir )
      S.y = -S.y;
    else
      S.x = -S.x;
  }
  return true;
}


bool ON_Mesh::EvaluateMeshGeometry( const ON_Surface& srf )
{
  bool rc = false;
  const int vcount = VertexCount();
  const bool bHasSurfaceParameters = HasSurfaceParameters();
  if ( bHasSurfaceParameters )
  {
    const bool bHasVertexNormals = HasVertexNormals();
    m_N.SetCapacity(vcount);
    int vi, side, hint[2];
    ON_3dPoint point;
    ON_3dVector normal, Ds, Dt, Dss, Dst, Dtt, K1, K2;
    const ON_2dPoint* srf_st;
    double s, t, kgauss, kmean;
    side = 0;
    hint[0] = 0;
    hint[1] = 0;
    const double smax = srf.Domain(0)[1];
    const double tmax = srf.Domain(1)[1];
    if ( HasPrincipalCurvatures() ) 
    {
      for ( vi = 0; vi < vcount; vi++ ) 
      {
        //ON_2fPoint& tex = m_T[vi];
        // convert texture coordinates to normalizied texture coordinates
        srf_st = &m_S[vi];
        s = srf_st->x;
        t = srf_st->y;
        // 19 April 2006 Dale Lear - added side setter so singular normals
        //                           are correctly evaluated RR 12482
        side = ( smax == s ) ? ((tmax == t) ? 3 : 2) : ((tmax == t) ? 4 : 1);
        srf.Ev2Der( s, t, point, Ds, Dt, Dss, Dst, Dtt, side, hint );
        ON_EvNormal( side, Ds, Dt, Dss, Dst, Dtt, normal );
        ON_EvPrincipalCurvatures( Ds, Dt, Dss, Dst, Dtt, normal,
                                  &kgauss, &kmean, 
                                  &m_K[vi].k1, &m_K[vi].k2, 
                                  K1, K2 ); //m_K[vi].e1, m_K[vi].e2 );
        m_V[vi] = &point.x; // use ON_3fPoint double* conversion (quiets gcc)
        if ( bHasVertexNormals )
          m_N[vi] = &normal.x; // use ON_3fVector double* conversion (quiets gcc)
      }
      InvalidateCurvatureStats();
    }
    else if ( bHasVertexNormals ) 
    {
      for ( vi = 0; vi < vcount; vi++ ) 
      {
        //ON_2fPoint& tex = m_T[vi];
        srf_st = &m_S[vi];
        s = srf_st->x;
        t = srf_st->y;
        // 19 April 2006 Dale Lear - added side setter so singular normals
        //                           are correctly evaluated RR 12482
        side = ( smax == s ) ? ((tmax == t) ? 3 : 2) : ((tmax == t) ? 4 : 1);
        srf.EvNormal( s, t, point, normal, side, hint );
        m_V[vi] = &point.x; // use ON_3fPoint double* conversion (quiets gcc)
        m_N[vi] = &normal.x; // use ON_3fVector double* conversion (quiets gcc)
      }
    }
    else 
    {
      for ( vi = 0; vi < vcount; vi++ ) 
      {
        //ON_2fPoint& tex = m_T[vi];
        srf_st = &m_S[vi];
        s = srf_st->x;
        t = srf_st->y;
        srf.EvPoint( s, t, point, side, hint );
        m_V[vi] = &point.x;
      }
    }
    if ( HasFaceNormals() )
    {
      ComputeFaceNormals();
    }
    rc = true;

    m_Ctag.Default();
    InvalidateVertexBoundingBox();
    InvalidateVertexNormalBoundingBox();
    DeleteMeshParameters();
    DestroyTree();
  }
  return rc;
}

void ON_Mesh::SetMeshParameters( const ON_MeshParameters& mp )
{
  DeleteMeshParameters();
  m_mesh_parameters = new ON_MeshParameters(mp);
}

const ON_MeshParameters* ON_Mesh::MeshParameters() const
{
  return m_mesh_parameters;
}

void ON_Mesh::DeleteMeshParameters()
{
  if ( m_mesh_parameters ) {
    delete m_mesh_parameters;
    m_mesh_parameters = 0;
  }
}

static int compare3fPoint( const ON_3fPoint* a, const ON_3fPoint* b )
{
  if ( a->x < b->x ) return -1;
  if ( a->x > b->x ) return  1;
  if ( a->y < b->y ) return -1;
  if ( a->y > b->y ) return  1;
  if ( a->z < b->z ) return -1;
  if ( a->z > b->z ) return  1;
  return 0;
}

static int compare3dPoint( const ON_3dPoint* a, const ON_3dPoint* b )
{
  if ( a->x < b->x ) return -1;
  if ( a->x > b->x ) return  1;
  if ( a->y < b->y ) return -1;
  if ( a->y > b->y ) return  1;
  if ( a->z < b->z ) return -1;
  if ( a->z > b->z ) return  1;
  return 0;
}

typedef int (*ON_COMPAR_LPVOID_LPVOID)(const void*,const void*);

static 
int GetPointMap( int pt_count, const ON_3fPoint* fV, const ON_3dPoint* dV, ON_SimpleArray<int>& pt_map )
{
  // Builds a mapping array, pt_map[], such that the length of pt_map[] 
  // is pt_count and pt_map[i] == pt_map[j] if and only if pt[i] == pt[j]
  // as 3d points.  The values in map[] run from 0 to max_pt_index.
  int vt0, vt1;
  ON_3fPoint fp0;
  ON_3dPoint dp0;
  int* map;
  int* index;
  int max_pt_index = 0;
  if ( pt_count > 0 && (dV || fV) )
  {
    index = (int*)onmalloc(pt_count*sizeof(*index));
    
    if ( dV )
      ON_Sort( ON::quick_sort, index, dV, pt_count, sizeof(*dV), (ON_COMPAR_LPVOID_LPVOID)compare3dPoint );
    else
      ON_Sort( ON::quick_sort, index, fV, pt_count, sizeof(*fV), (ON_COMPAR_LPVOID_LPVOID)compare3fPoint );
    
    pt_map.SetCapacity( pt_count );
    pt_map.SetCount( pt_count );
    map = pt_map.Array();
    for ( vt0 = 0; vt0 < pt_count; vt0++ )
      map[vt0] = -1;

    if ( dV )
    {
      for (vt0 = 0; vt0 < pt_count; vt0 = vt1, max_pt_index++) 
      {
        dp0 = dV[index[vt0]];
        for ( vt1=vt0+1; vt1<pt_count && 0==compare3dPoint(&dp0,dV+index[vt1]); vt1++ ) {
          // empty
        }
        while ( vt0 < vt1 ) {
          map[index[vt0++]] = max_pt_index;
        }
      }
    }
    else
    {
      for (vt0 = 0; vt0 < pt_count; vt0 = vt1, max_pt_index++) 
      {
        fp0 = fV[index[vt0]];
        for ( vt1=vt0+1; vt1<pt_count && 0==compare3fPoint(&fp0,fV+index[vt1]); vt1++ ) {
          // empty
        }
        while ( vt0 < vt1 ) {
          map[index[vt0++]] = max_pt_index;
        }
      }
    }
    onfree(index);
  }
  if ( max_pt_index == 0 )
    pt_map.Destroy();
  return max_pt_index;
}

int ON_Mesh::CullDegenerateFaces()
{
  // 30 December 2003 Dale Lear - fixed bug that was not culling
  //     topologically degenerate faces.

  int bad_count = 0;
  int degenerate_count = 0;
  const int fcount = m_F.Count();
  const int vcount = m_V.Count();
  ON_MeshFace f;
  int fi;

  if ( fcount > 0 ) 
  {
    // use GetTopologyVertexMap() instead of calling Topology() because this mesh
    // may have lots of bogus faces that need to be culled.
    ON_SimpleArray<int> topv_map;
    const ON_3dPoint* dV = Mesh_dV(*this);
    const ON_3fPoint* fV = (0 == dV) ? m_V.Array() : 0;
    const int topv_count = GetPointMap( m_V.Count(), fV, dV, topv_map );
    if ( topv_count > 0 && topv_map.Count() == m_V.Count() ) 
    {
      ON_Workspace ws;
      const int* vtop = topv_map.Array();
      unsigned char* bBadFace = (unsigned char*)ws.GetMemory(fcount*sizeof(*bBadFace));
      memset( bBadFace, 0, fcount*sizeof(*bBadFace) );
      for ( fi = 0; fi < fcount; fi++ ) 
      {
        ON_MeshFace& f0 = m_F[fi];
        // set f.vi[] to values of topoligical indices
        {
          int f0vi = f0.vi[0];
          f.vi[0] = (f0vi < 0 || f0vi >= vcount) ? -1 : vtop[f0vi];

          f0vi = f0.vi[1];
          f.vi[1] = (f0vi < 0 || f0vi >= vcount) ? -1 : vtop[f0vi];

          f0vi = f0.vi[2];
          f.vi[2] = (f0vi < 0 || f0vi >= vcount) ? -1 : vtop[f0vi];

          f0vi = f0.vi[3];
          f.vi[3] = (f0vi < 0 || f0vi >= vcount) ? -1 : vtop[f0vi];
        }

        if ( !f.IsValid(topv_count) ) 
        {
          degenerate_count++;
          //f = m_F[fi];
          if ( f.vi[0] == f.vi[1] || f.vi[0] < 0 || f.vi[0] >= topv_count )
          {
            f0.vi[0] = f0.vi[1];
            f0.vi[1] = f0.vi[2];
            f0.vi[2] = f0.vi[3];
            f.vi[0] = f.vi[1];
            f.vi[1] = f.vi[2];
            f.vi[2] = f.vi[3];
          }

          if ( f.vi[1] == f.vi[2] || f.vi[1] < 0 || f.vi[1] >= topv_count )
          {
            f0.vi[1] = f0.vi[2];
            f0.vi[2] = f0.vi[3];
            f.vi[1] = f.vi[2];
            f.vi[2] = f.vi[3];
          }

          if ( f.vi[2] < 0 || f.vi[2] >= topv_count )
          {
            f0.vi[2] = f0.vi[3];
            f.vi[2] = f.vi[3];
          }

          if ( f.vi[3] < 0 || f.vi[3] >= topv_count )
          {
            f0.vi[3] = f0.vi[2];
            f.vi[3] = f.vi[2];
          }
          else if ( f.vi[0] == f.vi[3] && f.vi[2] != f.vi[3] )
          {
            f0.vi[0] = f0.vi[1];
            f0.vi[1] = f0.vi[2];
            f0.vi[2] = f0.vi[3];
            f.vi[0] = f.vi[1];
            f.vi[1] = f.vi[2];
            f.vi[2] = f.vi[3];
          }

          if ( !f0.IsValid(vcount) || !f.IsValid(topv_count) ) 
          {
            // face cannot be repaired by juggling vertex indices
            bBadFace[fi] = 1;
            bad_count++;
          }
        }
      }

      if ( bad_count > 0 ) 
      {
        //  remove bad faces.
        bool bHasFN = (m_FN.Count() == m_F.Count());
        if ( !bHasFN )
          m_FN.SetCount(0);

        int fcnt = 0;
        for ( fi = fcnt = 0; fi < fcount; fi++ )
        {
          if ( !bBadFace[fi] )
          {
            if ( fcnt < fi )
            {
              m_F[fcnt] = m_F[fi];
              if ( bHasFN )
                m_FN[fcnt] = m_FN[fi];
            }
            fcnt++;
          }
        }

        m_F.SetCount(fcnt);
        if ( bHasFN )
          m_FN.SetCount(fcnt);
      }

      if ( degenerate_count > 0 )
      {
        // mesh was modified - destroy information that was
        // calculated using the old mesh
        DestroyTree();
        DestroyPartition();
        DestroyTopology();
        m_invalid_count = 0;
        m_quad_count = 0;
        m_triangle_count = 0;
      }
    }
  }
  return degenerate_count;
}

int ON_Mesh::CullUnusedVertices()
{
  //int cullcount = 0;
  int vi, fi;
  ON_Workspace ws;
  CullDegenerateFaces();
  int fcnt = m_F.Count();
  int vcnt = m_V.Count();
  int * vmap = ws.GetIntMemory( vcnt );
  memset ( vmap, 0, vcnt*sizeof(vmap[0]) );
  for ( fi = 0; fi < fcnt; fi++ )
  {
    const ON_MeshFace& f = m_F[fi];
    vmap[f.vi[0]] = 1;
    vmap[f.vi[1]] = 1;
    vmap[f.vi[2]] = 1;
    vmap[f.vi[3]] = 1;
  }

  int newvcnt = 0;
  for ( vi = 0; vi < vcnt; vi++ )
  {
    if ( vmap[vi] )
      vmap[vi] = newvcnt++;
    else {
      vmap[vi] = -1;
    }
  }

  if ( newvcnt == 0 )
    Destroy();
  else if ( newvcnt < vcnt )
  {
    DestroyTopology();

    // buffer will hold up to vcnt 3d points
    void* buffer = ws.GetMemory(vcnt*9*sizeof(double));

    if ( HasSurfaceParameters() ) {
      ON_2dPoint* s = (ON_2dPoint*)buffer;
      for ( vi = 0; vi < vcnt; vi++ )
      {
        if ( vmap[vi]>=0 )
          s[vmap[vi]] = m_S[vi];
      }
      memcpy( m_S.Array(), s, newvcnt*sizeof(s[0]) );
      m_S.SetCount(newvcnt);
    }

    if ( HasDoublePrecisionVertices() )
    {
      ON_3dPointArray& D = DoublePrecisionVertices();
      if ( vcnt == D.Count() )
      {
        bool bValidDoubles = DoublePrecisionVerticesAreValid();
        ON_3dPoint* s = (ON_3dPoint*)buffer;
        for ( vi = 0; vi < vcnt; vi++ )
        {
          if ( vmap[vi]>=0 )
            s[vmap[vi]] = D[vi];
        }
        memcpy( D.Array(), s, newvcnt*sizeof(s[0]) );
        D.SetCount(newvcnt);
        if ( bValidDoubles )
          SetDoublePrecisionVerticesAsValid();
      }
      else
      {
        DestroyDoublePrecisionVertices();
      }
    }

    if ( HasVertexNormals() ) {
      ON_3fVector* v = (ON_3fVector*)buffer;
      for ( vi = 0; vi < vcnt; vi++ )
      {
        if ( vmap[vi]>=0 )
          v[vmap[vi]] = m_N[vi];
      }
      memcpy( m_N.Array(), v, newvcnt*sizeof(v[0]) );
      m_N.SetCount(newvcnt);
    }

    if ( HasTextureCoordinates() ) {
      ON_2fPoint* t = (ON_2fPoint*)buffer;
      for ( vi = 0; vi < vcnt; vi++ )
      {
        if ( vmap[vi]>=0 )
          t[vmap[vi]] = m_T[vi];
      }
      memcpy( m_T.Array(), t, newvcnt*sizeof(t[0]) );
      m_T.SetCount(newvcnt);
    }

    if ( HasPrincipalCurvatures() ) {
      ON_SurfaceCurvature* k = (ON_SurfaceCurvature*)buffer;
      for ( vi = 0; vi < vcnt; vi++ )
      {
        if ( vmap[vi]>=0 )
          k[vmap[vi]] = m_K[vi];
      }
      memcpy( m_K.Array(), k, newvcnt*sizeof(k[0]) );
      m_K.SetCount(newvcnt);
    }

    if ( HasVertexColors() ) {
      ON_Color* c = (ON_Color*)buffer;
      for ( vi = 0; vi < vcnt; vi++ )
      {
        if ( vmap[vi]>=0 )
          c[vmap[vi]] = m_C[vi];
      }
      memcpy( m_C.Array(), c, newvcnt*sizeof(c[0]) );
      m_C.SetCount(newvcnt);
    }

    {
      bool bValidSingles = SinglePrecisionVerticesAreValid();
      ON_3fPoint* p = (ON_3fPoint*)buffer;
      for ( vi = 0; vi < vcnt; vi++ )
      {
        if ( vmap[vi]>=0 )
          p[vmap[vi]] = m_V[vi];
      }
      memcpy( m_V.Array(), p, newvcnt*sizeof(p[0]) );
      m_V.SetCount(newvcnt);
      if ( bValidSingles )
        SetSinglePrecisionVerticesAsValid();
    }

    for ( fi = 0; fi < fcnt; fi++ )
    {
      ON_MeshFace& f = m_F[fi];
      f.vi[0] = vmap[f.vi[0]];
      f.vi[1] = vmap[f.vi[1]];
      f.vi[2] = vmap[f.vi[2]];
      f.vi[3] = vmap[f.vi[3]];
    }

  }
  return vcnt - newvcnt;
}

bool ON_Mesh::Compact()
{
  // CullDegenerateFaces(); // CullUnusedVertices() does this
  CullUnusedVertices();
  m_V.Shrink();
  m_F.Shrink();
  m_N.Shrink();
  m_FN.Shrink();
  m_K.Shrink();
  m_C.Shrink();
  m_S.Shrink();
  m_T.Shrink();
  return true;
}

//
//   ON_SurfaceCurvature
//
double ON_SurfaceCurvature::GaussianCurvature() const
{
  return k1*k2;
}

double ON_SurfaceCurvature::MeanCurvature() const
{
  return 0.5*(k1+k2);
}

double ON_SurfaceCurvature::MinimumRadius() const
{
  double k;
  k = (fabs(k1)>=fabs(k2)) ? fabs(k1) : fabs(k2); // k = maximum directional curvature
  k = ( k > 1.0e-300 ) ? 1.0/k : 1.0e300;         // 1/k = minimum radius of curvature
  return k;
}

double ON_SurfaceCurvature::MaximumRadius() const
{
  double k;
  if ( k1*k2 <= 0.0 ) {
    // if principal curvatures have opposite signs, there
    // is a direction with zero directional curvature
    k = 0.0;
  }
  else {
    k = (fabs(k1)<=fabs(k2)) ? fabs(k1) : fabs(k2);
  }
  // k = minimum directional curvature
  k = ( k > 1.0e-300 ) ? 1.0/k : 1.0e300; // 1/k = maximum radius of curvature
  return k;
}

//double ON_SurfaceCurvature::NormalCurvature(const ON_3dVector& tangent) const
//{
//  double c = tangent*e1;
//  double s = tangent*e2;
//  return k1*c*c + k2*s*s;
//}

