deprecated_point.h

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/****************************************************************************
* VCGLib                                                            o o     *
* Visual and Computer Graphics Library                            o     o   *
*                                                                _   O  _   *
* Copyright(C) 2004                                                \/)\/    *
* Visual Computing Lab                                            /\/|      *
* ISTI - Italian National Research Council                           |      *
*                                                                    \      *
* All rights reserved.                                                      *
*                                                                           *
* This program is free software; you can redistribute it and/or modify      *
* it under the terms of the GNU General Public License as published by      *
* the Free Software Foundation; either version 2 of the License, or         *
* (at your option) any later version.                                       *
*                                                                           *
* This program is distributed in the hope that it will be useful,           *
* but WITHOUT ANY WARRANTY; without even the implied warranty of            *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the             *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt)          *
* for more details.                                                         *
*                                                                           *
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/****************************************************************************
  History

$Log: not supported by cvs2svn $
Revision 1.9  2006/12/20 15:23:52  ganovelli
using of locally defined variable removed

Revision 1.8  2006/04/11 08:10:05  zifnab1974
changes necessary for gcc 3.4.5 on linux 64bit.

Revision 1.7  2005/12/12 11:22:32  ganovelli
compiled with gcc

Revision 1.6  2005/01/12 11:25:52  ganovelli
corrected Point<3

Revision 1.5  2004/10/20 16:45:21  ganovelli
first compiling version (MC,INtel,gcc)

Revision 1.4  2004/04/29 10:47:06  ganovelli
some siyntax error corrected

Revision 1.3  2004/04/05 12:36:43  tarini
unified version: PointBase version, with no guards "(N==3)"



Revision 1.1  2004/03/16 03:07:38  tarini
"dimensionally unified" version: first commit

****************************************************************************/

#ifndef __VCGLIB_POINT
#define __VCGLIB_POINT

#include <assert.h>
#include <vcg/math/base.h>
#include <vcg/space/space.h>

namespace vcg {

    namespace ndim{


//template <int N, class S>
//class Point;

template <int N, class S>
class Point
{
public:
        typedef S          ScalarType;
        typedef VoidType   ParamType;
        typedef Point<N,S> PointType;
        enum {Dimension=N};


protected:
    S _v[N];

public:


  inline Point () { };
//      inline Point ( const S nv[N] );

    inline S Ext( const int i ) const
    {
        if(i>=0 && i<=N) return _v[i];
        else             return 0;
    }

        template <int N2, class S2>
        inline void Import( const Point<N2,S2> & b )
        {
                _v[0] = ScalarType(b[0]);
                _v[1] = ScalarType(b[1]);
                if (N>2) { if (N2>2) _v[2] = ScalarType(b[2]); else _v[2] = 0;};
                if (N>3) { if (N2>3) _v[3] = ScalarType(b[3]); else _v[3] = 0;};
        }

        template <int N2, class S2>
  static inline PointType Construct( const Point<N2,S2> & b )
  {
        PointType p; p.Import(b);
    return p;
  }

        template <class S2>
        inline void ImportHomo( const Point<N-1,S2> & b )
        {
                _v[0] = ScalarType(b[0]);
                _v[1] = ScalarType(b[1]);
                if (N>2) { _v[2] = ScalarType(_v[2]); };
                _v[N-1] = 1.0;
        }

        template <int N2, class S2>
  static inline PointType Construct( const Point<N-1,S2> & b )
  {
        PointType p; p.ImportHomo(b);
    return p;
  }



