IceAABB.cpp

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// Precompiled Header
#include "Stdafx.h"

using namespace IceMaths;



AABB& AABB::Add(const AABB& aabb)
{
        // Compute new min & max values
        Point Min;      GetMin(Min);
        Point Tmp;      aabb.GetMin(Tmp);
        Min.Min(Tmp);

        Point Max;      GetMax(Max);
        aabb.GetMax(Tmp);
        Max.Max(Tmp);

        // Update this
        SetMinMax(Min, Max);
        return *this;
}



float AABB::MakeCube(AABB& cube) const
{
        Point Ext;      GetExtents(Ext);
        float Max = Ext.Max();

        Point Cnt;      GetCenter(Cnt);
        cube.SetCenterExtents(Cnt, Point(Max, Max, Max));
        return Max;
}



void AABB::MakeSphere(Sphere& sphere) const
{
        GetExtents(sphere.mCenter);
        sphere.mRadius = sphere.mCenter.Magnitude() * 1.00001f; // To make sure sphere::Contains(*this) succeeds
        GetCenter(sphere.mCenter);
}



bool AABB::IsInside(const AABB& box) const
{
        if(box.GetMin(0)>GetMin(0))     return false;
        if(box.GetMin(1)>GetMin(1))     return false;
        if(box.GetMin(2)>GetMin(2))     return false;
        if(box.GetMax(0)<GetMax(0))     return false;
        if(box.GetMax(1)<GetMax(1))     return false;
        if(box.GetMax(2)<GetMax(2))     return false;
        return true;
}



bool AABB::ComputePlanes(Plane* planes) const
{
        // Checkings
        if(!planes)     return false;

        Point Center, Extents;
        GetCenter(Center);
        GetExtents(Extents);

        // Writes normals
        planes[0].n = Point(1.0f, 0.0f, 0.0f);
        planes[1].n = Point(-1.0f, 0.0f, 0.0f);
        planes[2].n = Point(0.0f, 1.0f, 0.0f);
        planes[3].n = Point(0.0f, -1.0f, 0.0f);
        planes[4].n = Point(0.0f, 0.0f, 1.0f);
        planes[5].n = Point(0.0f, 0.0f, -1.0f);

        // Compute a point on each plane
        Point p0 = Point(Center.x+Extents.x, Center.y, Center.z);
        Point p1 = Point(Center.x-Extents.x, Center.y, Center.z);
        Point p2 = Point(Center.x, Center.y+Extents.y, Center.z);
        Point p3 = Point(Center.x, Center.y-Extents.y, Center.z);
        Point p4 = Point(Center.x, Center.y, Center.z+Extents.z);
        Point p5 = Point(Center.x, Center.y, Center.z-Extents.z);

        // Compute d
        planes[0].d = -(planes[0].n|p0);
        planes[1].d = -(planes[1].n|p1);
        planes[2].d = -(planes[2].n|p2);
        planes[3].d = -(planes[3].n|p3);
        planes[4].d = -(planes[4].n|p4);
        planes[5].d = -(planes[5].n|p5);

        return true;
}



bool AABB::ComputePoints(Point* pts)    const
{
        // Checkings
        if(!pts)        return false;

        // Get box corners
        Point min;      GetMin(min);
        Point max;      GetMax(max);

        //     7+------+6                       0 = ---
        //     /|     /|                        1 = +--
        //    / |    / |                        2 = ++-
        //   / 4+---/--+5                       3 = -+-
        // 3+------+2 /    y   z        4 = --+
        //  | /    | /     |  /         5 = +-+
        //  |/     |/      |/           6 = +++
        // 0+------+1      *---x        7 = -++

        // Generate 8 corners of the bbox
        pts[0] = Point(min.x, min.y, min.z);
        pts[1] = Point(max.x, min.y, min.z);
        pts[2] = Point(max.x, max.y, min.z);
        pts[3] = Point(min.x, max.y, min.z);
        pts[4] = Point(min.x, min.y, max.z);
        pts[5] = Point(max.x, min.y, max.z);
        pts[6] = Point(max.x, max.y, max.z);
        pts[7] = Point(min.x, max.y, max.z);

        return true;
}



const Point* AABB::GetVertexNormals()   const
{
        static float VertexNormals[] = 
        {
                -INVSQRT3,      -INVSQRT3,      -INVSQRT3,
                INVSQRT3,       -INVSQRT3,      -INVSQRT3,
                INVSQRT3,       INVSQRT3,       -INVSQRT3,
                -INVSQRT3,      INVSQRT3,       -INVSQRT3,
                -INVSQRT3,      -INVSQRT3,      INVSQRT3,
                INVSQRT3,       -INVSQRT3,      INVSQRT3,
                INVSQRT3,       INVSQRT3,       INVSQRT3,
                -INVSQRT3,      INVSQRT3,       INVSQRT3
        };
        return (const Point*)VertexNormals;
}