//double ON_SurfaceCurvature::NormalSectionCurvature( const ON_3dVector& section_normal, const ON_3dVector& surface_normal ) const
//{
//  ON_3dVector tangent = ON_CrossProduct( section_normal, surface_normal );
//  if ( fabs(tangent.x) <= ON_SQRT_EPSILON && fabs(tangent.y) <= ON_SQRT_EPSILON && fabs(tangent.z) <= ON_SQRT_EPSILON )
//    tangent.Zero();
//  else
//    tangent.Unitize();
//  return NormalCurvature(tangent);
//}

ON_MeshTopology::ON_MeshTopology() 
: m_mesh(0)
, m_memchunk(0)
, m_b32IsValid(0)
{
}

ON_MeshTopology::~ON_MeshTopology()
{
  Destroy();
}

void ON_MeshTopology::Destroy()
{
  m_topv_map.Destroy();
  m_topv.Destroy();
  m_tope.Destroy();
  m_topf.Destroy();
  struct memchunk *p, *n;
  n = m_memchunk;
  while(n)
  {
    p = n;
    n = n->next;
    onfree(p);
  }
  m_memchunk = 0;
  if ( -1 != m_b32IsValid)
    m_b32IsValid = 0;
}

void ON_MeshTopology::EmergencyDestroy()
{
  m_mesh = 0;
  m_topv_map.EmergencyDestroy();
  m_topv.EmergencyDestroy();
  m_tope.EmergencyDestroy();
  m_topf.EmergencyDestroy();
  m_memchunk = 0;
  m_b32IsValid = 0;
}

int ON_MeshTopology::TopVertexCount() const
{
  return m_topv.Count();
}

// number of topoligical edges
int ON_MeshTopology::TopEdgeCount() const
{
  return m_tope.Count();
}

// number of topoligical faces (same as m_mesh.FaceCount())
int ON_MeshTopology::TopFaceCount() const
{
  return m_topf.Count();
}

ON_3fPoint ON_MeshTopology::TopVertexPoint( int vtopi ) const
{
  return m_mesh->m_V[m_topv[vtopi].m_vi[0]];
}

ON_Line ON_MeshTopology::TopEdgeLine( int tope_index ) const
{
  ON_Line L(ON_UNSET_POINT,ON_UNSET_POINT);
  if ( m_mesh && tope_index >= 0 && tope_index < m_tope.Count() )
  {
    const int* topvi = m_tope[tope_index].m_topvi;
    if (   topvi[0] >= 0 && topvi[0] < m_topv.Count() 
        && topvi[1] >= 0 && topvi[1] < m_topv.Count() )
    {
      const ON_MeshTopologyVertex& v0 = m_topv[topvi[0]];
      const ON_MeshTopologyVertex& v1 = m_topv[topvi[1]];
      if ( v0.m_v_count > 0 && v0.m_vi && v1.m_v_count > 0 && v1.m_vi )
      {
        int vi0 = v0.m_vi[0];
        int vi1 = v1.m_vi[0];
        int vcount = m_mesh->m_V.Count();
        if ( vi0 >= 0 && vi0 < vcount && vi1 >= 0 && vi1 < vcount )
        {
          L.from = m_mesh->m_V[vi0];
          L.to   = m_mesh->m_V[vi1];
        }
      }
    }
  }
  return L;
}

// returns index of edge that connects topological vertices
// returns -1 if no edge is found.
int ON_MeshTopology::TopEdge( int vtopi0, int vtopi1 ) const
{
  int i0, i1, ei, vi0;
  if ( vtopi0 > vtopi1 ) {vi0 = vtopi0; vtopi0 = vtopi1; vtopi1 = vi0;}
  if ( vtopi0 < vtopi1 ) {
    const int tope_count = TopEdgeCount();
    const ON_MeshTopologyEdge* tope = m_tope.Array(); // to speed array access
    i0 = 0;
    i1 = tope_count;
    while ( i0 < i1 )
    {
      ei = (i0+i1)/2;
      vi0 = tope[ei].m_topvi[0];
      if ( vi0 < vtopi0 ) {
        if ( i0 == ei )
          break;
        i0 = ei;
      }
      else if ( vi0 > vtopi0 ) {
        if ( i1 == ei )
          break;
        i1 = ei;
      }
      else {
        while (ei > 0 && tope[ei-1].m_topvi[0] == vtopi0 )
          ei--;
        while ( ei < tope_count && tope[ei].m_topvi[0] == vtopi0 ) {
          if ( tope[ei].m_topvi[1] == vtopi1 )
            return ei;
          ei++;
        }
        break;
      }
    }
  }
  return -1;
}

bool ON_MeshTopology::GetTopFaceVertices( int fi, int topvi[4] ) const
{
  if ( fi >= 0 && fi < m_mesh->m_F.Count() ) {
    const int* fvi = m_mesh->m_F[fi].vi;
    topvi[0] = m_topv_map[fvi[0]];
    topvi[1] = m_topv_map[fvi[1]];
    topvi[2] = m_topv_map[fvi[2]];
    topvi[3] = m_topv_map[fvi[3]];
  }
  return true;
}

bool ON_MeshTopology::SortVertexEdges() const
{
  bool rc = true;
  int topvi, topv_count = m_topv.Count();
  for ( topvi = 0; topvi < topv_count; topvi++ )
  {
    if ( !SortVertexEdges(topvi) )
      rc = false;
  }
  return rc;
}

// TODO make public and add to header file new ON_SortIntArray
static
void ON_ReverseIntArray(
        int* e,    // array of ints
        size_t  nel   // length of array
        )
{
  int ei;
  size_t i;
  nel--;
  for ( i = 0; i<nel; i++, nel--)
  {
    ei = e[i];
    e[i] = e[nel];
    e[nel] = ei;
  }
}

bool ON_MeshTopology::SortVertexEdges(int topvi) const
{
  if ( topvi < 0 || topvi >= m_topv.Count() )
    return false;

  const ON_MeshTopologyVertex& topv = m_topv[topvi];
  if ( topv.m_tope_count < 2 )
    return true;

  // Divide the edges that use this vertex into two sets:
  //   e1f[] = indices of edges that bound 1 face, 3 or 
  //           more faces, or no faces (in that order).
  //   e2f[] = indices of edges that bound exactly 2 faces.
  int i, j;
  int topei;
  int vei;
  int efcnt;
  int* new_tope = (int*)alloca(5*topv.m_tope_count*sizeof(new_tope[0]));
  int* e2f  = new_tope + topv.m_tope_count;
  int* e1f  = e2f + topv.m_tope_count;
  int e1fcnt = 0;
  int e2fcnt = 0;
  {
    int* e3f  = e1f + topv.m_tope_count; // e3f[] = edges with 3 or more faces
    int* e0f  = e3f + topv.m_tope_count; // e0f[] = edges with no faces
    int e3fcnt = 0;
    int e0fcnt = 0;

    for ( vei = 0; vei < topv.m_tope_count; vei++ )
    {
      topei = topv.m_topei[vei];
      if ( topei >= 0 && topei < m_tope.Count() )
      {
        const ON_MeshTopologyEdge& tope = m_tope[topei];
        if ( tope.m_topvi[0] == topvi || tope.m_topvi[1] == topvi )
        {
          efcnt = m_tope[topei].m_topf_count;
          if ( efcnt < 0 )
          {
            ON_ERROR("ON_MeshTopology::SortVertexEdges(int topvi) - m_tope[topei].m_topf_count < 0"); 
            return false;
          }
          switch(efcnt)
          {
          case 0: // edge has no faces 
            // (never happens if topology is from a valid ON_Mesh.)
            e0f[e0fcnt++] = topei;                                   
            break;

          case 1: // edge has exactly one face
            e1f[e1fcnt++] = topei; 
            break;

          case 2: // edge has exactly two faces
            e2f[e2fcnt++] = topei;
            break;

          default: // edge has 3 or more faces
            // (happens when mesh is non-manifold)
            e3f[e3fcnt++] = topei;
            break;
          }
        }
      }
    }
  
    // append list of non-manifold edges (3 or more faces) to e1f[]
    for ( i = 0; i < e3fcnt; i++ )
    {
      e1f[e1fcnt++] = e3f[i];
    }

    // append list of wire edges (0 faces) to e1f[]
    for ( i = 0; i < e0fcnt; i++ )
    {
      e1f[e1fcnt++] = e0f[i];
    }

    e0fcnt = 0;
    e3fcnt = 0;
    e0f = 0;
    e3f = 0;
  }

  // Put the edge indices in new_tope[] in radial order.
  // NOTE: The code below works for non-oriented meshes and
  //       non-manifold meshes.  If you change the code, you
  //       must make sure that it still works in these cases.
  if ( e1fcnt + e2fcnt != topv.m_tope_count )
  {
    ON_ERROR("ON_MeshTopology::SortVertexEdges() input vertex had bogus m_topei[]");
    return false;
  }
  int fi = -1;
  int next_topei = -1;
  int efi, fecnt, fei, next_fei;
  vei = 0;
  int vei0 = 0;
  int vei1 = 0;
  int elist_dir = 0;
  while(vei < topv.m_tope_count)
  {
    if ( next_topei >= 0 )
    {
      // continue with this group of edges
      topei = next_topei;
      next_topei = -1;
    }
    else if ( e1fcnt > 0 )
    {
      // start a new group of edges
      topei = *e1f++;
      e1fcnt--;
      vei1 = vei;
    }
    else if ( e2fcnt > 0 )
    {
      // start a new group of edges
      // (this only happens in non-manifold cases)
      topei = *e2f++;
      e2fcnt--;
      vei1 = vei;
    }
    else
    {
      ON_ERROR("ON_MeshTopology::SortVertexEdges() input vertex had bogus topology information.");
      return false;
    }

    if ( vei0 < vei1 )
    {
      if ( 1 == elist_dir )
      {
        // 30 December 2003 Dale Lear added this feature
        //   edges new_tope[vei0],...,new_tope[vei1-1] are radially sorted
        //   but the order is not counterclockwise with respect to
        //   the normal of the face attached to the first edge.
        //   So, this group of edges in new_tope[] needs to
        //   be reversed.
        ON_ReverseIntArray( new_tope+vei0, vei1-vei0 );
      }
      elist_dir = 0;
      vei0 = vei1;
    }

    new_tope[vei++] = topei;

    // search faces connected to tope for the next edge
    const ON_MeshTopologyEdge& tope = m_tope[topei];
    for ( efi = 0; next_topei < 0 && efi < tope.m_topf_count; efi++ )
    {
      fi = tope.m_topfi[efi];
      if ( fi < 0 || fi >= m_topf.Count() )
      {
        // bogus face index into m_topf[] array
        continue;
      }

      // find fei so that topf.m_topei[fei] = topei
      const ON_MeshTopologyFace& topf = m_topf[fi];
      fecnt = topf.IsQuad() ? 4 : 3;
      for ( fei = 0; fei < fecnt; fei++ )
      {
        if ( topf.m_topei[fei] != topei )
          continue;

        if ( tope.m_topvi[0] == topvi )
        {
          next_fei = ( topf.m_reve[fei] ) ?  1 : -1;
        }
        else
        {
          next_fei = ( topf.m_reve[fei] ) ? -1 :  1;
        }

        if ( 0 == elist_dir )
          elist_dir = next_fei;

        next_fei = (fei+next_fei+fecnt)%fecnt;
        next_topei = topf.m_topei[next_fei];

        // next_topei = candidate for the next edge
        //  Check to see that it is available by
        //  finding it in the e1f[] or e2f[] arrays.
        j = 0;
        for ( i = 0; i < e1fcnt; i++ )
        {
          if ( next_topei == e1f[i] )
          {
            // found it in the e1f list.
            for ( j = i+1; j < e1fcnt; j++ )
              e1f[j-1] = e1f[j];
            e1fcnt--;
            break;
          }
        }
        if ( 0 == j )
        {
          // search the e2f[] list
          for ( i = 0; i < e2fcnt; i++ )
          {
            if ( next_topei == e2f[i] )
            {
              for ( j = i+1; j < e2fcnt; j++ )
                e2f[j-1] = e2f[j];
              e2fcnt--;
              break;
            }
          }
        }
        if ( 0 == j )
        {
          // the candidate was already used, check the next
          // face attached to this edge.
          next_topei = -1;
        }
        else
        {
          break;
        }
      }
    }
  }

  if ( topv.m_tope_count != vei )
  {
    ON_ERROR("ON_MeshTopology::SortVertexEdges() edge sorting error.");
    return false;
  }

  vei1 = vei;
  if ( vei0 < vei1 )
  {
    if ( 1 == elist_dir )
    {
      // 30 December 2003 Dale Lear added this feature
      //   edges new_tope[vei0],...,new_tope[vei1-1] are radially sorted
      //   but the order is not counterclockwise with respect to
      //   the normal of the face attached to the first edge.
      //   So, this group of edges in new_tope[] needs to
      //   be reversed.
      ON_ReverseIntArray( new_tope+vei0, vei1-vei0 );
    }
    elist_dir = 0;
    vei0 = vei1;
  }

  int* topv_m_topei = const_cast<int*>(topv.m_topei);
  for ( vei = 0; vei < topv.m_tope_count; vei++ )
  {
    topv_m_topei[vei] = new_tope[vei];
  }

  return true;
}

int* ON_MeshTopology::GetIntArray(int length)
{
  int* a = 0;
  if ( length > 0 ) {
    struct memchunk* pm;
    pm = (struct memchunk*)onmalloc(length*sizeof(*a) + sizeof(*pm));
    if ( pm ) {
      pm->next = m_memchunk;
      m_memchunk = pm++;
      a = (int*)pm;
    }
  }
  return a;
}

bool ON_MeshTopologyFace::IsTriangle() const
{
  return ( m_topei[2] == m_topei[3] && m_topei[0] != m_topei[1] )
         ? true : false;
}

bool ON_MeshTopologyFace::IsQuad() const
{
  return ( m_topei[2] != m_topei[3] ) ? true : false;
}

bool ON_MeshTopologyFace::IsValid() const
{
  return ( m_topei[0] != m_topei[1] ) ? true : false;
}


bool ON_MeshTopology::IsValid() const
{
  ON_Workspace ws;
  int topvi, topei, topfi, vi, fi, j, jmax, k, tfvi[4];
  ON_3fPoint p;

  WaitUntilReady(0);

  // simple checks
  if ( 1 != m_b32IsValid )
    return false;
  if ( !m_mesh )
    return false;
  if ( this != &(m_mesh->Topology()) )
    return false;
  const int v_count = m_mesh->VertexCount();
  const int f_count = m_mesh->FaceCount();
  const int topv_count = TopVertexCount();
  const int tope_count = TopEdgeCount();
  const int topf_count = TopFaceCount();
  if ( topv_count > v_count || topv_count < 0 )
    return false;
  if ( topv_count == 0 && v_count > 0 )
    return false;
  if ( topf_count != f_count )
    return false;
  if ( f_count > 0 && tope_count < 3 )
    return false;
  if ( m_topv_map.Count() != v_count )
    return false;

  // check vertex information
  for ( vi = 0; vi < v_count; vi++ ) {
    topvi = m_topv_map[vi];
    if ( topvi < 0 || topvi >= topv_count )
      return false;
  }

  char* vCheck = (char*)ws.GetMemory( v_count*sizeof(*vCheck) );
  memset( vCheck, 0, v_count*sizeof(*vCheck) );
  for ( topvi = 0; topvi < topv_count; topvi++ )
  {
    const ON_MeshTopologyVertex& topv = m_topv[topvi];
    if ( topv.m_v_count <= 0 )
      return false;
    if ( !topv.m_vi )
      return false;
    p = TopVertexPoint(topvi);
    for ( j = 0; j < topv.m_v_count; j++ ) {
      vi = topv.m_vi[j];
      if ( vi < 0 )
        return false;
      if ( vi >= v_count )
        return false;
      if ( vCheck[vi] != 0 )
        return false; // mesh.m_V[vi] is referenced multiple times
      if ( compare3fPoint( &p, &m_mesh->m_V[vi] ) )
        return false; // mesh.m_V[vi] not at same location as topv
      if ( m_topv_map[vi] != topvi )
        return false; 
      vCheck[vi] = 1;
    }

    // check that edges in m_topei[] list have topvi has a start/end
    if ( topv.m_tope_count < 0 )
      return false;
    if ( topv.m_tope_count == 0 && topv.m_topei )
      return false; // array should be NULL
    if ( topv.m_tope_count > 0 && !topv.m_topei )
      return false; // array should not be NULL
    for ( j = 0; j < topv.m_tope_count; j++ ) {
      topei = topv.m_topei[j];
      if ( topei < 0 )
        return false;
      if ( topei >= tope_count )
        return false;
      const ON_MeshTopologyEdge& tope = m_tope[topei];
      if ( tope.m_topvi[0] != topvi && tope.m_topvi[1] != topvi )
        return false; // edge doesn't reference this top vtx
      for ( k = 0; k < j; k++ ) {
        if ( topv.m_topei[k] == topei )
          return false; // edge listed multiple times
      }
    }
  }

  // make sure every mesh.m_V[] maps to a topoligical vertex
  for ( vi = 0; vi < v_count; vi++ ) {
    if ( vCheck[vi] != 1 )
      return false; // mesh.m_V[vi] is not referenced
    topvi = m_topv_map[vi];
    if ( topvi < 0 )
      return false;
    if ( topvi >= topv_count )
      return false;
    const ON_MeshTopologyVertex& topv = m_topv[topvi];
    for ( j = 0; j < topv.m_v_count; j++ ) {
      if ( topv.m_vi[j] == vi )
        break;
    }
    if ( j >= topv.m_v_count )
      return false; // bogus m_topv_map[] array
  }