        inline S & operator [] ( const int i )
        {
                assert(i>=0 && i<N);
                return _v[i];
        }
        inline const S & operator [] ( const int i ) const
        {
                assert(i>=0 && i<N);
                return _v[i];
        }
  inline const S &X() const { return _v[0]; }
    inline const S &Y() const { return _v[1]; }
    inline const S &Z() const { static_assert(N>2); return _v[2]; }
    inline const S &W() const { return _v[N-1]; }
    inline S &X() { return _v[0]; }
    inline S &Y() { return _v[1]; }
    inline S &Z() { static_assert(N>2); return _v[2]; }
    inline S &W() { return _v[N-1]; }
    inline const S * V() const
    {
        return _v;
    }
        inline S * V()
        {
                return _v;
        }
    inline S & V( const int i )
    {
        assert(i>=0 && i<N);
        return _v[i];
    }
    inline const S & V( const int i ) const
    {
        assert(i>=0 && i<N);
        return _v[i];
    }



        inline void SetZero()
        {
                for(unsigned int ii = 0; ii < Dimension;++ii)
                        V(ii) = S();
        }

        inline PointType operator + ( PointType const & p) const
        {
                PointType res;
                for(unsigned int ii = 0; ii < Dimension;++ii)
                        res[ii] = V(ii) + p[ii];
                return res;
        }

        inline PointType operator - ( PointType const & p) const
        {
                PointType res;
                for(unsigned int ii = 0; ii < Dimension;++ii)
                        res[ii] = V(ii) - p[ii];
                return res;
        }

        inline PointType operator * ( const S s ) const
        {
                PointType res;
                for(unsigned int ii = 0; ii < Dimension;++ii)
                        res[ii] = V(ii) * s;
                return res;
        }

        inline PointType operator / ( const S s ) const
        {
                PointType res;
                for(unsigned int ii = 0; ii < Dimension;++ii)
                        res[ii] = V(ii) / s;
                return res;
        }

        inline PointType & operator += ( PointType const & p)
        {
                for(unsigned int ii = 0; ii < Dimension;++ii)
                        V(ii) += p[ii];
                return *this;
        }

        inline PointType & operator -= ( PointType const & p)
        {
                for(unsigned int ii = 0; ii < Dimension;++ii)
                        V(ii) -= p[ii];
                return *this;
        }

        inline PointType & operator *= ( const S s )
        {
                for(unsigned int ii = 0; ii < Dimension;++ii)
                        V(ii) *= s;
                return *this;
        }

        inline PointType & operator /= ( const S s )
        {
                for(unsigned int ii = 0; ii < Dimension;++ii)
                        V(ii) *= s;
                return *this;
        }

        inline PointType operator - () const
        {
                PointType res;
                for(unsigned int ii = 0; ii < Dimension;++ii)
                        res[ii] = - V(ii);
                return res;
        }



    inline S operator * ( PointType const & p ) const;

        inline S StableDot ( const PointType & p ) const;




        inline S Norm() const;
        template <class PT> static S Norm(const PT &p );
        inline S SquaredNorm() const;
        template <class PT> static S SquaredNorm(const PT &p );
        inline PointType & Normalize();
        template <class PT> static PointType & Normalize(const PT &p);
        inline PointType & HomoNormalize();

        inline S NormInfinity() const;
        inline S NormOne() const;



        inline S operator % ( PointType const & p ) const;

        inline S Sum() const;
        inline S Max() const;
        inline S Min() const;
        inline int MaxI() const;
        inline int MinI() const;


        inline PointType & Scale( const PointType & p );


        void ToPolar( S & ro, S & tetha, S & fi ) const
        {
                ro = Norm();
                tetha = (S)atan2( _v[1], _v[0] );
                fi    = (S)acos( _v[2]/ro );
        }


        inline bool operator == ( PointType const & p ) const;
        inline bool operator != ( PointType const & p ) const;
        inline bool operator <  ( PointType const & p ) const;
        inline bool operator >  ( PointType const & p ) const;
        inline bool operator <= ( PointType const & p ) const;
        inline bool operator >= ( PointType const & p ) const;


        inline PointType LocalToGlobal(ParamType p) const{
                return *this; }

  inline ParamType GlobalToLocal(PointType /*p*/) const{
      return ParamType(); }