const udword* AABB::GetEdges() const
{
        static udword Indices[] = {
        0, 1,   1, 2,   2, 3,   3, 0,
        7, 6,   6, 5,   5, 4,   4, 7,
        1, 5,   6, 2,
        3, 7,   4, 0
        };
        return Indices;
}



const Point* AABB::GetEdgeNormals() const
{
        static float EdgeNormals[] = 
        {
                0,                      -INVSQRT2,      -INVSQRT2,      // 0-1
                INVSQRT2,       0,                      -INVSQRT2,      // 1-2
                0,                      INVSQRT2,       -INVSQRT2,      // 2-3
                -INVSQRT2,      0,                      -INVSQRT2,      // 3-0

                0,                      INVSQRT2,       INVSQRT2,       // 7-6
                INVSQRT2,       0,                      INVSQRT2,       // 6-5
                0,                      -INVSQRT2,      INVSQRT2,       // 5-4
                -INVSQRT2,      0,                      INVSQRT2,       // 4-7

                INVSQRT2,       -INVSQRT2,      0,                      // 1-5
                INVSQRT2,       INVSQRT2,       0,                      // 6-2
                -INVSQRT2,      INVSQRT2,       0,                      // 3-7
                -INVSQRT2,      -INVSQRT2,      0                       // 4-0
        };
        return (const Point*)EdgeNormals;
}

// ===========================================================================
//  (C) 1996-98 Vienna University of Technology
// ===========================================================================
//  NAME:       bboxarea
//  TYPE:       c++ code
//  PROJECT:    Bounding Box Area
//  CONTENT:    Computes area of 2D projection of 3D oriented bounding box
//  VERSION:    1.0
// ===========================================================================
//  AUTHORS:    ds      Dieter Schmalstieg
//              ep      Erik Pojar
// ===========================================================================
//  HISTORY:
//
//  19-sep-99 15:23:03  ds      last modification
//  01-dec-98 15:23:03  ep      created
// ===========================================================================

//----------------------------------------------------------------------------
// SAMPLE CODE STARTS HERE
//----------------------------------------------------------------------------

// NOTE: This sample program requires OPEN INVENTOR!

//indexlist: this table stores the 64 possible cases of classification of
//the eyepoint with respect to the 6 defining planes of the bbox (2^6=64)
//only 26 (3^3-1, where 1 is "inside" cube) of these cases are valid.
//the first 6 numbers in each row are the indices of the bbox vertices that
//form the outline of which we want to compute the area (counterclockwise
//ordering), the 7th entry means the number of vertices in the outline.
//there are 6 cases with a single face and and a 4-vertex outline, and
//20 cases with 2 or 3 faces and a 6-vertex outline. a value of 0 indicates
//an invalid case.


// Original list was made of 7 items, I added an 8th element:
// - to padd on a cache line
// - to repeat the first entry to avoid modulos
//
// I also replaced original ints with sbytes.