  // check edges
  for ( topei = 0; topei < tope_count; topei++ ) {
    const ON_MeshTopologyEdge& tope = m_tope[topei];
    if ( tope.m_topvi[0] < 0 || tope.m_topvi[0] >= topv_count )
      return false;
    if ( tope.m_topvi[1] < 0 || tope.m_topvi[1] >= topv_count )
      return false;
    if ( tope.m_topvi[0] == tope.m_topvi[1] )
      return false;

    const ON_MeshTopologyVertex& topv0 = m_topv[tope.m_topvi[0]];
    for ( j = 0; j < topv0.m_tope_count; j++ ) {
      if ( topv0.m_topei[j] == topei )
        break;
    }
    if ( j >= topv0.m_tope_count )
      return false; // start vtx not linked to edge

    const ON_MeshTopologyVertex& topv1 = m_topv[tope.m_topvi[1]];
    for ( j = 0; j < topv1.m_tope_count; j++ ) {
      if ( topv1.m_topei[j] == topei )
        break;
    }
    if ( j >= topv1.m_tope_count )
      return false; // end vtx not linked to edge

    if ( tope.m_topf_count < 0 )
      return false;
    if ( tope.m_topf_count == 0 && tope.m_topfi )
      return false; // array should be NULL
    if ( tope.m_topf_count > 0 && !tope.m_topfi )
      return false; // array should not be NULL
    for ( j = 0; j < tope.m_topf_count; j++ ) {
      fi = tope.m_topfi[j];
      if ( fi < 0 || fi >= f_count )
        return false;
      const ON_MeshTopologyFace& topf = m_topf[fi];
      for ( k = 0; k < 4; k++ ) {
        if ( topf.m_topei[k] == topei )
          break;
      }
      if ( k >= 4 )
        return false; // edge not in face's list
    }
  }

  // check faces
  for ( fi = 0; fi < f_count; fi++ ) {
    topfi = fi;
    const ON_MeshTopologyFace& topf = m_topf[topfi];
    const ON_MeshFace& f = m_mesh->m_F[fi];
    if ( topf.m_topei[0] < 0 || topf.m_topei[0] >= tope_count )
      return false;
    if ( topf.m_topei[1] < 0 || topf.m_topei[1] >= tope_count )
      return false;
    if ( topf.m_topei[2] < 0 || topf.m_topei[2] >= tope_count )
      return false;
    if ( topf.m_topei[3] < 0 || topf.m_topei[3] >= tope_count )
      return false;
    tfvi[0] = m_topv_map[f.vi[0]];
    tfvi[1] = m_topv_map[f.vi[1]];
    tfvi[2] = m_topv_map[f.vi[2]];
    tfvi[3] = m_topv_map[f.vi[3]];
    if (    topf.m_topei[0] != 0 || topf.m_topei[1] != 0 
         || topf.m_topei[2] != 0 || topf.m_topei[3] != 0 ) {
      if ( !f.IsValid(v_count) )
        return false;
      if ( f.IsTriangle() ) {
        if (topf.m_topei[2] != topf.m_topei[3] )
          return false;
        jmax = 3;
      }
      else {
        if (topf.m_topei[2] == topf.m_topei[3] )
          return false;
        jmax = 4;
      }
      for ( j = 0; j < jmax; j++ ) {
        const ON_MeshTopologyEdge& tope = m_tope[topf.m_topei[j]];
        for ( k = 0; k < tope.m_topf_count; k++ ) {
          if ( tope.m_topfi[k] == topfi )
            break;
        }
        if ( k >= tope.m_topf_count )
          return false;

        // topedge m_tope[topf.m_topei[j]] ENDS at topvtx m_topv[tfvi[j]]
        if ( topf.m_reve[j] ) {
          if ( tope.m_topvi[1] != tfvi[(j+3)%4] )
            return false;
          if ( tope.m_topvi[0] != tfvi[j] )
            return false;
        }
        else {
          if ( tope.m_topvi[0] != tfvi[(j+3)%4] )
            return false;
          if ( tope.m_topvi[1] != tfvi[j] )
            return false;
        }
      }      
    }
    else {
      // all topf.m_topei[] must be zeros
      if (    topf.m_topei[0] != 0 || topf.m_topei[1] != 0 
           || topf.m_topei[2] != 0 || topf.m_topei[3] != 0 )
        return false;
    }
  }
  return true;
}

void ON_MeshTopology::Dump( ON_TextLog& dump ) const
{
  ON_3fPoint p;
  int vi, ei, fi, j;
  const int topv_count = m_topv.Count();
  const int tope_count = m_tope.Count();
  const int topf_count = m_topf.Count();

  // topological vertex information
  for ( vi = 0; vi < topv_count; vi++ ) {
    const ON_MeshTopologyVertex& v = m_topv[vi];
    dump.Print("topv %d: ",vi);
    if (m_mesh) {
      // dump geometric location of this vertex
      p = m_mesh->m_V[v.m_vi[0]];
      dump.Print("{%g,%g,%g} ", p.x, p.y, p.z);
    }

    // list all mesh geometry viertices that are coincident with this
    // topological vertex
    dump.Print("(");
    for ( j = 0; j < v.m_v_count; j++ ) {
      if ( j )
        dump.Print(",");
      dump.Print("m_V[%d]",v.m_vi[j]);
    }

    // list all toplogical edges that begin/end at this topological vertex
    dump.Print(") (");
    for ( j = 0; j < v.m_tope_count; j++ ) {
      if ( j )
        dump.Print(",");
      dump.Print("%d",v.m_topei[j]);
    }
    dump.Print(")\n");
  }

  // topological edge information
  for ( ei = 0; ei < tope_count; ei++ ) {
    const ON_MeshTopologyEdge& e = m_tope[ei];
    dump.Print("tope %d: topv%d to topvv%d (", ei, e.m_topvi[0], e.m_topvi[1] );
    // list all mesh topolical faces attached to this topolical edge
    for ( j = 0; j < e.m_topf_count; j++ ) {
      if (j)
        dump.Print(",");
      dump.Print("f%d",e.m_topfi[j]);
    }
    dump.Print(")\n");
  }

  // topological face information
  // mesh m_F[] index = mesh topology m_topf[] index
  for ( fi = 0; fi < topf_count; fi++ ) {
    const ON_MeshTopologyFace& f = m_topf[fi];
    dump.Print("topf %d: (",fi);
    for ( j = 0; j < 4; j++ ) {
      if ( j == 3 && f.m_topei[3] == f.m_topei[2] )
        break; // triangular face
      if (j)
        dump.Print(",");
      dump.Print("%ce%d",f.m_reve[j]?'-':'+',f.m_topei[j]);
    }
    dump.Print(")\n");
  }
}


bool ON_MeshTopology::Create()
{
  // When -1 == m_b32IsValid, this ON_MeshTopology
  // is the m_top field on an ON_Mesh and is being
  // created in an ON_Mesh::Topology() call and a
  // sleep lock is used to keep ON_Mesh::Topology()
  // thread safe.
  //
  // When 0 == m_b32IsValid, this ON_MeshTopology
  // is being created stand alone.
  //
  // When 1 == m_b32IsValid, this ON_MeshTopology
  // is already created and valid.

  if ( 1 == m_b32IsValid )
    return true;

  const int b32IsValid0 = m_b32IsValid;

  if ( 0 == b32IsValid0 )
  {
    // no sleep lock is being used
    m_b32IsValid = -1;
  }
  int b32IsValid = b32IsValid0;

  while ( 0 == b32IsValid || -1 == b32IsValid ) 
  {
    // while() is for flow control - this is a while() {... break;} statment.
    Destroy();
    b32IsValid = 0;

    // build vertex topology information
    const int fcount = m_mesh->FaceCount();
    const int vcount = m_mesh->VertexCount();
    if ( 0 == vcount )
      break;

    int* vindex = GetIntArray(vcount);
    m_topv_map.SetCapacity( vcount );
    m_topv_map.SetCount( vcount );
    if (  0 == m_mesh->GetVertexLocationIds( 0, m_topv_map.Array(), vindex ) )
    {
      Destroy();
      break;
    }

    {
      int topv_count = m_topv_map[vindex[vcount-1]]+1;
      m_topv_map.SetCapacity( vcount );
      m_topv_map.SetCount( vcount );
      m_topv.SetCapacity( topv_count );
      int vt0, vt1, topvi;
      ON_3fPoint p0;
      for (vt0 = 0; vt0 < vcount; vt0 = vt1)
      {
        topvi = m_topv.Count();
#if defined(ON_DEBUG)
        if ( topvi != m_topv_map[vindex[vt0]] )
        {
          // 20 April 2010 Dale Lear:
          //  If you get this error, save the mesh and tell Dale Lear.
          ON_ERROR("ON_MeshTopology::Create() - topvi != vertex id from GetVertexLocationIds()");
        }
#endif
        ON_MeshTopologyVertex& topv = m_topv.AppendNew();
        topv.m_vi = vindex+vt0;
        for ( vt1=vt0+1; vt1<vcount && topvi == m_topv_map[vindex[vt1]]; vt1++ ) {
          // empty
        }
        topv.m_v_count = vt1-vt0;
      }
    }

    // build edge topology information
    const int topv_count = m_topv.Count();
    if ( topv_count >= 2 ) 
    {
      bool rc = false;
      int ei, ecnt, fi, vi0, vi1, efi, topfvi[4];
      ON_MeshFace f;

      if ( fcount > 0 && vcount > 0 ) 
      {
        // When working on this code be sure to test bug# 9271 and 9254 and file fsv_r4.3dm
        ON_Workspace ws;
        struct ON_MeshFaceSide* e = (struct ON_MeshFaceSide*)ws.GetMemory( 4*fcount*sizeof(*e) );
        ecnt = m_mesh->GetMeshFaceSideList( m_topv_map.Array(), e );
        
        if ( ecnt > 0 ) 
        {
          rc = true;
          ON_SortMeshFaceSidesByVertexIndex( ecnt, e );

          // count number of topological edges and allocate storage
          int etop_count = 0;
          ei = 0;
          while( ei < ecnt ) 
          {
            vi0 = e[ei].vi[0];
            vi1 = e[ei].vi[1];
            ei++;
            while (ei < ecnt && e[ei].vi[0] == vi0 && e[ei].vi[1] == vi1 )
              ei++;
            etop_count++;
          }
          m_tope.SetCapacity(etop_count);

          // fill in the m_tope[] array information
          int* efindex = GetIntArray(ecnt);
          for ( ei = 0; ei < ecnt; /*empty*/ )
          {
            ON_MeshTopologyEdge& tope = m_tope.AppendNew();
            tope.m_topvi[0] = vi0 = e[ei].vi[0];
            tope.m_topvi[1] = vi1 = e[ei].vi[1];
            tope.m_topfi = efindex;
            tope.m_topf_count = 0;
            *efindex++ = e[ei].fi;
            tope.m_topf_count++;
            ei++;
            while( ei < ecnt && e[ei].vi[0] == vi0 && e[ei].vi[1] == vi1 ) 
            {
              *efindex++ = e[ei].fi;
              tope.m_topf_count++;
              ei++;
            }
          }
          efindex = 0; // memory deallocated by ~ON_MeshTopology()

          // connect vertices to edges;
          ecnt = m_tope.Count();
          int* ve_count = (int*)onmalloc(topv_count*sizeof(*ve_count));
          // set ve_count[topvi] = number of edges that begin or end at m_topv[topvi]
          memset( ve_count, 0, topv_count*sizeof(*ve_count));
          for ( ei = 0; ei < ecnt; ei++ ) {
            const ON_MeshTopologyEdge& tope = m_tope[ei];
            ve_count[tope.m_topvi[0]]++;
            ve_count[tope.m_topvi[1]]++;
          }
          // allocate and distribute storage for the mopv.m_topei[] array
          int* vei = GetIntArray(2*ecnt);
          for ( vi0 = 0; vi0 < topv_count; vi0++ ) {
            ON_MeshTopologyVertex& topv = m_topv[vi0];
            if ( ve_count[vi0] > 0 ) {
              topv.m_topei = vei;
              vei += ve_count[vi0];
            }
          }
          onfree(ve_count); ve_count = 0;
          vei = 0; // memory deallocated by ~ON_MeshTopology()

          // fill in the m_topv[].m_topei[] values
          for ( ei = 0; ei < ecnt; ei++ ) {
            ON_MeshTopologyEdge& tope = m_tope[ei];
            ON_MeshTopologyVertex& topv0 = m_topv[tope.m_topvi[0]];
            ON_MeshTopologyVertex& topv1 = m_topv[tope.m_topvi[1]];
            vei = const_cast<int*>(topv0.m_topei);
            vei[topv0.m_tope_count++] = ei;
            vei = const_cast<int*>(topv1.m_topei);
            vei[topv1.m_tope_count++] = ei;
          }

          // build face topology information
          m_topf.SetCapacity(fcount);
          m_topf.SetCount(fcount);
          memset( m_topf.Array(), 0, fcount*sizeof(ON_MeshTopologyFace) );
          for ( fi = 0; fi < fcount; fi++ ) {
            ON_MeshTopologyFace& f = m_topf[fi];
            f.m_topei[0] = -1;
            f.m_topei[1] = -1;
            f.m_topei[2] = -1;
            f.m_topei[3] = -1;
          }
          for ( ei = 0; ei < ecnt; ei++ ) {
            ON_MeshTopologyEdge& tope = m_tope[ei];
            for (efi = 0; efi < tope.m_topf_count; efi++ ) {
              // Because ON_MeshFace.vi[2] == ON_MeshFace.vi[3] for triangles,
              // we have topf.m_topei[j] BEGIN at ON_MeshFace.vi[(j+3)%4] and END at ON_MeshFace.vi[j]
              fi = tope.m_topfi[efi];
              f = m_mesh->m_F[fi];
              topfvi[0] = m_topv_map[f.vi[0]];
              topfvi[1] = m_topv_map[f.vi[1]];
              topfvi[2] = m_topv_map[f.vi[2]];
              topfvi[3] = m_topv_map[f.vi[3]];
              ON_MeshTopologyFace& topf = m_topf[fi];
              vi0 = tope.m_topvi[0];
              vi1 = tope.m_topvi[1];
              // unroll loop for speed
              if      ( vi0 == topfvi[3] && vi1 == topfvi[0] ) {
                topf.m_topei[0] = ei;
                topf.m_reve[0] = 0;
              }
              else if ( vi0 == topfvi[0] && vi1 == topfvi[1] ) {
                topf.m_topei[1] = ei;
                topf.m_reve[1] = 0;
              }
              else if ( vi0 == topfvi[1] && vi1 == topfvi[2] ) {
                topf.m_topei[2] = ei;
                topf.m_reve[2] = 0;
              }
              else if ( vi0 == topfvi[2] && vi1 == topfvi[3] ) {
                topf.m_topei[3] = ei;
                topf.m_reve[3] = 0;
              }
              else if ( vi1 == topfvi[3] && vi0 == topfvi[0] ) {
                topf.m_topei[0] = ei;
                topf.m_reve[0] = 1;
              }
              else if ( vi1 == topfvi[0] && vi0 == topfvi[1] ) {
                topf.m_topei[1] = ei;
                topf.m_reve[1] = 1;
              }
              else if ( vi1 == topfvi[1] && vi0 == topfvi[2] ) {
                topf.m_topei[2] = ei;
                topf.m_reve[2] = 1;
              }
              else if ( vi1 == topfvi[2] && vi0 == topfvi[3] ) {
                topf.m_topei[3] = ei;
                topf.m_reve[3] = 1;
              }
            }
          }
          for ( fi = 0; fi < fcount; fi++ ) {
            ON_MeshTopologyFace& f = m_topf[fi];
            bool bIsGood = false;
            if (    f.m_topei[0] >= 0 && f.m_topei[1] >= 0 && f.m_topei[2] >=0 
                 && f.m_topei[0] != f.m_topei[1] 
                 && f.m_topei[1] != f.m_topei[2] 
                 && f.m_topei[2] != f.m_topei[0] 
                 ) {
              if ( m_mesh->m_F[fi].IsTriangle() ) {
                bIsGood = true;
                f.m_topei[3] = f.m_topei[2];
              }
              else if (   f.m_topei[3] >= 0 
                       && f.m_topei[0] != f.m_topei[3] 
                       && f.m_topei[1] != f.m_topei[3] 
                       && f.m_topei[2] != f.m_topei[3] ) {
                bIsGood = true;
              }
            }
            if ( !bIsGood ) {
              f.m_topei[0] = 0;
              f.m_topei[1] = 0;
              f.m_topei[2] = 0;
              f.m_topei[3] = 0;
              f.m_reve[0] = 0;
              f.m_reve[1] = 0;
              f.m_reve[2] = 0;
              f.m_reve[3] = 0;
            }
          }

        }
      }
    }

    b32IsValid = 1;
    break;
  }

  if ( -1 != b32IsValid0 )
  {
    // no sleep lock is in use
    m_b32IsValid = b32IsValid;
  }

  if ( 1 != b32IsValid )
  {
    Destroy();
  }

  return (1 == b32IsValid);
}

struct tagFPT
{
  int x, y, z;
};