}; // end class definition









template <class S>
class Point2 : public Point<2,S> {
public:
        typedef S ScalarType;
        typedef Point2 PointType;
        using Point<2,S>::_v;
        using Point<2,S>::V;
        using Point<2,S>::W;



        inline Point2 (){}

        inline Point2 ( const S a, const S b){
                _v[0]=a; _v[1]=b;  };

        inline Point2 operator ~ () const {
                return Point2 ( -_v[2], _v[1] );
        }

        inline ScalarType &Angle(){
                return math::Atan2(_v[1],_v[0]);}

        inline Point2 & ToPolar(){
                ScalarType t = Angle();
                _v[0] = Norm();
                _v[1] = t;
                return *this;}

        inline Point2 & ToCartesian() {
                ScalarType l = _v[0];
                _v[0] = (ScalarType)(l*math::Cos(_v[1]));
                _v[1] = (ScalarType)(l*math::Sin(_v[1]));
                return *this;}

        inline Point2 & Rotate( const ScalarType rad ){
                ScalarType t = _v[0];
                ScalarType s = math::Sin(rad);
                ScalarType c = math::Cos(rad);
                _v[0] = _v[0]*c - _v[1]*s;
                _v[1] =   t *s + _v[1]*c;
                return *this;}



        inline void Zero(){
                _v[0]=0; _v[1]=0;  };

        inline Point2 ( const S nv[2] ){
                _v[0]=nv[0]; _v[1]=nv[1];   };

        inline Point2 operator + ( Point2 const & p) const {
                return Point2( _v[0]+p._v[0], _v[1]+p._v[1]); }

        inline Point2 operator - ( Point2 const & p) const {
                return Point2( _v[0]-p._v[0], _v[1]-p._v[1]); }

        inline Point2 operator * ( const S s ) const {
                return Point2( _v[0]*s, _v[1]*s  ); }

        inline Point2 operator / ( const S s ) const {
                S t=1.0/s;
                return Point2( _v[0]*t, _v[1]*t   ); }

        inline Point2 operator - () const {
                return Point2 ( -_v[0], -_v[1]  ); }

        inline Point2 & operator += ( Point2 const & p ) {
                _v[0] += p._v[0]; _v[1] += p._v[1];   return *this; }

        inline Point2 & operator -= ( Point2 const & p ) {
                _v[0] -= p._v[0]; _v[1] -= p._v[1];   return *this; }

        inline Point2 & operator *= ( const S s ) {
                _v[0] *= s; _v[1] *= s;  return *this; }

        inline Point2 & operator /= ( const S s ) {
                S t=1.0/s; _v[0] *= t; _v[1] *= t;   return *this; }

        inline S Norm() const {
                return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1]   );}

        template <class PT> static S Norm(const PT &p ) {
                return math::Sqrt( p.V(0)*p.V(0) + p.V(1)*p.V(1)  );}

        inline S SquaredNorm() const {
                return ( _v[0]*_v[0] + _v[1]*_v[1] );}

        template <class PT> static S SquaredNorm(const PT &p ) {
                return ( p.V(0)*p.V(0) + p.V(1)*p.V(1) );}

    inline S operator * ( Point2 const & p ) const {
    return ( _v[0]*p._v[0] + _v[1]*p._v[1]) ; }

        inline bool operator == ( Point2 const & p ) const {
                return _v[0]==p._v[0] && _v[1]==p._v[1] ;}

        inline bool operator != ( Point2 const & p ) const {
                return _v[0]!=p._v[0] || _v[1]!=p._v[1] ;}

        inline bool operator <  ( Point2 const & p ) const{
                return (_v[1]!=p._v[1])?(_v[1]< p._v[1]) : (_v[0]<p._v[0]); }

        inline bool operator >  ( Point2 const & p ) const      {
                return (_v[1]!=p._v[1])?(_v[1]> p._v[1]) : (_v[0]>p._v[0]); }

        inline bool operator <= ( Point2 const & p ) {
                return (_v[1]!=p._v[1])?(_v[1]< p._v[1]) : (_v[0]<=p._v[0]); }

