Added Various missing functions: SetShearXY, SetShearXZ, SetShearYZ, SetScale for point3 and Decompose
Completed *=(scalar); made uniform GetRow and GetColumn
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@ -24,6 +24,9 @@
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History
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$Log: not supported by cvs2svn $
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Revision 1.25 2005/04/14 11:35:09 ponchio
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*** empty log message ***
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Revision 1.24 2005/03/18 00:14:39 cignoni
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removed small gcc compiling issues
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@ -123,7 +126,7 @@ public:
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///@{
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/** $name Contrutors
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/** $name Constructors
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* No automatic casting and default constructor is empty
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*/
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Matrix44() {};
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@ -154,43 +157,29 @@ public:
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const T *operator[](const int i) const;
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// return a copy of the i-th column
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Point4<T> GetColumn(const int& i)const{
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assert(i >=0);
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assert(i<4);
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int first = i<<2;
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return Point4<T>(_a[first],_a[first+1],_a[first+2],_a[first+3]);
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Point4<T> GetColumn4(const int& i)const{
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assert(i>=0 && i<4);
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return Point4<T>(ElementAt(0,i),ElementAt(1,i),ElementAt(2,i),ElementAt(3,i));
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//return Point4<T>(_a[i],_a[i+4],_a[i+8],_a[i+12]);
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}
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// return the i-th row
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Point4<T> & GetColumn4(const int& i)const{
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assert(i >=0);
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assert(i<4);
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int first = i<<2;
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return Point4<T>(_a[first],_a[first+4],_a[first+8],_a[first+12]);
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Point3<T> GetColumn3(const int& i)const{
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assert(i>=0 && i<4);
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return Point3<T>(ElementAt(0,i),ElementAt(1,i),ElementAt(2,i));
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}
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// return a copy of the i-th row
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Point4<T> Row4(const int& i)const{
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assert(i >=0);
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assert(i<4);
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return *((Point4<T>*)(&_a[i<<2]));
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Point4<T> GetRow4(const int& i)const{
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assert(i>=0 && i<4);
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return Point4<T>(ElementAt(i,0),ElementAt(i,1),ElementAt(i,2),ElementAt(i,3));
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// return *((Point4<T>*)(&_a[i<<2])); alternativa forse + efficiente
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}
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Point3<T> GetColumn3(const int& i)const{
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assert(i >=0);
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assert(i<4);
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int first = i <<2;
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return Point3<T>(_a[first],_a[first+4],_a[first+8]);
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}
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// return a copy of the i-th row
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Point3<T> Row3(const int& i)const{
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assert(i >=0);
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assert(i<4);
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return *((Point3<T>*)(&_a[i<<2]));
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Point3<T> GetRow3(const int& i)const{
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assert(i>=0 && i<4);
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return Point3<T>(ElementAt(i,0),ElementAt(i,1),ElementAt(i,2));
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// return *((Point4<T>*)(&_a[i<<2])); alternativa forse + efficiente
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}
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Matrix44 operator+(const Matrix44 &m) const;
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Matrix44 operator-(const Matrix44 &m) const;
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Matrix44 operator*(const Matrix44 &m) const;
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@ -213,9 +202,14 @@ public:
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void SetZero();
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void SetIdentity();
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void SetDiagonal(const T k);
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Matrix44 &SetScale(const T sx, const T sy, const T sz);
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Matrix44 &SetTranslate(const Point3<T> &t);
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Matrix44 &SetScale(const T sx, const T sy, const T sz);
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Matrix44 &SetScale(const Point3<T> &t);
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Matrix44 &SetTranslate(const Point3<T> &t);
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Matrix44 &SetTranslate(const T sx, const T sy, const T sz);
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Matrix44 &SetShearXY(const T sz);
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Matrix44 &SetShearXZ(const T sy);
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Matrix44 &SetShearYZ(const T sx);
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///use radiants for angle.
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Matrix44 &SetRotate(T AngleRad, const Point3<T> & axis);
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@ -289,7 +283,7 @@ template <class T> T Matrix44<T>::ElementAt(const int row, const int col) const
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//template <class T> const T &Matrix44<T>::operator[](const int i) const {
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// assert(i >= 0 && i < 16);
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// return ((T *)_a)[i];
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//}
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//}
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template <class T> T *Matrix44<T>::operator[](const int i) {
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assert(i >= 0 && i < 16);
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return _a+i*4;
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@ -398,8 +392,8 @@ template < class PointType , class T > void operator*=( std::vector<PointType> &
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}
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template <class T> void Matrix44<T>::operator*=( const T k ) {
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for(int i = 0; i < 4; i++)
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operator[](i) *= k;
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for(int i = 0; i < 16; i++)
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_a[i] *= k;
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}
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@ -419,6 +413,10 @@ template <class T> void Matrix44<T>::SetDiagonal(const T k) {
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ElementAt(3, 3) = 1;
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}
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template <class T> Matrix44<T> &Matrix44<T>::SetScale(const Point3<T> &t) {
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SetScale(t[0], t[1], t[2]);
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return *this;
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}
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template <class T> Matrix44<T> &Matrix44<T>::SetScale(const T sx, const T sy, const T sz) {
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SetZero();
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ElementAt(0, 0) = sx;
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@ -465,6 +463,135 @@ template <class T> Matrix44<T> &Matrix44<T>::SetRotate(T AngleRad, const Point3<
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return *this;
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}
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template <class T> Matrix44<T> & Matrix44<T>:: SetShearXY( const T sh) {// shear the X coordinate as the Y coordinate change
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SetIdentity();
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ElementAt(1,0) = sh;
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return *this;
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}
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template <class T> Matrix44<T> & Matrix44<T>:: SetShearXZ( const T sh) {// shear the X coordinate as the Z coordinate change
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SetIdentity();
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ElementAt(2,0) = sh;
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return *this;
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}
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template <class T> Matrix44<T> &Matrix44<T>:: SetShearYZ( const T sh) {// shear the Y coordinate as the Z coordinate change
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SetIdentity();
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ElementAt(2,1) = sh;
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return *this;
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}
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/*
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Data una matrice non proiettiva (in cui l'ultima riga e' (0,0,0,1)
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la decompone in una sequenza (nell'ordine) di
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Scale,Shear,Rotation e Translation
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- ShearV e' un vettore di tre scalari che indicano
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ShearXY, ShearXZ e ShearYZ
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- RotateV e' un vettore di tre scalari che indicano la sequenza di rotazioni
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in assi x,y,z
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Genera una una matrice lasciandoci dentro solo la rototraslazione.