//static int compare_fpt( const struct tagFPT* a, const struct tagFPT* b )
//{
//  if ( a->x < b->x )
//    return -1;
//  if ( a->x > b->x )
//    return 1;
//  if ( a->y < b->y )
//    return -1;
//  if ( a->y > b->y )
//    return 1;
//  if ( a->z < b->z )
//    return -1;
//  if ( a->z > b->z )
//    return 1;
//  return 0;
//}

static int compare_pmark( const int* a, const int* b )
{
  if ( *a < *b )
    return -1;
  if ( *a > *b )
    return 1;
  if ( a < b )
    return -1;
  if ( a > b )
    return 1;
  return 0;
}

static int compare_vmap( const void* a, const void* b )
{
  int i = *((int*)a);
  int j = *((int*)b);
  if ( i < j )
    return -1;
  if ( i > j )
    return 1;
  return 0;
}

static int DupVertex( ON_Mesh* mesh, int vi )
{
  int vertex_count = mesh->m_V.Count();
  ON_3fVector n;
  ON_3fPoint v;
  ON_Color c;
  ON_2fPoint t;
  ON_SurfaceCurvature k;
  v = mesh->m_V[vi];
  mesh->m_V.Append(v);
  if (mesh->m_N.Count() == vertex_count) {
    n = mesh->m_N[vi];
    mesh->m_N.Append(n);
  }
  if (mesh->m_T.Count() == vertex_count) {
    t = mesh->m_T[vi];
    mesh->m_T.Append(t);
  }
  if (mesh->m_K.Count() == vertex_count) {
    k = mesh->m_K[vi];
    mesh->m_K.Append(k);
  }
  if (mesh->m_C.Count() == vertex_count) {
    c = mesh->m_C[vi];
    mesh->m_C.Append(c);
  }
  return vertex_count;
}


static int AddToPartition( ON_Mesh* mesh, ON_SimpleArray<int>& pmark, int vi, int partition_mark, int fi0 )
{
  bool b = true;
  int i, fi, new_vi, face_count, *fvi;
  i = pmark[vi];
  if ( !i ) {
    pmark[vi] = partition_mark;
  }
  else if ( i != partition_mark && i != partition_mark-1 ) {
    if ( i == partition_mark-2 )
      pmark[vi] = partition_mark-1; // vertex vi shared between two partitions
    else {
      new_vi = DupVertex(mesh,vi);
      face_count = mesh->m_F.Count();
      for ( fi = fi0; fi < face_count; fi++ ) {
        fvi = mesh->m_F[fi].vi;
        if ( fvi[0] == vi )
          fvi[0] = new_vi;
        if ( fvi[1] == vi )
          fvi[1] = new_vi;
        if ( fvi[2] == vi )
          fvi[2] = new_vi;
        if ( fvi[3] == vi )
          fvi[3] = new_vi;
      }
      pmark.Append(partition_mark);
    }
  }
  else
    b = false; // vertex already in this partition
  return b;
}

bool ON_MeshPartition_IsValid( const ON_MeshPartition& p, const ON_Mesh& mesh )
{
  bool rc = false;
  const int* fvi;
  int j, tcnt, fi, parti, partcount;
  partcount = p.m_part.Count();
  rc = ( partcount > 0 );
  if ( p.m_partition_max_triangle_count < 1 )
    rc = false;
  if ( p.m_partition_max_vertex_count < 3 )
    rc = false;
  for ( parti = 0; parti < partcount && rc; parti++ ) {
    const ON_MeshPart& part = p.m_part[parti];
    if ( part.triangle_count < 1 )
      rc = false;
    if ( part.vertex_count < 1 )
      rc = false;
    if ( part.vertex_count != part.vi[1] - part.vi[0] )
      rc = false;
    tcnt = 0;
    for ( fi = part.fi[0]; fi < part.fi[1]; fi++ ) {
      fvi = mesh.m_F[fi].vi;
      tcnt++;
      if ( fvi[2] != fvi[3] )
        tcnt++;
      for ( j = 0; j < 4; j++ ) {
        if ( fvi[j] < part.vi[0] || fvi[j] >= part.vi[1] )
          rc = false;
      }
    }
    if ( tcnt != part.triangle_count )
      rc = false;
    if ( parti ) {
      if ( part.fi[0] != p.m_part[parti-1].fi[1] )
        rc = false;
      if ( part.vi[0] > p.m_part[parti-1].vi[1] )
        rc = false;
    }
  }
  if ( partcount ) {
    if ( p.m_part[0].fi[0] != 0 || p.m_part[partcount-1].fi[1] != mesh.m_F.Count() )
      rc = false;
  }
  return rc;
}

static
bool ON_Mesh_CreatePartition_SortFaces(const ON_Mesh& mesh, int* fmap )
{
  ON_RTree rt;
  if ( !rt.CreateMeshFaceTree(&mesh) )
    return false;

  const int mesh_F_count = mesh.m_F.Count();
  int fmap_count = 0;

  const ON_RTreeBranch* branch;
  ON_RTreeIterator rit(rt);
  for ( rit.First(); 0 != (branch = rit.Value()); rit.Next() )
  {
    if ( fmap_count > mesh_F_count )
      break;
    fmap[fmap_count++] = (int)(branch->m_id);
  }  

  if ( fmap_count != mesh_F_count )
  {
    ON_ERROR("ON_Mesh::CreatePartition unable to get fmap[]");
    return false;
  }

  return true;
}

const ON_MeshPartition* ON_Mesh::CreatePartition( 
              int partition_max_vertex_count, // maximum number of vertices in a partition
              int partition_max_triangle_count // maximum number of triangles in a partition
              )
{
  ON_Workspace ws;
  bool bNeedFaceSort = true;
  if ( m_partition ) 
  {
    bNeedFaceSort = false;
    if (   m_partition->m_partition_max_triangle_count > partition_max_triangle_count
        || m_partition->m_partition_max_vertex_count > partition_max_vertex_count )
        DestroyPartition();
  }
  if ( !m_partition ) 
  {
    // TODO: create one
    struct ON_MeshPart p;
    int vertex_count = VertexCount();
    const int face_count = FaceCount();
    const int triangle_count = TriangleCount() + 2*QuadCount();
    m_partition = new ON_MeshPartition();
    int k = triangle_count/partition_max_triangle_count;
    if ( k < vertex_count/partition_max_vertex_count )
      k = vertex_count/partition_max_vertex_count;
    k++;
    m_partition->m_part.Reserve(k);
    if ( vertex_count   <= partition_max_vertex_count && 
         triangle_count <= partition_max_triangle_count ) 
    {
      m_partition->m_partition_max_vertex_count = vertex_count;
      m_partition->m_partition_max_triangle_count = triangle_count;
      memset(&p,0,sizeof(p));
      p.vi[0] = 0;
      p.vi[1] = vertex_count;
      p.fi[0] = 0;
      p.fi[1] = face_count;
      p.vertex_count = vertex_count;
      p.triangle_count = triangle_count;
      m_partition->m_part.Append(p);
    }
    else 
    {
      int fi;
      int* fvi;
      DestroyTopology();

      // sort faces
      int* fmap = (int*)ws.GetMemory( face_count*sizeof(fmap[0]) );
      if ( !ON_Mesh_CreatePartition_SortFaces(*this,fmap) )
      {
        for ( fi = 0; fi < face_count; fi++ )
          fmap[fi] = fi;
      }

      //ON_SimpleArray<struct tagFPT> fpt(face_count);
      //fpt.SetCount(face_count);
      //if ( HasTextureCoordinates() )
      //{
      //  ON_2fPoint fcenter;
      //  ON_BoundingBox bbox = ON_PointListBoundingBox(2,0,m_T.Count(),2,&m_T[0].x);
      //  const ON_Interval txdom(bbox.m_min.x,bbox.m_max.x);
      //  const ON_Interval tydom(bbox.m_min.y,bbox.m_max.y);
      //  for ( fi = 0; fi < face_count; fi++ ) {
      //    fvi = m_F[fi].vi;
      //    if ( fvi[2] == fvi[3] ) {
      //      fcenter = 0.333333333333333333f*(m_T[fvi[0]] + m_T[fvi[1]] + m_T[fvi[2]]);
      //    }
      //    else {
      //      fcenter = 0.25f*(m_T[fvi[0]] + m_T[fvi[1]] + m_T[fvi[2]] + m_T[fvi[3]]);
      //    }
      //    fpt[fi].x = (int)floor(txdom.NormalizedParameterAt(fcenter.x)*100);
      //    fpt[fi].y = (int)floor(tydom.NormalizedParameterAt(fcenter.y)*100);
      //    fpt[fi].z = 0;
      //  }
      //}
      //else
      //{
      //  ON_3dPoint fcenter;
      //  ON_BoundingBox bbox = BoundingBox();
      //  const ON_Interval vxdom(bbox.m_min.x,bbox.m_max.x);
      //  const ON_Interval vydom(bbox.m_min.y,bbox.m_max.y);
      //  const ON_Interval vzdom(bbox.m_min.z,bbox.m_max.z);
      //  for ( fi = 0; fi < face_count; fi++ ) {
      //    fvi = m_F[fi].vi;
      //    if ( fvi[2] == fvi[3] ) {
      //      fcenter = 0.333333333333333333f*(m_V[fvi[0]] + m_V[fvi[1]] + m_V[fvi[2]]);
      //    }
      //    else {
      //      fcenter = 0.25f*(m_V[fvi[0]] + m_V[fvi[1]] + m_V[fvi[2]] + m_V[fvi[3]]);
      //    }
      //    fpt[fi].x = (int)floor(vxdom.NormalizedParameterAt(fcenter.x)*100);
      //    fpt[fi].y = (int)floor(vydom.NormalizedParameterAt(fcenter.y)*100);
      //    fpt[fi].z = (int)floor(vzdom.NormalizedParameterAt(fcenter.z)*100);
      //  }
      //}
      //fpt.Sort( ON::quick_sort, fmap, compare_fpt ); 
      m_F.Permute( fmap );
      if ( m_FN.Count() == face_count )
        m_FN.Permute( fmap );

      // sort vertices
      ON_SimpleArray<int>pmark(2*vertex_count);
      pmark.SetCount(vertex_count);
      pmark.Zero();
      int fi0, fi1, partition_mark, partition_vertex_count, partition_triangle_count;
      fi1 = 0;
      fi0 = 0;
      for ( partition_mark = 3, fi0 = 0; fi0 < face_count; fi0 = fi1, partition_mark += 2 ) 
      {
        partition_vertex_count = 0;
        partition_triangle_count = 0;
        for ( fi1 = fi0; 
              fi1 < face_count
              && partition_triangle_count+2 <= partition_max_triangle_count
              && partition_vertex_count+4 <= partition_max_vertex_count;
              fi1++ ) 
        {
          fvi = m_F[fi1].vi;
          partition_triangle_count++;
          if ( AddToPartition( this, pmark, fvi[0], partition_mark, fi0 ) )
            partition_vertex_count++;
          if ( AddToPartition( this, pmark, fvi[1], partition_mark, fi0 ) )
            partition_vertex_count++;
          if ( AddToPartition( this, pmark, fvi[2], partition_mark, fi0 ) )
            partition_vertex_count++;
          if ( fvi[2] != fvi[3] ) {
            partition_triangle_count++; // quads = 2 triangles
            if ( AddToPartition( this, pmark, fvi[3], partition_mark, fi0 ) )
              partition_vertex_count++;
          }
        }
        if ( fi0 < fi1 ) {
          struct ON_MeshPart p;
          memset(&p,0,sizeof(p));
          p.fi[0] = fi0;
          p.fi[1] = fi1;
          p.vertex_count = partition_vertex_count;
          p.triangle_count = partition_triangle_count;
          m_partition->m_part.Append(p);
        }
        if ( partition_triangle_count > m_partition->m_partition_max_triangle_count )
          m_partition->m_partition_max_triangle_count = partition_triangle_count;
        if ( partition_vertex_count > m_partition->m_partition_max_vertex_count )
          m_partition->m_partition_max_vertex_count = partition_vertex_count;
      }

      // the calls to AddToPartition() may have increased vertex count
      vertex_count = m_V.Count();

      // sort vertices
      int* vmap = (int*)ws.GetMemory( vertex_count*sizeof(vmap[0]) );
      pmark.Sort( ON::quick_sort, vmap, compare_pmark );
      m_V.Permute( vmap );
      if ( m_N.Count() == vertex_count )
        m_N.Permute( vmap );
      if ( m_T.Count() == vertex_count )
        m_T.Permute( vmap );
      if ( m_K.Count() == vertex_count )
        m_K.Permute( vmap );
      if ( m_C.Count() == vertex_count )
        m_C.Permute( vmap );
      pmark.Permute( vmap );
      // pamv[] = inverse of mapv permutation
      int* pamv = (int*)ws.GetMemory( vertex_count*sizeof(pamv[0]) );
      ON_Sort( ON::quick_sort, pamv, vmap, vertex_count, sizeof(vmap[0]), compare_vmap );
      for ( fi = 0; fi < face_count; fi++ ) {
        fvi = m_F[fi].vi;
        fvi[0] = pamv[fvi[0]];
        fvi[1] = pamv[fvi[1]];
        fvi[2] = pamv[fvi[2]];
        fvi[3] = pamv[fvi[3]];
      }

      // fill in m_part.vi[]
      int m, pi, partition_count = m_partition->m_part.Count();
      int vi0, vi1, vi2, vi3;
      for (vi2 = 0; vi2 < vertex_count && pmark[vi2]<2; vi2++)
      {/*empty for body*/}
      vi3=vi2;
      for ( pi = 0; pi < partition_count; pi++ ) {
        vi0 = vi2;
        vi1 = vi3;
        m = 2*pi + 4;
        for ( vi2 = vi3; vi2 < vertex_count && pmark[vi2] <  m; vi2++) 
        {/*empty for body*/}
        for ( vi3 = vi2; vi3 < vertex_count && pmark[vi3] <= m; vi3++) 
        {/*empty for body*/}
        m_partition->m_part[pi].vi[0] = vi0;
        m_partition->m_part[pi].vi[1] = vi3;
      }
    }
    // debugging - test partition
    if ( m_partition && !ON_MeshPartition_IsValid( *m_partition, *this ) ) {
      delete m_partition;
      m_partition = 0;
    }
  }

  return m_partition;
}

const ON_MeshPartition* ON_Mesh::Partition() const
{
  return m_partition;
}

void ON_Mesh::DestroyPartition()
{
  if ( m_partition ) {
    delete m_partition;
    m_partition = 0;
  }
}

ON_MeshPartition::ON_MeshPartition()
{
  m_partition_max_vertex_count = 0;
  m_partition_max_triangle_count = 0;
  m_part = 0;
}

ON_MeshPartition::~ON_MeshPartition()
{
  m_part.Destroy();
}


ON_Mesh* ON_Mesh::MeshPart( 
  const ON_MeshPart& mesh_part,
  ON_Mesh* mesh 
  ) const
{
  if ( this == mesh )
  {
    ON_ERROR("ON_Mesh::MeshPart this == mesh");
    return 0;
  }

  if ( mesh )
    mesh->Destroy();

  if (    mesh_part.fi[0] < 0 
       || mesh_part.fi[1] > m_F.Count()
       || mesh_part.fi[0] > mesh_part.fi[1]
       )
  {
    ON_ERROR("ON_Mesh::MeshPart mesh_part.fi[] is not valid");
    return 0;
  }

  if (    mesh_part.vi[0] < 0
       || mesh_part.vi[1] > m_V.Count()
       || mesh_part.vi[0] >= mesh_part.vi[1]
       )
  {
    ON_ERROR("ON_Mesh::MeshPart mesh_part.vi[] is not valid");
    return 0;
  }

  const int submesh_V_count = mesh_part.vi[1] - mesh_part.vi[0];
  const int submesh_F_count = mesh_part.fi[1] - mesh_part.fi[0];

  const bool bHasVertexNormals = HasVertexNormals();
  const bool bHasTextureCoordinates = HasTextureCoordinates();
  const bool bHasVertexColors = HasVertexColors();
  const bool bHasFaceNormals = HasFaceNormals();
  const bool bHasSurfaceParameters = HasSurfaceParameters();
  const bool bHasPrincipalCurvatures = HasPrincipalCurvatures();
  const bool bHasHiddenVertices = HiddenVertexCount() > 0;

  ON_Mesh* submesh = (0 != mesh)
                   ? mesh
                   : new ON_Mesh(mesh_part.triangle_count,
                                 mesh_part.vertex_count,
                                 bHasVertexNormals,
                                 bHasTextureCoordinates
                                 );

  if ( bHasVertexColors )
    submesh->m_C.Reserve(submesh_V_count);
  if ( bHasSurfaceParameters )
    submesh->m_S.Reserve(submesh_V_count);
  if ( bHasPrincipalCurvatures )
    submesh->m_K.Reserve(submesh_V_count);
  if ( bHasHiddenVertices )
    submesh->m_H.Reserve(submesh_V_count);
  if ( bHasFaceNormals )
    submesh->m_FN.Reserve(submesh_F_count);

  // put vertex information into submesh
  const int vi0 = mesh_part.vi[0];
  const int vi1 = mesh_part.vi[1];
  for ( int vi = vi0; vi < vi1; vi++ )
  {
    submesh->m_V.Append(m_V[vi]);
    if ( bHasVertexNormals )
      submesh->m_N.Append(m_N[vi]);
    if ( bHasTextureCoordinates )
      submesh->m_T.Append(m_T[vi]);
    if ( bHasVertexColors )
      submesh->m_C.Append(m_C[vi]);
    if ( bHasSurfaceParameters )
      submesh->m_S.Append(m_S[vi]);
    if ( bHasPrincipalCurvatures )
      submesh->m_K.Append(m_K[vi]);
    if ( bHasHiddenVertices )
    {
      bool bHidden = m_H[vi];
      submesh->m_H.Append(bHidden);
      if ( bHidden )
        submesh->m_hidden_count++;
    }
  }
  if ( submesh->m_hidden_count <= 0 )
  {
    submesh->m_H.Destroy();
    submesh->m_hidden_count = 0;
  }

  // put face information into submesh
  int bad_face_count = 0;
  const int fi0 = mesh_part.fi[0];
  const int fi1 = mesh_part.fi[1];
  for ( int fi = fi0; fi < fi1; fi++ )
  {
    ON_MeshFace f = m_F[fi];
    f.vi[0] -= vi0;
    f.vi[1] -= vi0;
    f.vi[2] -= vi0;
    f.vi[3] -= vi0;
    if (    f.vi[0] >= submesh_V_count || f.vi[0] < 0 
         || f.vi[1] >= submesh_V_count || f.vi[1] < 0 
         || f.vi[2] >= submesh_V_count || f.vi[2] < 0 
         || f.vi[3] >= submesh_V_count || f.vi[3] < 0 
         )
    {
      bad_face_count++;
      ON_ERROR("ON_Mesh::MeshPart Invalid face in partition");
      continue;
    }
    submesh->m_F.Append(f);
    if ( bHasFaceNormals )
      submesh->m_FN.Append(m_FN[fi]);
  }

  if ( submesh->m_F.Count() < 1 && bad_face_count > 0 )
  {
    if ( submesh != mesh )
      delete submesh;
    else
      mesh->Destroy();

    submesh = 0;
  }

  return submesh;
}

ON_Mesh* ON_Mesh::DuplicateFace( int face_index, ON_Mesh* mesh ) const
{
  if ( mesh == this )
    return 0;
  if ( 0 != mesh )
    mesh->Destroy();
  if ( face_index < 0 || face_index >= m_F.Count() )
    return 0;
  const int vcnt = m_V.Count();
  if ( vcnt < 3 )
    return 0;

  const ON_3dPoint* dV = ( HasDoublePrecisionVertices() && DoublePrecisionVerticesAreValid() )
                        ? DoublePrecisionVertices().Array()
                        : 0;
  const ON_3fPoint* fV = (0 == dV) ? m_V.Array() : 0;
  bool bHasFaceNormals = HasFaceNormals();
  bool bHasVertexNormals = HasVertexNormals();
  bool bHasVertexColors = HasVertexColors();
  bool bHasTextureCoordinates = HasTextureCoordinates();
  bool bHasSurfaceParameters = HasSurfaceParameters();
  bool bHasPrincipalCurvatures = HasPrincipalCurvatures();