        inline bool operator >= ( Point2 const & p ) const {
                return (_v[1]!=p._v[1])?(_v[1]> p._v[1]) : (_v[0]>=p._v[0]); }

        inline Point2 & Normalize() {
                PointType n = Norm(); if(n!=0.0) { n=1.0/n;     _v[0]*=n;       _v[1]*=n;} return *this;}

        inline Point2 & HomoNormalize(){
                if (_v[2]!=0.0) {       _v[0] /= W(); W()=1.0; } return *this;}

        inline S NormInfinity() const {
                return math::Max( math::Abs(_v[0]), math::Abs(_v[1]) ); }

        inline S NormOne() const {
                return math::Abs(_v[0])+ math::Abs(_v[1]);}

        inline S operator % ( Point2 const & p ) const {
                return _v[0] * p._v[1] - _v[1] * p._v[0]; }

        inline S Sum() const {
                return _v[0]+_v[1];}

        inline S Max() const {
                return math::Max( _v[0], _v[1] ); }

        inline S Min() const {
                return math::Min( _v[0], _v[1] ); }

        inline int MaxI() const {
                return (_v[0] < _v[1]) ? 1:0; };

        inline int MinI() const {
          return (_v[0] > _v[1]) ? 1:0; };

        inline PointType & Scale( const PointType & p ) {
                _v[0] *= p._v[0]; _v[1] *= p._v[1];  return *this; }

        inline S StableDot ( const PointType & p ) const {
                return _v[0]*p._v[0] +_v[1]*p._v[1]; }

};

template <typename S>
class Point3 : public Point<3,S> {
public:
        typedef S ScalarType;
        typedef Point3<S>  PointType;
        using Point<3,S>::_v;
        using Point<3,S>::V;
        using Point<3,S>::W;




        inline Point3 ():Point<3,S>(){}
        inline Point3 ( const S a, const S b,  const S c){
                _v[0]=a; _v[1]=b; _v[2]=c; };

        inline PointType operator ^ ( PointType const & p ) const {
                return Point3 (
                        _v[1]*p._v[2] - _v[2]*p._v[1],
                        _v[2]*p._v[0] - _v[0]*p._v[2],
                        _v[0]*p._v[1] - _v[1]*p._v[0] );
        }


        inline void Zero(){
                _v[0]=0; _v[1]=0; _v[2]=0; };

        inline Point3 ( const S nv[3] ){
                _v[0]=nv[0]; _v[1]=nv[1]; _v[2]=nv[2];  };

        inline Point3 operator + ( Point3 const & p)  const{
                return Point3( _v[0]+p._v[0], _v[1]+p._v[1], _v[2]+p._v[2]); }

        inline Point3 operator - ( Point3 const & p) const {
                return Point3( _v[0]-p._v[0], _v[1]-p._v[1], _v[2]-p._v[2]); }

        inline Point3 operator * ( const S s ) const {
                return Point3( _v[0]*s, _v[1]*s , _v[2]*s  ); }

        inline Point3 operator / ( const S s ) const {
                S t=1.0/s;
                return Point3( _v[0]*t, _v[1]*t , _v[2]*t  ); }

        inline Point3 operator - () const {
                return Point3 ( -_v[0], -_v[1] , -_v[2]  ); }

        inline Point3 & operator += ( Point3 const & p ) {
                _v[0] += p._v[0]; _v[1] += p._v[1]; _v[2] += p._v[2];  return *this; }

        inline Point3 & operator -= ( Point3 const & p ) {
                _v[0] -= p._v[0]; _v[1] -= p._v[1]; _v[2] -= p._v[2];  return *this; }

        inline Point3 & operator *= ( const S s ) {
                _v[0] *= s; _v[1] *= s; _v[2] *= s; return *this; }

        inline Point3 & operator /= ( const S s ) {
                S t=1.0/s; _v[0] *= t; _v[1] *= t;  _v[2] *= t;   return *this; }

        inline S Norm() const {
                return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2]  );}

