Completed Shear Matrix code and comments,
Added use of swap inside Transpose Added more complete comments on the usage of Decompose
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@ -24,6 +24,10 @@
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History
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$Log: not supported by cvs2svn $
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Revision 1.26 2005/06/10 15:04:12 cignoni
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Added Various missing functions: SetShearXY, SetShearXZ, SetShearYZ, SetScale for point3 and Decompose
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Completed *=(scalar); made uniform GetRow and GetColumn
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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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@ -463,53 +467,92 @@ 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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/* Shear Matrixes
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XY
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1 k 0 0 x x+ky
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0 1 0 0 y y
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0 0 1 0 z z
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0 0 0 1 1 1
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1 0 k 0 x x+kz
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0 1 0 0 y y
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0 0 1 0 z z
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0 0 0 1 1 1
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1 1 0 0 x x
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0 1 k 0 y y+kz
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0 0 1 0 z z
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0 0 0 1 1 1
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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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ElementAt(0,1) = 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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ElementAt(0,2) = 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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ElementAt(1,2) = 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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Given a non singular, non projective matrix (e.g. with the last row equal to [0,0,0,1] )
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This procedure decompose it in a sequence of
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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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- ScaleV and Tranv are obiviously scaling and translation.
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- ShearV contains three scalars with, respectively
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ShearXY, ShearXZ e ShearYZ
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- RotateV contains the rotations (in degree!) around the x,y,z axis
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The input matrix is modified leaving inside it a simple roto translation.
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Genera una una matrice lasciandoci dentro solo la rototraslazione.
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Example:
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To obtain the original matrix the above transformation have to be applied in the strict following way:
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OriginalMatrix = Trn * Rtx*Rty*Rtz * ShearYZ*ShearXZ*ShearXY * Scl
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m=Decompose(ScV,ShV,RtV,TrV);
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Example Code:
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double srv() { return (double(rand()%40)-20)/2.0; } // small random value
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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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srand(time(0));
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Point3d ScV(10+srv(),10+srv(),10+srv()),ScVOut(-1,-1,-1);
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Point3d ShV(srv(),srv(),srv()),ShVOut(-1,-1,-1);
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Point3d RtV(10+srv(),srv(),srv()),RtVOut(-1,-1,-1);
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Point3d TrV(srv(),srv(),srv()),TrVOut(-1,-1,-1);
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Matrix44d Scl; Scl.SetScale(ScV);
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Matrix44d Sxy; Sxy.SetShearXY(ShV[0]);
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Matrix44d Sxz; Sxz.SetShearXZ(ShV[1]);
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Matrix44d Syz; Syz.SetShearYZ(ShV[2]);
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Matrix44d Rtx; Rtx.SetRotate(math::ToRad(RtV[0]),Point3d(1,0,0));
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Matrix44d Rty; Rty.SetRotate(math::ToRad(RtV[1]),Point3d(0,1,0));
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Matrix44d Rtz; Rtz.SetRotate(math::ToRad(RtV[2]),Point3d(0,0,1));
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Matrix44d Trn; Trn.SetTranslate(TrV);
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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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Matrix44d StartM = Trn * Rtx*Rty*Rtz * Syz*Sxz*Sxy *Scl;
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Matrix44d ResultM=StartM;
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Decompose(ResultM,ScVOut,ShVOut,RtVOut,TrVOut);
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Scl.SetScale(ScVOut);
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Sxy.SetShearXY(ShVOut[0]);
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Sxz.SetShearXZ(ShVOut[1]);
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Syz.SetShearYZ(ShVOut[2]);
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Rtx.SetRotate(math::ToRad(RtVOut[0]),Point3d(1,0,0));
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Rty.SetRotate(math::ToRad(RtVOut[1]),Point3d(0,1,0));
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Rtz.SetRotate(math::ToRad(RtVOut[2]),Point3d(0,0,1));
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Trn.SetTranslate(TrVOut);
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// Now Rebuild is equal to StartM
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Matrix44d RebuildM = Trn * Rtx*Rty*Rtz * Syz*Sxz*Sxy * Scl ;
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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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@ -518,7 +561,7 @@ bool Decompose(Matrix44<T> &M, Point3<T> &ScaleV, Point3<T> &ShearV, Point3<T> &
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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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// First Step recover the traslation
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TranV=M.GetColumn3(3);
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@ -624,9 +667,7 @@ template <class T> Point3<T> operator*(const Matrix44<T> &m, const Point3<T> &p)
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template <class T> Matrix44<T> &Transpose(Matrix44<T> &m) {
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for(int i = 1; i < 4; i++)
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for(int j = 0; j < i; j++) {
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T t = m.ElementAt(i, j);
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m.ElementAt(i, j) = m.ElementAt(j, i);
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m.ElementAt(j, i) = t;
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swap(m.ElementAt(i, j), m.ElementAt(j, i));
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}
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return m;
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}
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