  ON_MeshFace f = m_F[face_index];
  if ( dV )
  {
    if ( !f.IsValid(vcnt,dV) )
    {
      // invalid vertex indices - see if it can be fixed
      if ( !f.Repair(vcnt,dV) )
        return 0;
    }
  }
  else
  {
    if ( !f.IsValid(vcnt,fV) )
    {
      // invalid vertex indices - see if it can be fixed
      if ( !f.Repair(vcnt,fV) )
        return 0;
    }
  }
  const int newvcnt = f.IsTriangle() ? 3 : 4;
  if ( 0 == mesh )
    mesh = new ON_Mesh();
  ON_3dPointArray* newdV = 0;
  if ( dV )
  {
    newdV = &mesh->DoublePrecisionVertices();
    newdV->Reserve(newvcnt);
  }
  mesh->m_V.Reserve(newvcnt);
  mesh->m_F.Reserve(1);
  ON_MeshFace& newface = mesh->m_F.AppendNew();
  newface.vi[0] = 0;
  newface.vi[1] = 1;
  newface.vi[2] = 2;
  newface.vi[3] = (4 == newvcnt) ? 3 : newface.vi[2];

  if ( bHasFaceNormals )
  {
    mesh->m_FN.Reserve(1);
    mesh->m_FN.Append(m_FN[face_index]);
  }

  if ( bHasVertexNormals )
    mesh->m_N.Reserve(newvcnt);
  if ( bHasTextureCoordinates )
    mesh->m_T.Reserve(newvcnt);
  if ( bHasVertexColors )
    mesh->m_C.Reserve(newvcnt);
  if ( bHasSurfaceParameters )
    mesh->m_S.Reserve(newvcnt);
  if ( bHasPrincipalCurvatures )
    mesh->m_K.Reserve(newvcnt);
  for ( int vi = 0; vi < newvcnt; vi++ )
  {
    if ( dV )
      newdV->Append(dV[f.vi[vi]]);
    else
      mesh->m_V.Append(fV[f.vi[vi]]);
    if ( bHasVertexNormals )
      mesh->m_N.Append(m_N[f.vi[vi]]);
    if ( bHasTextureCoordinates )
      mesh->m_T.Append(m_T[f.vi[vi]]);
    if ( bHasVertexColors )
      mesh->m_C.Append(m_C[f.vi[vi]]);
    if ( bHasSurfaceParameters )
      mesh->m_S.Append(m_S[f.vi[vi]]);
    if ( bHasPrincipalCurvatures )
      mesh->m_K.Append(m_K[f.vi[vi]]);
  }
  if ( dV )
  {
    mesh->SetDoublePrecisionVerticesAsValid();
    mesh->UpdateSinglePrecisionVertices();
  }

  return mesh;
}


ON_OBJECT_IMPLEMENT(ON_MeshVertexRef,ON_Geometry,"C547B4BD-BDCD-49b6-A983-0C4A7F02E31A");

ON_OBJECT_IMPLEMENT(ON_MeshEdgeRef,ON_Geometry,"ED727872-463A-4424-851F-9EC02CB0F155");

ON_OBJECT_IMPLEMENT(ON_MeshFaceRef,ON_Geometry,"4F529AA5-EF8D-4c25-BCBB-162D510AA280");

ON_MeshVertexRef::ON_MeshVertexRef()
{
  m_mesh = 0;
  m_mesh_vi = -1;
  m_top_vi = -1;
}

ON_MeshVertexRef::~ON_MeshVertexRef()
{
  m_mesh = 0;
  m_mesh_vi = -1;
  m_top_vi = -1;
}

ON_MeshVertexRef& ON_MeshVertexRef::operator=(const ON_MeshVertexRef& src)
{
  if ( this != &src )
  {
    ON_Geometry::operator=(src);
    m_mesh = src.m_mesh;
    m_mesh_vi = src.m_mesh_vi;
    m_top_vi = src.m_top_vi;
  }
  return *this;
}


ON_BOOL32 ON_MeshVertexRef::IsValid( ON_TextLog* text_log ) const
{
  if ( 0 == m_mesh )
  {
    if ( 0 != text_log )
    {
      text_log->Print("m_mesh = NULL\n");
    }
    return false;
  }

  if ( -1 != m_mesh_vi )
  {
    if ( m_mesh_vi < 0 || m_mesh_vi >= m_mesh->m_V.Count() )
    {
      if ( 0 != text_log )
      {
        text_log->Print("m_mesh_vi = %d (should have 0 <= m_mesh_vi < %d)\n",m_mesh_vi,m_mesh->m_V.Count());
      }
      return false;
    }
  }
  else if ( -1 == m_top_vi )
  {
    if ( 0 != text_log )
    {
      text_log->Print("m_mesh_vi = -1 and m_top_vi = -1\n");
    }
    return false;
  }

  if ( -1 != m_top_vi )
  {
    const ON_MeshTopology* top = MeshTopology();
    if ( 0 == top )
    {
      if ( 0 != text_log )
      {
        text_log->Print("m_top_vi = %d and MeshTopology()=NULL\n",m_top_vi);
      }
      return false;
    }
    if ( m_top_vi < 0 || m_top_vi >= top->m_tope.Count() )
    {
      if ( 0 != text_log )
      {
        text_log->Print("m_top_vi = %d (should have 0 <= m_top_vi < %d)\n",m_top_vi,top->m_topv.Count());
      }
      return false;
    }

    if ( -1 != m_mesh_vi )
    {
      const ON_MeshTopologyVertex& topv = top->m_topv[m_top_vi];
      int i;
      for ( i = 0; i < topv.m_v_count; i++ )
      {
        if ( topv.m_vi[i] == m_mesh_vi )
          break;
      }
      if ( i >= topv.m_v_count )
      {
        if ( 0 != text_log )
        {
          text_log->Print("m_mesh_vi=%d is not in m_top->m_topv[m_top_vi=%d].m_vi[] array.\n",
                          m_mesh_vi,m_top_vi);
          
        }
        return false;
      }
    }
  }

  return true;
}

void ON_MeshVertexRef::Dump( ON_TextLog& text_log ) const
{
  text_log.Print("m_mesh=%08x m_mesh_vi=%d m_top_vi=%d\n",
                  m_mesh,m_mesh_vi,m_top_vi);
  ON_3dPoint v = Point();
  if ( v.IsValid() )
  {
    text_log.PushIndent();
    text_log.Print("Location: ");
    text_log.Print(v);
    text_log.Print("\n");
    text_log.PopIndent();
  }

}
unsigned int ON_MeshVertexRef::SizeOf() const
{
  unsigned int sz = sizeof(*this) - sizeof(ON_Geometry);
  sz += ON_Geometry::SizeOf();
  return sz;
}

ON::object_type ON_MeshVertexRef::ObjectType() const
{
  return ON::meshvertex_object;
}

// overrides of virtual ON_Geometry functions
int ON_MeshVertexRef::Dimension() const
{
  return 3;
}

ON_BOOL32 ON_MeshVertexRef::GetBBox(
       double* boxmin,
       double* boxmax,
       ON_BOOL32 bGrowBox
       ) const
{
  bool rc = false;
  ON_3dPoint v = Point();
  if ( v.IsValid() )
  {
    rc = ON_GetPointListBoundingBox( 3, 0, 1, 3, &v.x, boxmin, boxmax, bGrowBox?true:false );
  }
  return rc;
}

ON_BOOL32 ON_MeshVertexRef::Transform( 
       const ON_Xform& xform
       )
{
  return false;
}

const ON_MeshTopology* ON_MeshVertexRef::MeshTopology() const
{
  return (0 != m_mesh) ? &m_mesh->m_top : 0;
}

ON_3dPoint ON_MeshVertexRef::Point() const
{
  ON_3dPoint v = ON_UNSET_POINT;
  if ( 0 != m_mesh )
  {
    int vi = m_mesh_vi;
    if ( -1 == vi && m_top_vi >= 0 && m_top_vi < m_mesh->m_top.m_topv.Count() )
    {
      const ON_MeshTopologyVertex& topv = m_mesh->m_top.m_topv[m_top_vi];
      if ( topv.m_v_count > 0 )
        vi = topv.m_vi[0];
    }
    if ( vi >= 0 && vi < m_mesh->m_V.Count() )
      v = m_mesh->m_V[vi];
  }
  return v;
}

const ON_MeshTopologyVertex* ON_MeshVertexRef::MeshTopologyVertex() const
{
  const ON_MeshTopologyVertex* topv = 0;
  if ( 0 != m_mesh && m_top_vi >= 0 && m_top_vi < m_mesh->m_top.m_topv.Count() )
  {
    topv = &m_mesh->m_top.m_topv[m_top_vi];
  }
  return topv;
}

ON_MeshEdgeRef::ON_MeshEdgeRef()
{
  m_mesh = 0;
  m_top_ei = -1;
}

ON_MeshEdgeRef::~ON_MeshEdgeRef()
{
  m_mesh = 0;
  m_top_ei = -1;
}

ON_MeshEdgeRef& ON_MeshEdgeRef::operator=(const ON_MeshEdgeRef& src)
{
  if ( this != &src )
  {
    ON_Geometry::operator=(src);
    m_mesh = src.m_mesh;
    m_top_ei = src.m_top_ei;
  }
  return *this;
}


ON_BOOL32 ON_MeshEdgeRef::IsValid( ON_TextLog* text_log ) const
{
  if ( 0 == m_mesh)
  {
    if ( 0 != text_log )
    {
      text_log->Print("m_mesh = NULL\n");
    }
    return false;
  }

  if ( m_top_ei < 0 || m_top_ei >= m_mesh->m_top.m_tope.Count() )
  {
    if ( 0 != text_log )
    {
      text_log->Print("m_top_ei = %d (should have 0 <= m_top_ei < %d)\n",m_top_ei,m_mesh->m_top.m_tope.Count());
    }
    return false;
  }

  return true;
}

void ON_MeshEdgeRef::Dump( ON_TextLog& text_log ) const
{
  text_log.Print("m_mesh=%08x, m_top_ei=%d\n",m_mesh,m_top_ei);
  ON_Line line = Line();
  if ( line.from.IsValid() )
  {
    text_log.PushIndent();
    text_log.Print("Location: ");
    text_log.Print(line.from);
    text_log.Print(" to ");
    text_log.Print(line.to);
    text_log.Print("\n");
    text_log.PopIndent();
  }

}
unsigned int ON_MeshEdgeRef::SizeOf() const
{
  unsigned int sz = sizeof(*this) - sizeof(ON_Geometry);
  sz += ON_Geometry::SizeOf();
  return sz;
}

ON::object_type ON_MeshEdgeRef::ObjectType() const
{
  return ON::meshedge_object;
}

// overrides of virtual ON_Geometry functions
int ON_MeshEdgeRef::Dimension() const
{
  return 3;
}

ON_BOOL32 ON_MeshEdgeRef::GetBBox(
       double* boxmin,
       double* boxmax,
       ON_BOOL32 bGrowBox
       ) const
{
  bool rc = false;
  ON_Line line = Line();
  if ( line.from.IsValid() && line.to.IsValid() )
  {
    rc = ON_GetPointListBoundingBox( 3, 0, 2, 3, &line.from.x, boxmin, boxmax, bGrowBox?true:false );
  }
  return rc;
}

ON_BOOL32 ON_MeshEdgeRef::Transform( 
       const ON_Xform& xform
       )
{
  return false;
}

const ON_MeshTopology* ON_MeshEdgeRef::MeshTopology() const
{
  return (0 != m_mesh) ? &m_mesh->m_top : 0;
}

ON_Line ON_MeshEdgeRef::Line() const
{
  ON_Line line(ON_UNSET_POINT,ON_UNSET_POINT);
  const ON_MeshTopologyEdge* tope = MeshTopologyEdge();
  if ( 0 != tope )
  {
    ON_MeshVertexRef vr;
    vr.m_mesh = m_mesh;
    vr.m_top_vi = tope->m_topvi[0];
    line.from = vr.Point();
    if ( line.from.IsValid() )
    {
      vr.m_top_vi = tope->m_topvi[1];
      line.to = vr.Point();
      if ( !line.to.IsValid() )
        line.from = ON_UNSET_POINT;
    }
  }
  return line;
}

const ON_MeshTopologyEdge* ON_MeshEdgeRef::MeshTopologyEdge() const
{
  const ON_MeshTopologyEdge* tope = 0;
  if ( m_top_ei >= 0 )
  {
    const ON_MeshTopology* top = MeshTopology();
    if ( 0 != top && m_top_ei < top->m_tope.Count() )
      tope = &top->m_tope[m_top_ei];
  }
  return tope;
}



ON_MeshFaceRef::ON_MeshFaceRef()
{
  m_mesh = 0;
  m_mesh_fi = -1;
}

ON_MeshFaceRef::~ON_MeshFaceRef()
{
  m_mesh = 0;
  m_mesh_fi = -1;
}

ON_MeshFaceRef& ON_MeshFaceRef::operator=(const ON_MeshFaceRef& src)
{
  if ( this != &src )
  {
    ON_Geometry::operator=(src);
    m_mesh = src.m_mesh;
    m_mesh_fi = src.m_mesh_fi;
  }
  return *this;
}


ON_BOOL32 ON_MeshFaceRef::IsValid( ON_TextLog* text_log ) const
{
  if ( 0 == m_mesh)
  {
    if ( 0 != text_log )
    {
      text_log->Print("m_mesh = NULL\n");
    }
    return false;
  }

  if ( m_mesh_fi < 0 || m_mesh_fi >= m_mesh->m_F.Count() )
  {
    if ( 0 != text_log )
    {
      text_log->Print("m_mesh_fi = %d (should have 0 <= m_mesh_fi < %d)\n",m_mesh_fi,m_mesh->m_F.Count());
    }
    return false;
  }

  return true;
}

void ON_MeshFaceRef::Dump( ON_TextLog& text_log ) const
{
  text_log.Print("m_mesh=%08x, m_mesh_fi=%d\n",m_mesh,m_mesh_fi);
}

unsigned int ON_MeshFaceRef::SizeOf() const
{
  unsigned int sz = sizeof(*this) - sizeof(ON_Geometry);
  sz += ON_Geometry::SizeOf();
  return sz;
}

ON::object_type ON_MeshFaceRef::ObjectType() const
{
  return ON::meshface_object;
}

// overrides of virtual ON_Geometry functions
int ON_MeshFaceRef::Dimension() const
{
  return 3;
}

ON_BOOL32 ON_MeshFaceRef::GetBBox(
       double* boxmin,
       double* boxmax,
       ON_BOOL32 bGrowBox
       ) const
{
  bool rc = false;
  if ( 0 != m_mesh && m_mesh_fi >= 0 && m_mesh_fi < m_mesh->m_F.Count() )
  {
    const int vcnt = m_mesh->m_V.Count();
    const int* Fvi = m_mesh->m_F[m_mesh_fi].vi;
    ON_3dPoint v[4];
    //int count = 0;
    int i;
    for ( i = 0; i < 4; i++ )
    {
      if ( Fvi[i] >= 0 && Fvi[i] < vcnt )
      {
        v[i] = m_mesh->m_V[Fvi[i]];
      }
      else
        return false;
    }
    rc = ON_GetPointListBoundingBox( 3, 0, 4, 3, &v[0].x, boxmin, boxmax, bGrowBox?true:false );
  }
  return rc;
}

ON_BOOL32 ON_MeshFaceRef::Transform( 
       const ON_Xform& xform
       )
{
  return false;
}

const ON_MeshTopology* ON_MeshFaceRef::MeshTopology() const
{
  return (0 != m_mesh) ? &m_mesh->m_top : 0;
}



const ON_MeshFace* ON_MeshFaceRef::MeshFace() const
{
  const ON_MeshFace* f = 0;
  if ( 0 != m_mesh && m_mesh_fi >= 0 && m_mesh_fi < m_mesh->m_F.Count() )
  {
    f = &m_mesh->m_F[m_mesh_fi];
  }
  return f;
}


const ON_MeshTopologyFace* ON_MeshFaceRef::MeshTopologyFace() const
{
  const ON_MeshTopologyFace* topf = 0;
  if ( m_mesh_fi >= 0 )
  {
    const ON_MeshTopology* top = MeshTopology();
    if ( 0 != top && m_mesh_fi < top->m_topf.Count() )
      topf = &top->m_topf[m_mesh_fi];
  }
  return topf;
}

ON_MeshVertexRef ON_Mesh::VertexRef(int mesh_V_index) const
{
  ON_MeshVertexRef vr;
  if ( mesh_V_index >= 0 && mesh_V_index < m_V.Count() )
  {
    vr.m_mesh = this;
    vr.m_mesh_vi = mesh_V_index;
    if ( m_top.m_topv_map.Count() == m_V.Count() )
    {
      vr.m_top_vi = m_top.m_topv_map[mesh_V_index];
    }
  }

  return vr;
}

ON_MeshVertexRef ON_Mesh::VertexRef(ON_COMPONENT_INDEX ci) const
{
  ON_MeshVertexRef vr;

  //int vertex_index = -1;
  switch (ci.m_type)
  {
  case ON_COMPONENT_INDEX::meshtop_vertex:
    vr = m_top.VertexRef(ci);
    break;
  case ON_COMPONENT_INDEX::mesh_vertex:
    if ( ci.m_index >= 0 && ci.m_index < m_V.Count() )
    {
      vr.m_mesh = this;
      vr.m_mesh_vi = ci.m_index;
      if ( m_top.m_topv_map.Count() == m_V.Count() )
      {
        vr.m_top_vi = m_top.m_topv_map[vr.m_mesh_vi];
      }
    }
    break;
  default:
    // intentionally skipping other enum values (also quiets gcc warnings)
    break;
  }

  return vr;
}


ON_MeshEdgeRef ON_Mesh::EdgeRef(int tope_index) const
{
  return m_top.EdgeRef(tope_index);
}

ON_MeshEdgeRef ON_Mesh::EdgeRef(ON_COMPONENT_INDEX ci) const
{
  return m_top.EdgeRef(ci);
}