        template <class PT> static S Norm(const PT &p ) {
                return math::Sqrt( p.V(0)*p.V(0) + p.V(1)*p.V(1) + p.V(2)*p.V(2)  );}

        inline S SquaredNorm() const {
                return ( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2]  );}

        template <class PT> static S SquaredNorm(const PT &p ) {
                return ( p.V(0)*p.V(0) + p.V(1)*p.V(1) + p.V(2)*p.V(2)  );}

    inline S operator * ( PointType const & p ) const {
    return ( _v[0]*p._v[0] + _v[1]*p._v[1] + _v[2]*p._v[2]) ; }

        inline bool operator == ( PointType const & p ) const {
                return _v[0]==p._v[0] && _v[1]==p._v[1] && _v[2]==p._v[2] ;}

        inline bool operator != ( PointType const & p ) const {
                return _v[0]!=p._v[0] || _v[1]!=p._v[1] || _v[2]!=p._v[2] ;}

        inline bool operator <  ( PointType const & p ) const{
                return  (_v[2]!=p._v[2])?(_v[2]< p._v[2]):
                                        (_v[1]!=p._v[1])?(_v[1]< p._v[1]) : (_v[0]<p._v[0]); }

        inline bool operator >  ( PointType const & p ) const   {
                return  (_v[2]!=p._v[2])?(_v[2]> p._v[2]):
                                        (_v[1]!=p._v[1])?(_v[1]> p._v[1]) : (_v[0]>p._v[0]); }

        inline bool operator <= ( PointType const & p ) {
                return  (_v[2]!=p._v[2])?(_v[2]< p._v[2]):
                                        (_v[1]!=p._v[1])?(_v[1]< p._v[1]) : (_v[0]<=p._v[0]); }

        inline bool operator >= ( PointType const & p ) const {
                return  (_v[2]!=p._v[2])?(_v[2]> p._v[2]):
                                        (_v[1]!=p._v[1])?(_v[1]> p._v[1]) : (_v[0]>=p._v[0]); }

        inline PointType & Normalize() {
                S n = Norm();
                if(n!=0.0) {
                        n=S(1.0)/n;
                _v[0]*=n;       _v[1]*=n;       _v[2]*=n; }
                return *this;}

        inline PointType & HomoNormalize(){
                if (_v[2]!=0.0) {       _v[0] /= W();   _v[1] /= W(); W()=1.0; }
                return *this;}

        inline S NormInfinity() const {
                return math::Max( math::Max( math::Abs(_v[0]), math::Abs(_v[1]) ),
                                                        math::Abs(_v[3])  ); }

        inline S NormOne() const {
                return math::Abs(_v[0])+ math::Abs(_v[1])+math::Max(math::Abs(_v[2]));}

        inline S operator % ( PointType const & p ) const {
                S t = (*this)*p; /* Area, general formula */
                return math::Sqrt( SquaredNorm() * p.SquaredNorm() - (t*t) );};

        inline S Sum() const {
                return _v[0]+_v[1]+_v[2];}

        inline S Max() const {
                return math::Max( math::Max( _v[0], _v[1] ),  _v[2] ); }

        inline S Min() const {
                return math::Min( math::Min( _v[0], _v[1] ),  _v[2] ); }

        inline int MaxI() const {
                int i= (_v[0] < _v[1]) ? 1:0; if (_v[i] < _v[2]) i=2; return i;};

        inline int MinI() const {
                int i= (_v[0] > _v[1]) ? 1:0; if (_v[i] > _v[2]) i=2; return i;};

        inline PointType & Scale( const PointType & p ) {
                _v[0] *= p._v[0]; _v[1] *= p._v[1]; _v[2] *= p._v[2]; return *this; }

        inline S StableDot ( const PointType & p ) const {
                S k0=_v[0]*p._v[0],     k1=_v[1]*p._v[1], k2=_v[2]*p._v[2];
                int exp0,exp1,exp2;
                frexp( double(k0), &exp0 );
                frexp( double(k1), &exp1 );
                frexp( double(k2), &exp2 );
                if( exp0<exp1 )
                        if(exp0<exp2) return (k1+k2)+k0; else return (k0+k1)+k2;
                else
                        if(exp1<exp2) return (k0+k2)+k1; else return (k0+k1)+k2;
        }