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Example:
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m=Decompose(ScV,ShV,RtV,TrV);
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Matrix44d Scl; Scl.Scale(ScV[0],ScV[1],ScV[2]);
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Matrix44d Sxy; Sxy.ShearXY(ShV[0]);
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Matrix44d Sxz; Sxz.ShearXZ(ShV[1]);
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Matrix44d Syz; Syz.ShearYZ(ShV[2]);
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Matrix44d Rtx; Rtx.Rotate(RtV[0],Point3d(1,0,0));
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Matrix44d Rty; Rty.Rotate(RtV[1],Point3d(0,1,0));
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Matrix44d Rtz; Rtz.Rotate(RtV[2],Point3d(0,0,1));
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Matrix44d Trn; Trn.Translate(TrV[0],TrV[1],TrV[2]);
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// Rebuild e' uguale a Orig, prima della decompose
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Matrix44d Rebuild = Scl * Sxy*Sxz*Syz * Rtx*Rty*Rtz * Trn;
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*/
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template <class T>
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bool Decompose(Matrix44<T> &M, Point3<T> &ScaleV, Point3<T> &ShearV, Point3<T> &RotV,Point3<T> &TranV)
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{
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if(!(M[3][0]==0 && M[3][1]==0 && M[3][2]==0 && M[3][3]==1) ) // the matrix is projective
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return false;
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if(math::Abs(M.Determinant())<1e-10) return false; // matrix should be at least invertible...
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// First Step recover the traslation
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TranV=M.GetColumn3(3);
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// Second Step Recover Scale and Shearing interleaved
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ScaleV[0]=Norm(M.GetColumn3(0));
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Point3d R[3];
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R[0]=M.GetColumn3(0);
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R[0].Normalize();
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ShearV[0]=R[0]*M.GetColumn3(1); // xy shearing
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R[1]= M.GetColumn3(1)-R[0]*ShearV[0];
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assert(math::Abs(R[1]*R[0])<1e-10);
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ScaleV[1]=Norm(R[1]); // y scaling
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R[1]=R[1]/ScaleV[1];
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ShearV[0]=ShearV[0]/ScaleV[1];
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ShearV[1]=R[0]*M.GetColumn3(2); // xz shearing
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R[2]= M.GetColumn3(2)-R[0]*ShearV[1];
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assert(math::Abs(R[2]*R[0])<1e-10);
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R[2] = R[2]-R[1]*(R[2]*R[1]);
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assert(math::Abs(R[2]*R[1])<1e-10);
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assert(math::Abs(R[2]*R[0])<1e-10);
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ScaleV[2]=Norm(R[2]);
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ShearV[1]=ShearV[1]/ScaleV[2];
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R[2]=R[2]/ScaleV[2];
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assert(math::Abs(R[2]*R[1])<1e-10);
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assert(math::Abs(R[2]*R[0])<1e-10);
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ShearV[2]=R[1]*M.GetColumn3(2); // yz shearing
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ShearV[2]=ShearV[2]/ScaleV[2];
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int i,j;
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for(i=0;i<3;++i)
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for(j=0;j<3;++j)
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M[i][j]=R[j][i];
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// Third and last step: Recover the rotation
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//now the matrix should be a pure rotation matrix so its determinant is +-1
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double det=M.Determinant();
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if(math::Abs(det)<1e-10) return false; // matrix should be at least invertible...
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assert(math::Abs(math::Abs(det)-1.0)<1e-10); // it should be +-1...
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if(det<0) {
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ScaleV *= -1;
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M *= -1;
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}
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double alpha,beta,gamma; // rotations around the x,y and z axis
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beta=asin( M[0][2]);
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double cosbeta=cos(beta);
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if(math::Abs(cosbeta) > 1e-5)
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{
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alpha=asin(-M[1][2]/cosbeta);
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if((M[2][2]/cosbeta) < 0 ) alpha=M_PI-alpha;
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gamma=asin(-M[0][1]/cosbeta);
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if((M[0][0]/cosbeta)<0) gamma = M_PI-gamma;
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}
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else
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{
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alpha=asin(-M[1][0]);
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if(M[1][1]<0) alpha=M_PI-alpha;
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gamma=0;
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}
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RotV[0]=math::ToDeg(alpha);
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RotV[1]=math::ToDeg(beta);
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RotV[2]=math::ToDeg(gamma);
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return true;
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}
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template <class T> T Matrix44<T>::Determinant() const {
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LinearSolve<T> solve(*this);
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