ON_MeshFaceRef ON_Mesh::FaceRef(int mesh_F_index) const
{
  ON_MeshFaceRef fr;

  if ( mesh_F_index >= 0 && mesh_F_index < m_F.Count() )
  {
    fr.m_mesh = this;
    fr.m_mesh_fi = mesh_F_index;
  }

  return fr;
}

ON_MeshFaceRef ON_Mesh::FaceRef(ON_COMPONENT_INDEX ci) const
{
  ON_MeshFaceRef fr;

  if ( ci.m_type == ON_COMPONENT_INDEX::mesh_face )
  {
    if ( ci.m_index >= 0 && ci.m_index < m_F.Count() )
    {
      fr.m_mesh = this;
      fr.m_mesh_fi = ci.m_index;
    }
  }

  return fr;
}

ON_MeshVertexRef ON_MeshTopology::VertexRef(ON_COMPONENT_INDEX ci) const
{
  ON_MeshVertexRef vr;
  if ( ci.m_index >= 0 )
  {
    switch(ci.m_type)
    {
    case ON_COMPONENT_INDEX::mesh_vertex:
      if (m_mesh)
      {
        vr = m_mesh->VertexRef(ci);
      }
      break;
    case ON_COMPONENT_INDEX::meshtop_vertex:
      if ( ci.m_index < m_topv.Count() )
      {
        vr.m_mesh = m_mesh;
        vr.m_top_vi = ci.m_index;
        if ( m_topv[ci.m_index].m_vi && 1 == m_topv[ci.m_index].m_v_count )
        {
          vr.m_mesh_vi = m_topv[ci.m_index].m_vi[0];
        }
      }
      break;
    default:
      // intentionally skip other ON_COMPONENT_INDEX::TYPE
      // enum values.
      break;
    }
  }
  return vr;  
}

ON_MeshVertexRef ON_MeshTopology::VertexRef(int topv_index) const
{
  ON_MeshVertexRef vr;

  if ( topv_index >= 0 && topv_index < m_topv.Count() )
  {
    vr.m_mesh = m_mesh;
    vr.m_top_vi = topv_index;
    if ( 1 == m_topv[topv_index].m_v_count )
    {
      vr.m_mesh_vi = m_topv[topv_index].m_vi[0];
    }
  }

  return vr;
}

ON_MeshEdgeRef ON_MeshTopology::EdgeRef(ON_COMPONENT_INDEX ci) const
{
  ON_MeshEdgeRef er;
  if ( ON_COMPONENT_INDEX::meshtop_edge == ci.m_type && ci.m_index >= 0 && ci.m_index < m_tope.Count() )
  {
    er.m_mesh = m_mesh;
    er.m_top_ei = ci.m_index;
  }
  return er;
}

ON_MeshEdgeRef ON_MeshTopology::EdgeRef(int tope_index) const
{
  ON_MeshEdgeRef er;

  if ( tope_index >= 0 && tope_index < m_tope.Count() )
  {
    er.m_mesh = m_mesh;
    er.m_top_ei = tope_index;
  }

  return er;
}

ON_MeshFaceRef ON_MeshTopology::FaceRef(ON_COMPONENT_INDEX ci) const
{
  ON_MeshFaceRef fr;
  if ( m_mesh )
  {
    fr = m_mesh->FaceRef(ci.m_index);
  }
  return fr;
}

ON_MeshFaceRef ON_MeshTopology::FaceRef(int topf_index) const
{
  return ( 0 != m_mesh ) ? m_mesh->FaceRef(topf_index) : ON_MeshFaceRef();
}


/*
ON_Mesh::COMPONENT_TYPE ON_Mesh::ComponentIndexType( int component_index )
{
  switch( (mesh_component_mask & component_index) )
  {
  case mesh_vertex:    return mesh_vertex;
  case meshtop_vertex: return meshtop_vertex;
  case meshtop_edge:   return meshtop_edge;
  case mesh_face:      return mesh_face;
  }
  return mesh_component_unset;
}
*/

ON_COMPONENT_INDEX ON_MeshVertexRef::ComponentIndex() const
{
  ON_COMPONENT_INDEX ci(ON_COMPONENT_INDEX::invalid_type,-1);
  if ( m_mesh_vi >= 0 )
  {
    if ( 0 == m_mesh || m_mesh_vi < m_mesh->m_V.Count() )
    {
      ci.Set(ON_COMPONENT_INDEX::mesh_vertex,m_mesh_vi);
    }
  }
  else if ( m_top_vi >= 0 )
  {
    if ( 0 == m_mesh )
    {
      // not enough information to perform validation check
      // assume this is a persistent index to be resolved
      // later and press on
      ci.Set(ON_COMPONENT_INDEX::meshtop_vertex,m_top_vi);
    }
    else if (m_top_vi < m_mesh->m_V.Count())
    {
      if ( 0 == m_mesh->m_top.m_topv.Count() )
      {
        // not enough information to perform validation check
        // assume this is a persistent index to be resolved
        // later and press on
        ci.Set(ON_COMPONENT_INDEX::meshtop_vertex,m_top_vi);
      }
      else if ( m_top_vi < m_mesh->m_top.m_topv.Count() )
      {
        // m_top is constructed and m_top_vi is valid
        ci.Set(ON_COMPONENT_INDEX::meshtop_vertex,m_top_vi);
      }
    }
  }
  return ci;
}

ON_COMPONENT_INDEX ON_MeshEdgeRef::ComponentIndex() const
{
  ON_COMPONENT_INDEX ci(ON_COMPONENT_INDEX::invalid_type,-1);
  if ( m_top_ei >= 0 )
  {
    if ( 0 == m_mesh || 0 == m_mesh->m_top.m_tope.Count() )
    {
      // not enough information to perform validation check
      // assume this is a persistent index to be resolved
      // later and press on
      ci.Set(ON_COMPONENT_INDEX::meshtop_edge,m_top_ei);
    }
    else if ( m_top_ei < m_mesh->m_top.m_tope.Count() )
    {
      // valid index
      ci.Set(ON_COMPONENT_INDEX::meshtop_edge,m_top_ei);
    }
  }
  return ci;
}

ON_COMPONENT_INDEX ON_MeshFaceRef::ComponentIndex() const
{
  ON_COMPONENT_INDEX ci(ON_COMPONENT_INDEX::invalid_type,-1);
  if ( m_mesh_fi >= 0 )
  {
    if ( 0 == m_mesh || m_mesh_fi < m_mesh->m_F.Count() )
    {
      ci.Set(ON_COMPONENT_INDEX::mesh_face,m_mesh_fi);
    }
  }
  return ci;
}

ON_Geometry* ON_Mesh::MeshComponent( 
  ON_COMPONENT_INDEX ci
  ) const
{
  ON_Geometry* component = 0;
  if ( ci.m_index >= 0 )
  {
    switch( ci.m_type )
    {
    case ON_COMPONENT_INDEX::mesh_vertex: 
      {
        ON_MeshVertexRef r = VertexRef(ci);
        component = new ON_MeshVertexRef(r);
      }
      break;

    case ON_COMPONENT_INDEX::meshtop_vertex:
      {
        ON_MeshVertexRef r = Topology().VertexRef(ci);
        component = new ON_MeshVertexRef(r);
      }
      break;

    case ON_COMPONENT_INDEX::meshtop_edge:
      {
        ON_MeshEdgeRef r = EdgeRef(ci);
        component = new ON_MeshEdgeRef(r);
      }
      break;

    case ON_COMPONENT_INDEX::mesh_face:
      {
        ON_MeshFaceRef r = FaceRef(ci);
        component = new ON_MeshFaceRef(r);
      }
      break;

    default:
      // intentionally skip other ON_COMPONENT_INDEX::TYPE
      // enum values.
      break;
    }
  }
  return component;
}

ON_3dVector ON_TriangleNormal(
        const ON_3dPoint& A,
        const ON_3dPoint& B,
        const ON_3dPoint& C
        )
{
  // N = normal to triangle's plane
  ON_3dVector N;
  double a, b, c, d;
  N.x = A.y*(B.z-C.z) + B.y*(C.z-A.z) + C.y*(A.z-B.z);
  N.y = A.z*(B.x-C.x) + B.z*(C.x-A.x) + C.z*(A.x-B.x);
  N.z = A.x*(B.y-C.y) + B.x*(C.y-A.y) + C.x*(A.y-B.y);

  a = fabs(N.x);
  b = fabs(N.y);
  c = fabs(N.z);
  if ( b > a )
  {
    if ( c > b )
    {
      // c is largest
      if ( c > ON_DBL_MIN )
      {
        a /= c; b /= c; d = c*sqrt(1.0 + a*a + b*b);
      }
      else
      {
        d = c;
      }
    }
    else
    {
      if ( b > ON_DBL_MIN )
      {
        // b is largest
        a /= b; c /= b; d = b*sqrt(1.0 + c*c + a*a);
      }
      else
      {
        d = b;
      }
    }
  }
  else if ( c > a )
  {
    // c is largest
    if ( c > ON_DBL_MIN )
    {
      a /= c; b /= c; d = c*sqrt(1.0 + a*a + b*b);
    }
    else
    {
      d = c;
    }
  }
  else if ( a > ON_DBL_MIN )
  {
    // a is largest
    b /= a; c /= a; d = a*sqrt(1.0 + b*b + c*c);
  }
  else
  {
    d = a;
  }

  if ( d > 0.0 )
  {
    N.x /= d; N.y /= d; N.z /= d;
  }

  return N;
}

bool ON_GetTrianglePlaneEquation(
        const ON_3dPoint& A,
        const ON_3dPoint& B,
        const ON_3dPoint& C,
        double* a,
        double* b,
        double* c,
        double* d,
        double* evaluation_tol
        )
{
  const ON_3dVector N(ON_TriangleNormal(A,B,C));
  const double dd( -(N.x*A.x + N.y*A.y + N.z*A.z) );
  
  *a = N.x;
  *b = N.y;
  *c = N.z;
  *d = dd;
  
  if ( 0 != evaluation_tol )
  {
    *evaluation_tol = fabs(N.x*A.x + N.y*A.y + N.z*A.z + dd);
    double e = fabs(N.x*B.x + N.y*B.y + N.z*B.z + dd);
    if ( e > *evaluation_tol )
      *evaluation_tol = e;
    e = fabs(N.x*C.x + N.y*C.y + N.z*C.z + dd);
    if ( e > *evaluation_tol )
      *evaluation_tol = e;
    *evaluation_tol *= (1.0 + ON_EPSILON);
  }

  return (0.0 != N.x || 0.0 != N.y || 0.0 != N.z);
}

const bool* ON_Mesh::HiddenVertexArray() const
{
  return ( ( m_hidden_count > 0 && m_H.Count() == m_V.Count() ) ? m_H.Array() : 0);
}

void ON_Mesh::DestroyHiddenVertexArray()
{
  m_H.Destroy();
  m_hidden_count = 0;
}

int ON_Mesh::HiddenVertexCount() const
{
  return ((m_H.Count() == m_V.Count()) ? m_hidden_count : 0);
}

void ON_Mesh::SetVertexHiddenFlag( int meshvi, bool bHidden )
{
  const int vcount = m_V.Count();
  if ( meshvi >= 0 && meshvi < vcount )
  {
    if ( bHidden )
    {
      if ( vcount != m_H.Count() )
      {
        m_H.SetCapacity(vcount);
        m_H.SetCount(vcount);
        m_H.Zero();
        m_H[meshvi] = true;
        m_hidden_count = 1;
      }
      else if ( false == m_H[meshvi] )
      {
        m_H[meshvi] = true;
        m_hidden_count++;
      }
    }
    else
    {
      // show this vertex
      if ( m_hidden_count > 0 && vcount == m_H.Count() )
      {
        if  ( m_H[meshvi] )
        {
          m_H[meshvi] = false;
          m_hidden_count--;
          if ( 0 == m_hidden_count )
          {
            DestroyHiddenVertexArray();
          }
        }
      }
      else if ( m_hidden_count > 0 || m_H.Capacity() > 0 )
      {
        // if m_H exists, it is bogus.
        DestroyHiddenVertexArray();
      }
    }
  }
}


bool ON_Mesh::VertexIsHidden(int meshvi) const
{
  const int vcount = m_V.Count();
  return ((m_hidden_count > 0 && meshvi >= 0 && meshvi < vcount && vcount == m_H.Count()) 
          ? m_H[meshvi]
          : false);
}

bool ON_Mesh::FaceIsHidden(int meshfi) const
{
  const bool* bHiddenVertex = HiddenVertexArray();
  if ( bHiddenVertex && meshfi >= 0 && meshfi < m_F.Count() )
  {
    ON_MeshFace f = m_F[meshfi];
    if ( bHiddenVertex[f.vi[0]] || bHiddenVertex[f.vi[1]] || bHiddenVertex[f.vi[2]] || bHiddenVertex[f.vi[3]] )
      return true;
  }
  return false;
}

bool ON_MeshTopology::TopVertexIsHidden( int topvi ) const
{
  const bool* bHiddenVertex = m_mesh ? m_mesh->HiddenVertexArray() : 0;
  if ( bHiddenVertex && topvi >= 0 && topvi < m_topv.Count() )
  {
    const ON_MeshTopologyVertex& topv = m_topv[topvi];
    int i;
    for ( i = 0; i < topv.m_v_count; i++ )
    {
      if ( !bHiddenVertex[topv.m_vi[i]] )
        return false;
    }
    return true;
  }
  return false;
}

bool ON_MeshTopology::TopEdgeIsHidden( int topei ) const
{
  // ugly - but faster than calling TopVertexIsHidden()
  const bool* bHiddenVertex = m_mesh ? m_mesh->HiddenVertexArray() : 0;
  if ( bHiddenVertex && topei >= 0 && topei < m_tope.Count()  )
  {
    const ON_MeshTopologyEdge& tope = m_tope[topei];
    const ON_MeshTopologyVertex& topv0 = m_topv[tope.m_topvi[0]];
    const ON_MeshTopologyVertex& topv1 = m_topv[tope.m_topvi[1]];
    int i;

    for ( i = 0; i < topv0.m_v_count; i++ )
    {
      if ( !bHiddenVertex[topv0.m_vi[i]] )
        break;
    }
    if ( i >= topv0.m_v_count )
      return true;

    for ( i = 0; i < topv1.m_v_count; i++ )
    {
      if ( !bHiddenVertex[topv1.m_vi[i]] )
        return false;
    }

    return true;
  }
  return false;
}

bool ON_MeshTopology::TopFaceIsHidden( int topfi ) const
{
  // topology and mesh face indices are the same
  return m_mesh ? m_mesh->FaceIsHidden(topfi) : false;
}


ON_MappingTag::ON_MappingTag()
{
  Default();
}

void ON_MappingTag::Dump( ON_TextLog& text_log ) const
{
  text_log.Print("Texture/color coordinates tag:\n");
  text_log.PushIndent();
  text_log.Print("mapping id: "); text_log.Print(m_mapping_id); text_log.Print("\n");
  text_log.Print("mapping crc: %08x\n",m_mapping_crc);
  text_log.Print("mesh xform:\n");
  text_log.PushIndent(); text_log.Print(m_mesh_xform); text_log.PopIndent();
  text_log.PushIndent();
  text_log.Print(m_mesh_xform);
  text_log.PopIndent();
  text_log.PopIndent();
}

void ON_MappingTag::Transform( const ON_Xform& xform )
{
  if ( !ON_UuidIsNil(m_mapping_id) )
  {
    // Update mapping transformation.
    // Do NOT change the value of m_mapping_crc.
    m_mesh_xform = xform*m_mesh_xform;
  }
}

void ON_MappingTag::SetDefaultSurfaceParameterMappingTag()
{
  ON_TextureMapping srfp_mapping;
  srfp_mapping.m_type = ON_TextureMapping::srfp_mapping;
  srfp_mapping.m_mapping_id = ON_nil_uuid;
  Set(srfp_mapping); 
}

void ON_MappingTag::Set(const ON_TextureMapping& mapping)
{
  Default();
  m_mapping_id   = mapping.m_mapping_id;
  m_mapping_type = mapping.m_type;
  m_mapping_crc  = mapping.MappingCRC();
}

bool ON_MappingTag::IsSet() const
{
  return (0 != m_mapping_crc || !ON_UuidIsNil(m_mapping_id));
}

bool ON_MappingTag::IsDefaultSurfaceParameterMapping() const
{
  bool rc = (ON_TextureMapping::srfp_mapping == m_mapping_type);
  if ( rc )
  {
    // The crc needs to be checked to insure that m_uvw
    // was the identity.
    ON_TextureMapping tmp;
    tmp.m_type = ON_TextureMapping::srfp_mapping;
    rc = (m_mapping_crc == tmp.MappingCRC());
  }
  return rc;
}


void ON_MappingTag::Default()
{
  memset(this,0,sizeof(*this));
  m_mesh_xform.m_xform[0][0] = 1.0;
  m_mesh_xform.m_xform[1][1] = 1.0;
  m_mesh_xform.m_xform[2][2] = 1.0;
  m_mesh_xform.m_xform[3][3] = 1.0;
}

int ON_MappingTag::Compare( 
             const ON_MappingTag& other,
             bool bCompareId,
             bool bCompareCRC,
             bool bCompareXform
             ) const
{
  int rc = 0;
  if ( !rc && bCompareId )
  {
    rc = ON_UuidCompare(m_mapping_id,other.m_mapping_id);
  }
  if ( !rc && bCompareCRC )
  {
    rc = ((int)m_mapping_crc) - ((int)other.m_mapping_crc);
  }
  if ( !rc && bCompareXform )
  {
    rc = m_mesh_xform.Compare(other.m_mesh_xform);
  }
  return rc;
}



bool ON_MappingTag::Write(ON_BinaryArchive& archive) const
{
  bool rc = archive.BeginWrite3dmChunk(TCODE_ANONYMOUS_CHUNK,1,1);
  if (!rc)
    return false;

  for(;;)
  {
    rc = archive.WriteUuid(m_mapping_id);
    if(!rc) break;
    rc = archive.WriteInt(m_mapping_crc);
    if(!rc) break;
    rc = archive.WriteXform(m_mesh_xform);
    if(!rc) break;