};

template <typename S>
class Point4 : public Point<4,S> {
public:
        typedef S ScalarType;
        typedef Point4<S> PointType;
        using Point<3,S>::_v;
        using Point<3,S>::V;
        using Point<3,S>::W;



        inline Point4 (){}


        inline Point4 ( const S a, const S b,  const S c, const S d){
                _v[0]=a; _v[1]=b; _v[2]=c; _v[3]=d; };

        inline void Zero(){
                _v[0]=0; _v[1]=0; _v[2]=0; _v[3]=0; };

        inline Point4 ( const S nv[4] ){
                _v[0]=nv[0]; _v[1]=nv[1]; _v[2]=nv[2]; _v[3]=nv[3]; };

        inline Point4 operator + ( Point4 const & p) const {
                return Point4( _v[0]+p._v[0], _v[1]+p._v[1], _v[2]+p._v[2], _v[3]+p._v[3] ); }

        inline Point4 operator - ( Point4 const & p) const {
                return Point4( _v[0]-p._v[0], _v[1]-p._v[1], _v[2]-p._v[2], _v[3]-p._v[3] ); }

        inline Point4 operator * ( const S s ) const {
                return Point4( _v[0]*s, _v[1]*s , _v[2]*s , _v[3]*s ); }

        inline PointType operator ^ ( PointType const & p ) const {
                assert(0);
                return *this;
        }

        inline Point4 operator / ( const S s ) const {
                S t=1.0/s;
                return Point4( _v[0]*t, _v[1]*t , _v[2]*t , _v[3]*t ); }

        inline Point4 operator - () const {
                return Point4 ( -_v[0], -_v[1] , -_v[2] , -_v[3] ); }

        inline Point4 & operator += ( Point4 const & p ) {
                _v[0] += p._v[0]; _v[1] += p._v[1]; _v[2] += p._v[2]; _v[3] += p._v[3]; return *this; }

        inline Point4 & operator -= ( Point4 const & p ) {
                _v[0] -= p._v[0]; _v[1] -= p._v[1]; _v[2] -= p._v[2]; _v[3] -= p._v[3]; return *this; }

        inline Point4 & operator *= ( const S s ) {
                _v[0] *= s; _v[1] *= s; _v[2] *= s; _v[3] *= s; return *this; }

        inline Point4 & operator /= ( const S s ) {
                S t=1.0/s; _v[0] *= t; _v[1] *= t;  _v[2] *= t;  _v[3] *= t; return *this; }

        inline S Norm() const {
                return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] + _v[3]*_v[3] );}

        template <class PT> static S Norm(const PT &p ) {
                return math::Sqrt( p.V(0)*p.V(0) + p.V(1)*p.V(1) + p.V(2)*p.V(2) + p.V(3)*p.V(3) );}

        inline S SquaredNorm() const {
                return ( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] + _v[3]*_v[3] );}

        template <class PT> static S SquaredNorm(const PT &p ) {
                return ( p.V(0)*p.V(0) + p.V(1)*p.V(1) + p.V(2)*p.V(2) + p.V(3)*p.V(3) );}

    inline S operator * ( PointType const & p ) const {
    return ( _v[0]*p._v[0] + _v[1]*p._v[1] + _v[2]*p._v[2] + _v[3]*p._v[3] ); }

        inline bool operator == ( PointType const & p ) const {
                return _v[0]==p._v[0] && _v[1]==p._v[1] && _v[2]==p._v[2] && _v[3]==p._v[3];}

        inline bool operator != ( PointType const & p ) const {
                return _v[0]!=p._v[0] || _v[1]!=p._v[1] || _v[2]!=p._v[2] || _v[3]!=p._v[3];}