static const sbyte gIndexList[64][8] =
{
    {-1,-1,-1,-1,-1,-1,-1,   0}, // 0 inside
    { 0, 4, 7, 3, 0,-1,-1,   4}, // 1 left
    { 1, 2, 6, 5, 1,-1,-1,   4}, // 2 right
    {-1,-1,-1,-1,-1,-1,-1,   0}, // 3 -
    { 0, 1, 5, 4, 0,-1,-1,   4}, // 4 bottom
    { 0, 1, 5, 4, 7, 3, 0,   6}, // 5 bottom, left
    { 0, 1, 2, 6, 5, 4, 0,   6}, // 6 bottom, right
    {-1,-1,-1,-1,-1,-1,-1,   0}, // 7 -
    { 2, 3, 7, 6, 2,-1,-1,   4}, // 8 top
    { 0, 4, 7, 6, 2, 3, 0,   6}, // 9 top, left
    { 1, 2, 3, 7, 6, 5, 1,   6}, //10 top, right
    {-1,-1,-1,-1,-1,-1,-1,   0}, //11 -
    {-1,-1,-1,-1,-1,-1,-1,   0}, //12 -
    {-1,-1,-1,-1,-1,-1,-1,   0}, //13 -
    {-1,-1,-1,-1,-1,-1,-1,   0}, //14 -
    {-1,-1,-1,-1,-1,-1,-1,   0}, //15 -
    { 0, 3, 2, 1, 0,-1,-1,   4}, //16 front
    { 0, 4, 7, 3, 2, 1, 0,   6}, //17 front, left
    { 0, 3, 2, 6, 5, 1, 0,   6}, //18 front, right
    {-1,-1,-1,-1,-1,-1,-1,   0}, //19 -
    { 0, 3, 2, 1, 5, 4, 0,   6}, //20 front, bottom
    { 1, 5, 4, 7, 3, 2, 1,   6}, //21 front, bottom, left
    { 0, 3, 2, 6, 5, 4, 0,   6}, //22 front, bottom, right
    {-1,-1,-1,-1,-1,-1,-1,   0}, //23 -
    { 0, 3, 7, 6, 2, 1, 0,   6}, //24 front, top
    { 0, 4, 7, 6, 2, 1, 0,   6}, //25 front, top, left
    { 0, 3, 7, 6, 5, 1, 0,   6}, //26 front, top, right
    {-1,-1,-1,-1,-1,-1,-1,   0}, //27 -
    {-1,-1,-1,-1,-1,-1,-1,   0}, //28 -
    {-1,-1,-1,-1,-1,-1,-1,   0}, //29 -
    {-1,-1,-1,-1,-1,-1,-1,   0}, //30 -
    {-1,-1,-1,-1,-1,-1,-1,   0}, //31 -
    { 4, 5, 6, 7, 4,-1,-1,   4}, //32 back
    { 0, 4, 5, 6, 7, 3, 0,   6}, //33 back, left
    { 1, 2, 6, 7, 4, 5, 1,   6}, //34 back, right
    {-1,-1,-1,-1,-1,-1,-1,   0}, //35 -
    { 0, 1, 5, 6, 7, 4, 0,   6}, //36 back, bottom
    { 0, 1, 5, 6, 7, 3, 0,   6}, //37 back, bottom, left
    { 0, 1, 2, 6, 7, 4, 0,   6}, //38 back, bottom, right
    {-1,-1,-1,-1,-1,-1,-1,   0}, //39 -
    { 2, 3, 7, 4, 5, 6, 2,   6}, //40 back, top
    { 0, 4, 5, 6, 2, 3, 0,   6}, //41 back, top, left
    { 1, 2, 3, 7, 4, 5, 1,   6}, //42 back, top, right
    {-1,-1,-1,-1,-1,-1,-1,   0}, //43 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //44 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //45 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //46 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //47 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //48 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //49 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //50 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //51 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //52 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //53 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //54 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //55 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //56 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //57 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //58 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //59 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //60 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //61 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}, //62 invalid
    {-1,-1,-1,-1,-1,-1,-1,   0}  //63 invalid
};

const sbyte* AABB::ComputeOutline(const Point& local_eye, sdword& num)  const
{
        // Get box corners
        Point min;      GetMin(min);
        Point max;      GetMax(max);

        // Compute 6-bit code to classify eye with respect to the 6 defining planes of the bbox
        int pos = ((local_eye.x < min.x) ?  1 : 0)      // 1 = left
                        + ((local_eye.x > max.x) ?  2 : 0)      // 2 = right
                        + ((local_eye.y < min.y) ?  4 : 0)      // 4 = bottom
                        + ((local_eye.y > max.y) ?  8 : 0)      // 8 = top
                        + ((local_eye.z < min.z) ? 16 : 0)      // 16 = front
                        + ((local_eye.z > max.z) ? 32 : 0);     // 32 = back

        // Look up number of vertices in outline
        num = (sdword)gIndexList[pos][7];
        // Zero indicates invalid case
        if(!num) return null;

        return &gIndexList[pos][0];
}

// calculateBoxArea: computes the screen-projected 2D area of an oriented 3D bounding box

//const Point&          eye,            //eye point (in bbox object coordinates)
//const AABB&                   box,            //3d bbox
//const Matrix4x4&      mat,            //free transformation for bbox
//float width, float height, int& num)
float AABB::ComputeBoxArea(const Point& eye, const Matrix4x4& mat, float width, float height, sdword& num)      const
{
        const sbyte* Outline = ComputeOutline(eye, num);
        if(!Outline)    return -1.0f;

        // Compute box vertices
        Point vertexBox[8], dst[8];
        ComputePoints(vertexBox);

        // Transform all outline corners into 2D screen space
        for(sdword i=0;i<num;i++)
        {
                HPoint Projected;
                vertexBox[Outline[i]].ProjectToScreen(width, height, mat, Projected);
                dst[i] = Projected;
        }

        float Sum = (dst[num-1][0] - dst[0][0]) * (dst[num-1][1] + dst[0][1]);

        for(int i=0; i<num-1; i++)
                Sum += (dst[i][0] - dst[i+1][0]) * (dst[i][1] + dst[i+1][1]);

        return Sum * 0.5f;      //return computed value corrected by 0.5
}