    // 1.1 fields
    rc = archive.WriteInt(m_mapping_type);
    if (!rc) break;

    break;
  }

  if ( !archive.EndWrite3dmChunk() )
    rc = false;
  
  return rc;
}

bool ON_MappingTag::Read(ON_BinaryArchive& archive)
{
  Default();
  int mjv = 0, mnv = 0;
  bool rc = archive.BeginRead3dmChunk(TCODE_ANONYMOUS_CHUNK,&mjv,&mnv);
  if (!rc)
    return false;

  for(;;)
  {
    rc = (1 == mjv);
    if (!rc) break;
    rc = archive.ReadUuid(m_mapping_id);
    if(!rc) break;
    if ( 0 == ON_UuidCompare(&obsolete_default_srfp_mapping_id,&m_mapping_id) )
      m_mapping_id = ON_nil_uuid;
    rc = archive.ReadInt(&m_mapping_crc);
    if(!rc) break;
    rc = archive.ReadXform(m_mesh_xform);
    if(!rc) break;

    if ( mnv >= 1 )
    {
      // 1.1 fields
      int i = m_mapping_type;
      rc = archive.ReadInt(&i);
      if ( rc )
        m_mapping_type = ON_TextureMapping::TypeFromInt(i);
      if (!rc) break;
    }


    break;
  }

  if ( !archive.EndRead3dmChunk() )
    rc = false;
  
  return rc;
}

ON_TextureCoordinates::ON_TextureCoordinates()
{
  m_dim = 0;
}


//
// Double precision vertices
//

ON_OBJECT_IMPLEMENT(ON_MeshDoubleVertices,ON_UserData,"17F24E75-21BE-4a7b-9F3D-7F85225247E3");

ON_MeshDoubleVertices* ON_MeshDoubleVertices::Get(const ON_Mesh* mesh)
{
  return ON_MeshDoubleVertices::Cast(mesh->GetUserData(ON_MeshDoubleVertices::m_ON_MeshDoubleVertices_class_id.Uuid()));
}

ON_MeshDoubleVertices* ON_MeshDoubleVertices::Attach(const ON_Mesh* mesh)
{
  ON_MeshDoubleVertices* dv = ON_MeshDoubleVertices::Get(mesh);
  if ( 0 != dv )
    return 0;
  dv = new ON_MeshDoubleVertices();
  const_cast<ON_Mesh*>(mesh)->AttachUserData(dv);
  return dv;
}

ON_MeshDoubleVertices::ON_MeshDoubleVertices()
: ON_UserData()
, m_fcount(0)
, m_dcount(0)
, m_fCRC(0)
, m_dCRC(0)
{
  m_userdata_uuid = ON_MeshDoubleVertices::m_ON_MeshDoubleVertices_class_id.Uuid();
  m_application_uuid = ON_opennurbs5_id;
  m_userdata_copycount = 1;
}

ON_MeshDoubleVertices::~ON_MeshDoubleVertices()
{}

ON_BOOL32 ON_MeshDoubleVertices::IsValid( ON_TextLog* ) const
{
  return true;
}

void ON_MeshDoubleVertices::Dump( ON_TextLog& text_log ) const
{
  // TODO - print some double values
  ON_UserData::Dump(text_log);
}

unsigned int ON_MeshDoubleVertices::SizeOf() const
{
  return m_dV.SizeOfArray() + ON_UserData::SizeOf();
}

ON__UINT32 ON_MeshDoubleVertices::DataCRC(ON__UINT32 current_remainder) const
{
  current_remainder = ON_CRC32(current_remainder,sizeof(m_fcount),&m_fcount);
  current_remainder = ON_CRC32(current_remainder,sizeof(m_dcount),&m_dcount);
  current_remainder = ON_CRC32(current_remainder,sizeof(m_fCRC),&m_fCRC);
  current_remainder = ON_CRC32(current_remainder,sizeof(m_dCRC),&m_dCRC);
  current_remainder = m_dV.DataCRC(current_remainder);
  return current_remainder;  
}

ON_BOOL32 ON_MeshDoubleVertices::Write(ON_BinaryArchive& file) const
{
  bool rc = file.BeginWrite3dmChunk(TCODE_ANONYMOUS_CHUNK,1,0);
  if (!rc)
    return false;
  for(;;)
  {
    rc = file.WriteInt(m_fcount);
    if (!rc)
      break;
    rc = file.WriteInt(m_dcount);
    if (!rc)
      break;
    rc = file.WriteInt(m_fCRC);
    if (!rc)
      break;
    rc = file.WriteInt(m_dCRC);
    if (!rc)
      break;
    rc = file.WriteArray(m_dV);
    if (!rc)
      break;
    break;
  }
  if ( !file.EndWrite3dmChunk() )
    rc = false;
  return rc;
}

ON_BOOL32 ON_MeshDoubleVertices::Read(ON_BinaryArchive& file)
{
  m_fcount = 0;
  m_dcount = 0;
  m_fCRC = 0;
  m_dCRC = 0;
  m_dV.Destroy();

  int major_version = 0;
  int minor_version = 0;
  bool rc = file.BeginRead3dmChunk(TCODE_ANONYMOUS_CHUNK,&major_version,&minor_version);
  if (!rc)
    return false;
  for(;;)
  {
    rc = file.ReadInt(&m_fcount);
    if (!rc)
      break;
    rc = file.ReadInt(&m_dcount);
    if (!rc)
      break;
    rc = file.ReadInt(&m_fCRC);
    if (!rc)
      break;
    rc = file.ReadInt(&m_dCRC);
    if (!rc)
      break;
    rc = file.ReadArray(m_dV);
    if (!rc)
      break;
    break;
  }
  if ( !file.EndRead3dmChunk() )
    rc = false;
  return rc;
}

// virtual ON_UserData overrides
ON_BOOL32 ON_MeshDoubleVertices::GetDescription( ON_wString& description )
{
  description = L"ON_Mesh double precision vertices";
  return true;
}

ON_BOOL32 ON_MeshDoubleVertices::Archive() const
{
  // refuse to save garbage in files.

  if ( m_fcount != m_dcount )
  {
    ON_ERROR("m_fcount != m_dcount");
    return false;
  }

  if ( m_dcount != m_dV.Count() )
  {
    ON_ERROR("m_dcount != m_dV.Count()");
    return false;
  }

  if ( m_dCRC != DoubleCRC() )
  {
    ON_ERROR("m_dCRC != DoubleCRC()");
    return false;
  }

  const ON_Mesh* mesh = ON_Mesh::Cast( Owner() );
  if ( 0 == mesh )
  {
    ON_ERROR("0 = ON_Mesh::Cast( Owner() )");
    return false;
  }

  if ( m_fcount != mesh->m_V.Count() )
  {
    ON_ERROR("m_fcount != mesh->m_V.Count()");
    return false;
  }

  if ( m_fCRC != ON_MeshDoubleVertices::FloatCRC(mesh->m_V) )
  {
    ON_ERROR("m_fCRC != ON_MeshDoubleVertices::FloatCRC(mesh->m_V)");
    return false;
  }

  return true;
}

ON_BOOL32 ON_MeshDoubleVertices::Transform( const ON_Xform& xform )
{
  if ( !xform.IsIdentity() )
  {
    const ON__UINT32 crc0 = DoubleCRC();
    m_dV.Transform(xform);
    const ON__UINT32 crc1 = DoubleCRC();
    if ( crc0 == m_dCRC && m_dV.Count() == m_dcount )
      m_dCRC = crc1; // update m_dCRC so it stays valid
    else
      m_dCRC = (0==crc1)?1:0; // make sure m_dCRC is not valid
  }
  return true;
}

bool ON_Mesh::HasSynchronizedDoubleAndSinglePrecisionVertices() const
{
  ON_3fPoint P;
  const ON_MeshDoubleVertices* dv = ON_MeshDoubleVertices::Get(this);
  if ( 0 == dv )
    return false;
  int count = m_V.Count();
  if ( count != dv->m_dV.Count() )
    return false;
  const ON_3fPoint* FV = m_V.Array();
  const ON_3dPoint* DV = dv->m_dV.Array();
  while (count--)
  {
    // Compare float values.
    P.x = (float)DV->x;
    P.y = (float)DV->y;
    P.z = (float)DV->z;
    if ( !(P.x == FV->x && P.y == FV->y && P.z == FV->z) )
      return false;
  }
  return true;
}

bool ON_Mesh::HasDoublePrecisionVertices() const
{
  return ( 0 != ON_MeshDoubleVertices::Get(this));
}

void ON_Mesh::DestroyDoublePrecisionVertices()
{
  ON_MeshDoubleVertices* dv = ON_MeshDoubleVertices::Get(this);
  if ( dv )
    delete dv;
}

void ON_Mesh::EnableDoublePrecisionVertices(bool bEnableDoublePrecisionVertices)
{
  ON_MeshDoubleVertices* dv = ON_MeshDoubleVertices::Get(this);
  if ( bEnableDoublePrecisionVertices )
  {
    if ( 0 == dv )
    {
      dv = ON_MeshDoubleVertices::Attach(this);
      UpdateDoublePrecisionVertices();
    }
  }
  else
  {
    // destroy double precision vertices
    if ( 0 != dv )
      delete dv;
  }
}

ON__UINT32 ON_MeshDoubleVertices::FloatCRC( const ON_3fPointArray& V )
{
  return V.DataCRC(0);
}

ON__UINT32 ON_MeshDoubleVertices::DoubleCRC() const
{
  return m_dV.DataCRC(0);
}

void ON_Mesh::UpdateSinglePrecisionVertices()
{
  ON_MeshDoubleVertices* dv = ON_MeshDoubleVertices::Get(this);
  if ( 0 == dv )
    return;
  int count = dv->m_dV.Count();
  m_V.Reserve(count);
  m_V.SetCount(count);
  ON_3fPoint* fV = m_V.Array();
  const ON_3dPoint* dV = dv->m_dV.Array();
  while(count--)
  {
    fV->x = (float)dV->x;
    fV->y = (float)dV->y;
    fV->z = (float)dV->z;
    fV++;
    dV++;
  }
  dv->m_fcount = dv->m_dV.Count();
  dv->m_dcount = dv->m_dV.Count();
  dv->m_fCRC = ON_MeshDoubleVertices::FloatCRC(m_V);
  dv->m_dCRC = dv->DoubleCRC();
}

void ON_Mesh::UpdateDoublePrecisionVertices()
{
  ON_MeshDoubleVertices* dv = ON_MeshDoubleVertices::Get(this);
  if ( 0 == dv )
    return;
  int count = m_V.Count();
  bool bSelectiveUpdate = (count == dv->m_dV.Count());
  dv->m_dV.Reserve(count);
  dv->m_dV.SetCount(count);
  ON_3dPoint* dV = dv->m_dV.Array();
  const ON_3fPoint* fV = m_V.Array();
  if ( bSelectiveUpdate )
  {
    // double precision vertices already existed
    // and there is a reasonable chance that 
    // a subset of the float precision vertices
    // have been modified.  So, attempt to
    // keep the precision on double vertices
    // that alread agree with the float vertices
    // in float precision.
    ON_3fPoint P;
    while(count--)
    {
      P.x = (float)dV->x;
      P.y = (float)dV->y;
      P.z = (float)dV->z;
      if ( !(P.x == fV->x && P.y == fV->y && P.z == fV->z) )
      {
        // (float)dV != fV, so update dV
        dV->x = (double)fV->x;
        dV->y = (double)fV->y;
        dV->z = (double)fV->z;
      }
      dV++;
      fV++;
    }
  }
  else
  {
    while(count--)
    {
      dV->x = (double)fV->x;
      dV->y = (double)fV->y;
      dV->z = (double)fV->z;
      dV++;
      fV++;
    }
  }
  dv->m_fcount = m_V.Count();
  dv->m_dcount = m_V.Count();
  dv->m_fCRC = ON_MeshDoubleVertices::FloatCRC(m_V);
  dv->m_dCRC = dv->DoubleCRC();
}

void ON_Mesh::SetSinglePrecisionVerticesAsValid()
{
  ON_MeshDoubleVertices* dv = ON_MeshDoubleVertices::Get(this);
  if ( 0 == dv )
    return;
  dv->m_fcount = m_V.Count();
  dv->m_fCRC   = ON_MeshDoubleVertices::FloatCRC(m_V);
}

void ON_Mesh::SetDoublePrecisionVerticesAsValid()
{
  ON_MeshDoubleVertices* dv = ON_MeshDoubleVertices::Get(this);
  if ( 0 == dv )
    return;
  dv->m_dcount = dv->m_dV.Count();
  dv->m_dCRC   = dv->DoubleCRC();
}

bool ON_Mesh::SinglePrecisionVerticesAreValid() const
{
  const ON_MeshDoubleVertices* dv = ON_MeshDoubleVertices::Get(this);
  if ( 0 == dv )
    return true;
  return ( dv->m_fcount == m_V.Count() && dv->m_fCRC == ON_MeshDoubleVertices::FloatCRC(m_V) );
}

bool ON_Mesh::DoublePrecisionVerticesAreValid() const
{
  const ON_MeshDoubleVertices* dv = ON_MeshDoubleVertices::Get(this);
  if ( 0 == dv )
    return true;
  // DO NOT COMPARE dv->m_dV.Count() and m_V.Count() because m_V might be 
  // the bogus set of values.
  return ( dv->m_dcount == dv->m_dV.Count() && dv->m_dCRC == dv->DoubleCRC() );
}



ON_3dPointArray& ON_Mesh::DoublePrecisionVertices()
{
  ON_MeshDoubleVertices* dv = ON_MeshDoubleVertices::Get(this);

  bool bUpdate = false;
  if ( 0 == dv )
  {
    dv = ON_MeshDoubleVertices::Attach(this);
    bUpdate = true;
  }
  else if ( dv->m_dcount != dv->m_dV.Count()|| dv->m_dCRC != dv->DoubleCRC() )
  {
    if ( dv->m_fcount == m_V.Count() && dv->m_fCRC == ON_MeshDoubleVertices::FloatCRC(m_V) )
    bUpdate = true;
  }

  if ( bUpdate )
    UpdateDoublePrecisionVertices();

  return dv->m_dV;
}

ON_3dPoint ON_Mesh::Vertex(int vertex_index) const
{
  if ( vertex_index < 0 || vertex_index >= m_V.Count() )
    return ON_3dPoint::UnsetPoint;

  const ON_3fPoint F = m_V[vertex_index];
  ON_MeshDoubleVertices* dv = ON_MeshDoubleVertices::Get(this);
  if ( 0 != dv && dv->m_dV.Count() == m_V.Count() )
  {
    ON_3dPoint D = dv->m_dV[vertex_index];
    if ( F.x == (float)D.x && F.y == (float)D.y && F.z == (float)D.z )
    {
      // double precision vertex is valid
      return D;
    }
  }

  return F;
}

const ON_3dPointArray& ON_Mesh::DoublePrecisionVertices() const
{
  ON_Mesh& mesh = const_cast<ON_Mesh&>(*this);
  ON_3dPointArray& a = mesh.DoublePrecisionVertices();
  return a;
}

ON_3fPointArray& ON_Mesh::SinglePrecisionVertices()
{
  ON_MeshDoubleVertices* dv = ON_MeshDoubleVertices::Get(this);

  if ( 0 != dv )
  {
    if ( dv->m_fcount != m_V.Count()|| dv->m_fCRC != ON_MeshDoubleVertices::FloatCRC(m_V) )
    {
      if ( dv->m_dcount == dv->m_dV.Count() && dv->m_dCRC == dv->DoubleCRC() )
        UpdateSinglePrecisionVertices();
    }
  }

  return m_V;
}

const ON_3fPointArray& ON_Mesh::SinglePrecisionVertices() const
{
  ON_Mesh& mesh = const_cast<ON_Mesh&>(*this);
  ON_3fPointArray& a = mesh.SinglePrecisionVertices();
  return a;
}


//
// BEGIN ON_PerObjectMeshParameters user data class
//


class /*NEVER EXPORT THIS CLASS DEFINITION*/ ON_PerObjectMeshParameters : public ON_UserData
{
#if !defined(ON_BOZO_VACCINE_B5628CA982C44CAE9883487B3E4AB28B)
#error Never copy this class definition or put this definition in a header file!
#endif
  ON_OBJECT_DECLARE(ON_PerObjectMeshParameters);

public:
  ON_PerObjectMeshParameters();
  ~ON_PerObjectMeshParameters();
  // default copy constructor and operator= work fine.

public:
  // virtual ON_Object override
  ON_BOOL32 IsValid( ON_TextLog* text_log = NULL ) const;
  // virtual ON_Object override
  unsigned int SizeOf() const;
  // virtual ON_Object override
  ON__UINT32 DataCRC(ON__UINT32 current_remainder) const;
  // virtual ON_Object override
  ON_BOOL32 Write(ON_BinaryArchive& binary_archive) const;
  // virtual ON_Object override
  ON_BOOL32 Read(ON_BinaryArchive& binary_archive);
  // virtual ON_UserData override
  ON_BOOL32 Archive() const;
  // virtual ON_UserData override
  ON_BOOL32 GetDescription( ON_wString& description );

public:
  static
  ON_PerObjectMeshParameters* FindOrCreate( const ON_Object*, bool bCreate );

  ON_MeshParameters m_mp;
};

#undef ON_BOZO_VACCINE_B5628CA982C44CAE9883487B3E4AB28B

ON_OBJECT_IMPLEMENT(ON_PerObjectMeshParameters,ON_UserData,"B5628CA9-82C4-4CAE-9883-487B3E4AB28B");

ON_PerObjectMeshParameters* ON_PerObjectMeshParameters::FindOrCreate(const ON_Object* object,bool bCreate)
{
  if ( 0 == object )
    return 0;
  ON_PerObjectMeshParameters* ud = ON_PerObjectMeshParameters::Cast(object->GetUserData(ON_PerObjectMeshParameters::m_ON_PerObjectMeshParameters_class_id.Uuid()));
  if ( !ud && bCreate )
  {
    ud = new ON_PerObjectMeshParameters();
    const_cast< ON_Object* >(object)->AttachUserData(ud);
  }
  return ud;
}

ON_PerObjectMeshParameters::ON_PerObjectMeshParameters()
: m_mp(ON_MeshParameters::FastRenderMesh)
{
  m_userdata_uuid = ON_PerObjectMeshParameters::m_ON_PerObjectMeshParameters_class_id.Uuid();
  m_application_uuid = ON_opennurbs5_id;
  m_userdata_copycount = 1;
  m_mp.m_bCustomSettings = true;
  m_mp.m_bComputeCurvature = false;
}