        inline bool operator <  ( PointType const & p ) const{
                return  (_v[3]!=p._v[3])?(_v[3]< p._v[3]) : (_v[2]!=p._v[2])?(_v[2]< p._v[2]):
                                        (_v[1]!=p._v[1])?(_v[1]< p._v[1]) : (_v[0]<p._v[0]); }

        inline bool operator >  ( PointType const & p ) const   {
                return  (_v[3]!=p._v[3])?(_v[3]> p._v[3]) : (_v[2]!=p._v[2])?(_v[2]> p._v[2]):
                                        (_v[1]!=p._v[1])?(_v[1]> p._v[1]) : (_v[0]>p._v[0]); }

        inline bool operator <= ( PointType const & p ) {
                return  (_v[3]!=p._v[3])?(_v[3]< p._v[3]) : (_v[2]!=p._v[2])?(_v[2]< p._v[2]):
                                        (_v[1]!=p._v[1])?(_v[1]< p._v[1]) : (_v[0]<=p._v[0]); }

        inline bool operator >= ( PointType const & p ) const {
                return  (_v[3]!=p._v[3])?(_v[3]> p._v[3]) : (_v[2]!=p._v[2])?(_v[2]> p._v[2]):
                                        (_v[1]!=p._v[1])?(_v[1]> p._v[1]) : (_v[0]>=p._v[0]); }

        inline PointType & Normalize() {
                PointType n = Norm(); if(n!=0.0) { n=1.0/n;     _v[0]*=n;       _v[1]*=n;       _v[2]*=n; _v[3]*=n; }
                return *this;};

        template <class PT>  PointType & Normalize(const PT &p){
                PointType n = Norm(); if(n!=0.0) { n=1.0/n;     V(0)*=n;        V(1)*=n;        V(2)*=n; V(3)*=n; }
                return *this;};

        inline PointType & HomoNormalize(){
                if (_v[3]!=0.0) {       _v[0] /= W();   _v[1] /= W();   _v[2] /= W(); W()=1.0; }
                return *this;};

        inline S NormInfinity() const {
                return math::Max( math::Max( math::Abs(_v[0]), math::Abs(_v[1]) ),
                                                        math::Max( math::Abs(_v[2]), math::Abs(_v[3]) ) ); }

        inline S NormOne() const {
                return math::Abs(_v[0])+ math::Abs(_v[1])+math::Max(math::Abs(_v[2]),math::Abs(_v[3]));}

        inline S operator % ( PointType const & p ) const {
                S t = (*this)*p; /* Area, general formula */
                return math::Sqrt( SquaredNorm() * p.SquaredNorm() - (t*t) );};

        inline S Sum() const {
                return _v[0]+_v[1]+_v[2]+_v[3];}

        inline S Max() const {
                return math::Max( math::Max( _v[0], _v[1] ), math::Max( _v[2], _v[3] )); }

        inline S Min() const {
                return math::Min( math::Min( _v[0], _v[1] ), math::Min( _v[2], _v[3] )); }

        inline int MaxI() const {
                int i= (_v[0] < _v[1]) ? 1:0; if (_v[i] < _v[2]) i=2; if (_v[i] < _v[3]) i=3;
                return i;};

        inline int MinI() const {
                int i= (_v[0] > _v[1]) ? 1:0; if (_v[i] > _v[2]) i=2; if (_v[i] > _v[3]) i=3;
                return i;};

        inline PointType & Scale( const PointType & p ) {
                _v[0] *= p._v[0]; _v[1] *= p._v[1]; _v[2] *= p._v[2]; _v[3] *= p._v[3]; return *this; }