ON_PerObjectMeshParameters::~ON_PerObjectMeshParameters()
{
}

// virtual ON_Object override
ON_BOOL32 ON_PerObjectMeshParameters::IsValid( ON_TextLog* text_log ) const
{
  return true;
}

// virtual ON_Object override
unsigned int ON_PerObjectMeshParameters::SizeOf() const
{
  size_t sz = sizeof(*this) - sizeof(ON_UserData);
  return (unsigned int)sz;
}

// virtual ON_Object override
ON__UINT32 ON_PerObjectMeshParameters::DataCRC(ON__UINT32 current_remainder) const
{
  return m_mp.DataCRC(current_remainder);
}

// virtual ON_Object override
ON_BOOL32 ON_PerObjectMeshParameters::Write(ON_BinaryArchive& binary_archive) const
{
  if ( !binary_archive.BeginWrite3dmChunk(TCODE_ANONYMOUS_CHUNK,1,0) )
    return false;

  bool rc = false;
  for(;;)
  {
    if ( !binary_archive.BeginWrite3dmBigChunk(TCODE_ANONYMOUS_CHUNK,0) )
      break;
    bool mprc = m_mp.Write(binary_archive);
    if ( !binary_archive.EndWrite3dmChunk() )
      break;
    if ( !mprc )
      break;
    rc = true;
    break;
  }

  if ( !binary_archive.EndWrite3dmChunk() )
    rc = false;

  return rc;
}

// virtual ON_Object override
ON_BOOL32 ON_PerObjectMeshParameters::Read(ON_BinaryArchive& binary_archive)
{
  m_mp = ON_MeshParameters::FastRenderMesh;
  m_mp.m_bCustomSettings = true;
  m_mp.m_bComputeCurvature = false;

  int major_version = 0;
  int minor_version = 0;
  if ( !binary_archive.BeginRead3dmChunk(TCODE_ANONYMOUS_CHUNK,&major_version,&minor_version) )
    return false;
    
  bool rc = false;
  for(;;)
  {
    if ( 1 != major_version )
      break;

    unsigned int tcode(0);
    ON__INT64 value(0);
    if (!binary_archive.BeginRead3dmBigChunk(&tcode,&value))
      break;
    bool mprc = false;
    for(;;)
    {
      if (TCODE_ANONYMOUS_CHUNK != tcode )
        break;
      if (value <= 0)
        break;
      if (!m_mp.Read(binary_archive))
        break;
      mprc = true;
      break;
    }
    if (!binary_archive.EndRead3dmChunk())
      break;
    if (!mprc)
      break;

    rc = true;
    break;
  }

  if ( !binary_archive.EndRead3dmChunk() )
    rc = false;

  m_mp.m_bCustomSettings = true;
  m_mp.m_bComputeCurvature = false;

  return rc;
}

// virtual ON_UserData override
ON_BOOL32 ON_PerObjectMeshParameters::Archive() const
{
  return true;
}

// virtual ON_UserData override
ON_BOOL32 ON_PerObjectMeshParameters::GetDescription( ON_wString& description )
{
  description = L"Custom Render Mesh Parameters";
  return true;
}

//
// END ON_PerObjectMeshParameters user data class
//

const ON_MeshParameters* ON_3dmObjectAttributes::CustomRenderMeshParameters() const
{
  const ON_PerObjectMeshParameters* ud = ON_PerObjectMeshParameters::FindOrCreate(this,false);
  return (0 != ud) ? &ud->m_mp : 0;
}

bool ON_3dmObjectAttributes::SetCustomRenderMeshParameters( const ON_MeshParameters& mp )
{
  ON_PerObjectMeshParameters* ud = ON_PerObjectMeshParameters::FindOrCreate(this,true);
  if ( 0 == ud )
    return false;
  ud->m_mp = mp;
  ud->m_mp.m_bCustomSettings = true;
  ud->m_mp.m_bComputeCurvature = false;
  if ( 1 != ud->m_mp.m_texture_range && 2 != ud->m_mp.m_texture_range )
    ud->m_mp.m_texture_range = 2;
  return true;
}

void ON_3dmObjectAttributes::DeleteCustomRenderMeshParameters()
{
  ON_PerObjectMeshParameters* ud = ON_PerObjectMeshParameters::FindOrCreate(this,false);
  if ( 0 != ud )
    delete ud;
}

bool ON_3dmObjectAttributes::EnableCustomRenderMeshParameters(bool bEnable)
{
  ON_PerObjectMeshParameters* ud = ON_PerObjectMeshParameters::FindOrCreate(this,false);
  if ( 0 != ud )
    ud->m_mp.m_bCustomSettingsEnabled = bEnable ? true : false;
  return (!bEnable || 0 != ud);
}

void ON_Mesh::DestroyTree( bool bDeleteTree )
{
}


int* ON_Mesh_GetVidHelper( const int Vcount, const ON_3fPoint* fV, const ON_3dPoint* dV, int first_vid, int* Vid, int* Vindex );
static int comparefV( const void* a, const void* b )
{
  const float* af = (const float*)a;
  const float* bf = (const float*)b;
  if ( af[0] < bf[0] )
    return -1;
  if ( af[0] > bf[0] )
    return 1;
  if ( af[1] < bf[1] )
    return -1;
  if ( af[1] > bf[1] )
    return 1;
  if ( af[2] < bf[2] )
    return -1;
  if ( af[2] > bf[2] )
    return 1;
  return 0;
}

static int comparedV( const void* a, const void* b )
{
  const double* af = (const double*)a;
  const double* bf = (const double*)b;
  if ( af[0] < bf[0] )
    return -1;
  if ( af[0] > bf[0] )
    return 1;
  if ( af[1] < bf[1] )
    return -1;
  if ( af[1] > bf[1] )
    return 1;
  if ( af[2] < bf[2] )
    return -1;
  if ( af[2] > bf[2] )
    return 1;
  return 0;
}

int* ON_Mesh_GetVidHelper( const int Vcount, const ON_3fPoint* fV, const ON_3dPoint* dV, int first_vid, int* Vid, int* Vindex )
{
  // Used here and in opennurbs_plus_xmeshfast.cpp

  if ( Vcount <= 0 || (0 == dV && 0 == fV) )
    return 0;

  int Vmapbuffer[1024];
  int* Vmap;
  int id, i;
  const ON_3fPoint* fP0;
  const ON_3fPoint* fP1;
  const ON_3dPoint* dP0;
  const ON_3dPoint* dP1;
  if ( Vindex )
  {
    Vmap = Vindex;
  }
  else
  {
    Vmap = ( Vcount*sizeof(*Vmap) <= sizeof(Vmapbuffer) )
         ? &Vmapbuffer[0]
         : (int*)onmalloc( Vcount*sizeof(*Vmap) );
  }
  if ( 0 == Vmap )
    return 0;

  // The call to ON_Sort fills in Vmap[] with a permutation
  // of (0,1,...,Vcount-1) so that all coincident points
  // are adjacent in the Vmap[] list.  The vertex locations
  // are often partially sorted.  In the past, heap sort was
  // a better choice but the qsort in VC 2010
  // is now faster than heap sort.
  if ( 0 != dV )
    ON_Sort( ON::quick_sort, Vmap, dV, Vcount, sizeof(dV[0]), comparedV );  
  else
    ON_Sort( ON::quick_sort, Vmap, fV, Vcount, sizeof(fV[0]), comparefV );  

  // Assign a sequential one based index to each unique point location.
  if ( 0 == Vid )
    Vid = (int*)onmalloc(Vcount*sizeof(*Vid));

  if ( 0 != dV )
  {
    dP0 = dV + Vmap[0];
    id = first_vid;
    Vid[Vmap[0]] = id;
    for ( i = 1; i < Vcount; i++ )
    {
      dP1 = dV + Vmap[i];
      if ( dP0->x != dP1->x || dP0->y != dP1->y || dP0->z != dP1->z )
      {
        dP0 = dP1;
        id++;
      }
      Vid[Vmap[i]] = id;
    }
  }
  else
  {
    fP0 = fV + Vmap[0];
    id = first_vid;
    Vid[Vmap[0]] = id;
    for ( i = 1; i < Vcount; i++ )
    {
      fP1 = fV + Vmap[i];
      if ( fP0->x != fP1->x || fP0->y != fP1->y || fP0->z != fP1->z )
      {
        fP0 = fP1;
        id++;
      }
      Vid[Vmap[i]] = id;
    }
  }

  if ( 0 != Vmap && Vmap != &Vmapbuffer[0] && Vmap != Vindex )
    onfree(Vmap);

  return Vid;
}

int* ON_Mesh::GetVertexLocationIds( int first_vid, int* Vid, int* Vindex ) const
{
  const ON_3dPoint* dV = Mesh_dV(*this);
  const ON_3fPoint* fV = (0 == dV) ? m_V.Array() : 0;
  return ON_Mesh_GetVidHelper( m_V.Count(), fV, dV, first_vid, Vid, Vindex );
}

/*
Description:
  Helper to get edge info array needed by ON_Mesh::GetEdgeList()
  and ON_Mesh::IsClosed().
Parameters:
  Fcount - [in]
  F - [in]
  Vid - [in] array from ON_Mesh_GetVidHelper()
  Eid_list - [out]
    input array needs to be large enough to hold one element for
    each face side.  4*Fcount is always large enough.
*/

int ON_Mesh_GetEidHelper( 
      const int Vcount, 
      const int Fcount, 
      const ON_MeshFace* F, 
      const int* Vid, 
      ON_MeshFaceSide* Eid_list
      )
{
  // Used here and in opennurbs_plus_xmeshfast.cpp
  const int* fvi;
  int i, Vid0;
  int Eid_count = 0;
  struct ON_MeshFaceSide Eid;
  memset(&Eid,0,sizeof(Eid));

  if ( 0 == Vid )
  {
    // use mesh m_V[] index
    for ( Eid.fi = 0; Eid.fi < Fcount; Eid.fi++ )
    {
      fvi = F[Eid.fi].vi;

      // These checks are necessary to prevent crashes
      if ( fvi[0] < 0 || fvi[0] >= Vcount )
        continue;
      if ( fvi[1] < 0 || fvi[1] >= Vcount )
        continue;
      if ( fvi[2] < 0 || fvi[2] >= Vcount )
        continue;
      if ( fvi[3] < 0 || fvi[3] >= Vcount )
        continue;

      Eid.vi[0] = fvi[0];
      Vid0 = Eid.vi[1] = fvi[1];
      Eid.side = 0;
      if ( Eid.vi[0] < Eid.vi[1] )
      {
        Eid.dir = 0;
        Eid_list[Eid_count++] = Eid;
      }
      else if ( Eid.vi[0] > Eid.vi[1] )
      {
        i = Eid.vi[0]; Eid.vi[0] = Eid.vi[1]; Eid.vi[1] = i;
        Eid.dir = 1;
        Eid_list[Eid_count++] = Eid;
      }

      Eid.vi[0] = Vid0;
      Vid0 = Eid.vi[1] = fvi[2];
      Eid.side = 1;
      if ( Eid.vi[0] < Eid.vi[1] )
      {
        Eid.dir = 0;
        Eid_list[Eid_count++] = Eid;
      }
      else if ( Eid.vi[0] > Eid.vi[1] )
      {
        i = Eid.vi[0]; Eid.vi[0] = Eid.vi[1]; Eid.vi[1] = i;
        Eid.dir = 1;
        Eid_list[Eid_count++] = Eid;
      }

      if ( fvi[2] != fvi[3] )
      {
        // quad
        Eid.vi[0] = Vid0;
        Vid0 = Eid.vi[1] = fvi[3];
        Eid.side = 2;
        if ( Eid.vi[0] < Eid.vi[1] )
        {
          Eid.dir = 0;
          Eid_list[Eid_count++] = Eid;
        }
        else if ( Eid.vi[0] > Eid.vi[1] )
        {
          i = Eid.vi[0]; Eid.vi[0] = Eid.vi[1]; Eid.vi[1] = i;
          Eid.dir = 1;
          Eid_list[Eid_count++] = Eid;
        }
      }

      Eid.vi[0] = Vid0;
      Eid.vi[1] = fvi[0];
      Eid.side = 3;
      if ( Eid.vi[0] < Eid.vi[1] )
      {
        Eid.dir = 0;
        Eid_list[Eid_count++] = Eid;
      }
      else if ( Eid.vi[0] > Eid.vi[1] )
      {
        i = Eid.vi[0]; Eid.vi[0] = Eid.vi[1]; Eid.vi[1] = i;
        Eid.dir = 1;
        Eid_list[Eid_count++] = Eid;
      }
    }
  }
  else
  {
    // use Vid[mesh m_V[] index]

    for ( Eid.fi = 0; Eid.fi < Fcount; Eid.fi++ )
    {
      fvi = F[Eid.fi].vi;

      // These checks are necessary to prevent crashes
      if ( fvi[0] < 0 || fvi[0] >= Vcount )
        continue;
      if ( fvi[1] < 0 || fvi[1] >= Vcount )
        continue;
      if ( fvi[2] < 0 || fvi[2] >= Vcount )
        continue;
      if ( fvi[3] < 0 || fvi[3] >= Vcount )
        continue;

      Eid.vi[0] = Vid[fvi[0]];
      Vid0 = Eid.vi[1] = Vid[fvi[1]];
      Eid.side = 0;
      if ( Eid.vi[0] < Eid.vi[1] )
      {
        Eid.dir = 0;
        Eid_list[Eid_count++] = Eid;
      }
      else if ( Eid.vi[0] > Eid.vi[1] )
      {
        i = Eid.vi[0]; Eid.vi[0] = Eid.vi[1]; Eid.vi[1] = i;
        Eid.dir = 1;
        Eid_list[Eid_count++] = Eid;
      }

      Eid.vi[0] = Vid0;
      Vid0 = Eid.vi[1] = Vid[fvi[2]];
      Eid.side = 1;
      if ( Eid.vi[0] < Eid.vi[1] )
      {
        Eid.dir = 0;
        Eid_list[Eid_count++] = Eid;
      }
      else if ( Eid.vi[0] > Eid.vi[1] )
      {
        i = Eid.vi[0]; Eid.vi[0] = Eid.vi[1]; Eid.vi[1] = i;
        Eid.dir = 1;
        Eid_list[Eid_count++] = Eid;
      }

      if ( fvi[2] != fvi[3] )
      {
        // quad
        Eid.vi[0] = Vid0;
        Vid0 = Eid.vi[1] = Vid[fvi[3]];
        Eid.side = 2;
        if ( Eid.vi[0] < Eid.vi[1] )
        {
          Eid.dir = 0;
          Eid_list[Eid_count++] = Eid;
        }
        else if ( Eid.vi[0] > Eid.vi[1] )
        {
          i = Eid.vi[0]; Eid.vi[0] = Eid.vi[1]; Eid.vi[1] = i;
          Eid.dir = 1;
          Eid_list[Eid_count++] = Eid;
        }
      }

      Eid.vi[0] = Vid0;
      Eid.vi[1] = Vid[fvi[0]];
      Eid.side = 3;
      if ( Eid.vi[0] < Eid.vi[1] )
      {
        Eid.dir = 0;
        Eid_list[Eid_count++] = Eid;
      }
      else if ( Eid.vi[0] > Eid.vi[1] )
      {
        i = Eid.vi[0]; Eid.vi[0] = Eid.vi[1]; Eid.vi[1] = i;
        Eid.dir = 1;
        Eid_list[Eid_count++] = Eid;
      }
    }
  }

  return Eid_count;
}

int ON_Mesh::GetMeshFaceSideList( 
    const int* Vid,
    struct ON_MeshFaceSide*& sides
    ) const
{
  const int Vcount = m_V.Count(); 
  const int Fcount = m_F.Count(); 
  const ON_MeshFace* F = m_F.Array();

  if ( Fcount < 1 || 0 == F || Vcount < 2 )
    return 0;

  struct ON_MeshFaceSide* Elist = sides;
  if ( 0 == Elist )
  {
    Elist = (struct ON_MeshFaceSide*)onmalloc(4*Fcount*sizeof(Elist[0]));
    if ( 0 == Elist )
      return 0;
  }

  int sides_count = ON_Mesh_GetEidHelper( Vcount, Fcount, F, Vid, Elist );
  if ( sides_count <= 0 )
  {
    if ( 0 == sides )
      delete(Elist);
  }
  else if ( 0 == sides )
  {
    sides = Elist;
  }

  return sides_count;
}

#define ON_COMPILING_OPENNURBS_QSORT_FUNCTIONS
#define ON_SORT_TEMPLATE_STATIC_FUNCTION
#define ON_SORT_TEMPLATE_TYPE struct ON_MeshFaceSide

#define ON_SORT_TEMPLATE_COMPARE ON_qsort_MeshFaceSide_compare
static int ON_SORT_TEMPLATE_COMPARE( 
        ON_SORT_TEMPLATE_TYPE const * side1, 
        ON_SORT_TEMPLATE_TYPE const * side2 
        )
{
  if ( side1->vi[0] < side2->vi[0] )
    return -1;
  if ( side1->vi[0] > side2->vi[0] )
    return 1;
  if ( side1->vi[1] < side2->vi[1] )
    return -1;
  if ( side1->vi[1] > side2->vi[1] )
    return 1;
  if ( side1->fi < side2->fi )
    return -1;
  if ( side1->fi > side2->fi )
    return 1;
  if ( side1->side < side2->side )
    return -1;
  if ( side1->side > side2->side )
    return 1;
  return 0;
}

#define ON_QSORT_FNAME ON_qsort_MeshFaceSide
#include "pcl/surface/3rdparty/opennurbs/opennurbs_qsort_template.h"

void ON_SortMeshFaceSidesByVertexIndex( int sides_count, struct ON_MeshFaceSide* sides )
{
  if ( sides_count >= 2 && 0 != sides )
    ON_QSORT_FNAME( sides, sides_count );
}

#undef ON_COMPILING_OPENNURBS_QSORT_FUNCTIONS
#undef ON_SORT_TEMPLATE_STATIC_FUNCTION
#undef ON_SORT_TEMPLATE_TYPE
#undef ON_QSORT_FNAME