        inline S StableDot ( const PointType & p ) const {
                S k0=_v[0]*p._v[0],     k1=_v[1]*p._v[1], k2=_v[2]*p._v[2], k3=_v[3]*p._v[3];
                int exp0,exp1,exp2,exp3;
                frexp( double(k0), &exp0 );frexp( double(k1), &exp1 );
                frexp( double(k2), &exp2 );frexp( double(k3), &exp3 );
                if (exp0>exp1) { std::swap(k0,k1); std::swap(exp0,exp1); }
                if (exp2>exp3) { std::swap(k2,k3); std::swap(exp2,exp3); }
                if (exp0>exp2) { std::swap(k0,k2); std::swap(exp0,exp2); }
                if (exp1>exp3) { std::swap(k1,k3); std::swap(exp1,exp3); }
                if (exp2>exp3) { std::swap(k2,k3); std::swap(exp2,exp3); }
                return ( (k0 + k1) + k2 ) +k3; }

};


template <class S>
inline S Angle( Point3<S>  const & p1, Point3<S>  const & p2 )
{
        S w = p1.Norm()*p2.Norm();
        if(w==0) return -1;
        S t = (p1*p2)/w;
        if(t>1) t = 1;
        else if(t<-1) t = -1;
        return (S) acos(t);
}

// versione uguale alla precedente ma che assume che i due vettori siano unitari
template <class S>
inline S AngleN( Point3<S>  const & p1, Point3<S>  const & p2 )
{
        S w = p1*p2;
        if(w>1)
                w = 1;
        else if(w<-1)
                w=-1;
  return (S) acos(w);
}


template <int N,class S>
inline S Norm( Point<N,S> const & p )
{
    return p.Norm();
}

template <int N,class S>
inline S SquaredNorm( Point<N,S> const & p )
{
  return p.SquaredNorm();
}

template <int N,class S>
inline Point<N,S> & Normalize( Point<N,S> & p )
{
  p.Normalize();
  return p;
}

template <int N, class S>
inline S Distance( Point<N,S> const & p1,Point<N,S> const & p2 )
{
    return (p1-p2).Norm();
}

template <int N, class S>
inline S SquaredDistance( Point<N,S> const & p1,Point<N,S> const & p2 )
{
    return (p1-p2).SquaredNorm();
}


//template <typename S>
//struct Point2:public Point<2,S>{
//      inline Point2(){};
//      inline Point2(Point<2,S> const & p):Point<2,S>(p){} ;
//      inline Point2( const S a, const S b):Point<2,S>(a,b){};
//};
//
//template <typename S>
//struct Point3:public Point3<S> {
//      inline Point3(){};
//      inline Point3(Point3<S>  const & p):Point3<S> (p){}
//      inline Point3( const S a, const S b,  const S c):Point3<S> (a,b,c){};
//};
//
//
//template <typename S>
//struct Point4:public Point4<S>{
//      inline Point4(){};
//      inline Point4(Point4<S> const & p):Point4<S>(p){}
//      inline Point4( const S a, const S b,  const S c, const S d):Point4<S>(a,b,c,d){};
//};

typedef Point2<short>  Point2s;
typedef Point2<int>       Point2i;
typedef Point2<float>  Point2f;
typedef Point2<double> Point2d;
typedef Point2<short>  Vector2s;
typedef Point2<int>       Vector2i;
typedef Point2<float>  Vector2f;
typedef Point2<double> Vector2d;

typedef Point3<short>  Point3s;
typedef Point3<int>       Point3i;
typedef Point3<float>  Point3f;
typedef Point3<double> Point3d;
typedef Point3<short>  Vector3s;
typedef Point3<int>       Vector3i;
typedef Point3<float>  Vector3f;
typedef Point3<double> Vector3d;


typedef Point4<short>  Point4s;
typedef Point4<int>       Point4i;
typedef Point4<float>  Point4f;
typedef Point4<double> Point4d;
typedef Point4<short>  Vector4s;
typedef Point4<int>       Vector4i;
typedef Point4<float>  Vector4f;
typedef Point4<double> Vector4d;

//added only for backward compatibility
template<unsigned int N,typename S>
struct PointBase : Point<N,S>
{
        PointBase()
                :Point<N,S>()
        {
        }
};

} // end namespace ndim
} // end namespace vcg
#endif