openexr/imath/ImathMatrixAlgo.h

130                                             (const Matrix44<T> &mat,
134 template <class T>  Matrix44<T> sansScaling (const Matrix44<T> &mat,
138                                             (Matrix44<T> &mat,
142                                             (const Matrix44<T> &mat,
148                                             (const Matrix44<T> &mat,
152                                             (Matrix44<T> &mat,
156                                             (Matrix44<T> &mat,
162                                             (const Matrix44<T> &mat,
166                                             (const Matrix44<T> &mat,
169 template <class T>  Quat<T>	extractQuat (const Matrix44<T> &mat);
172                                     (const Matrix44<T> &mat,
181                                     (const Matrix44<T> &mat,
189                                     (const Matrix44<T> &mat,
255                                             (const Matrix33<T> &mat,
259 template <class T>  Matrix33<T> sansScaling (const Matrix33<T> &mat,
263                                             (Matrix33<T> &mat,
267                                             (const Matrix33<T> &mat,
273                                             (const Matrix33<T> &mat,
277                                             (Matrix33<T> &mat,
281                                             (Matrix33<T> &mat,
287                                             (const Matrix33<T> &mat,
290 template <class T>  bool	extractSHRT (const Matrix33<T> &mat,
312 extractScaling (const Matrix44<T> &mat, Vec3<T> &scl, bool exc)
315     Matrix44<T> M (mat);
326 sansScaling (const Matrix44<T> &mat, bool exc)
333     if (! extractSHRT (mat, scl, shr, rot, tran, exc))
334 	return mat;
348 removeScaling (Matrix44<T> &mat, bool exc)
355     if (! extractSHRT (mat, scl, shr, rot, tran, exc))
358     mat.makeIdentity ();
359     mat.translate (tran);
360     mat.rotate (rot);
361     mat.shear (shr);
369 extractScalingAndShear (const Matrix44<T> &mat,
372     Matrix44<T> M (mat);
383 sansScalingAndShear (const Matrix44<T> &mat, bool exc)
387     Matrix44<T> M (mat);
390 	return mat;
398 removeScalingAndShear (Matrix44<T> &mat, bool exc)
403     if (! extractAndRemoveScalingAndShear (mat, scl, shr, exc))
412 extractAndRemoveScalingAndShear (Matrix44<T> &mat,
423     row[0] = Vec3<T> (mat[0][0], mat[0][1], mat[0][2]);
424     row[1] = Vec3<T> (mat[1][0], mat[1][1], mat[1][2]);
425     row[2] = Vec3<T> (mat[2][0], mat[2][1], mat[2][2]);
497     // At this point, the upper 3x3 matrix in mat is orthonormal.
508     // The upper 3x3 matrix in mat is now a rotation matrix.
511 	mat[i][0] = row[i][0];
512 	mat[i][1] = row[i][1];
513 	mat[i][2] = row[i][2];
527 extractEulerXYZ (const Matrix44<T> &mat, Vec3<T> &rot)
533     Vec3<T> i (mat[0][0], mat[0][1], mat[0][2]);
534     Vec3<T> j (mat[1][0], mat[1][1], mat[1][2]);
535     Vec3<T> k (mat[2][0], mat[2][1], mat[2][2]);
574 extractEulerZYX (const Matrix44<T> &mat, Vec3<T> &rot)
580     Vec3<T> i (mat[0][0], mat[0][1], mat[0][2]);
581     Vec3<T> j (mat[1][0], mat[1][1], mat[1][2]);
582     Vec3<T> k (mat[2][0], mat[2][1], mat[2][2]);
621 extractQuat (const Matrix44<T> &mat)
631   tr = mat[0][0] + mat[1][1] + mat[2][2];
639      quat.v.x = (mat[1][2] - mat[2][1]) * s;
640      quat.v.y = (mat[2][0] - mat[0][2]) * s;
641      quat.v.z = (mat[0][1] - mat[1][0]) * s;
646      if (mat[1][1] > mat[0][0])
648      if (mat[2][2] > mat[i][i])
653      s = Math<T>::sqrt ((mat[i][i] - (mat[j][j] + mat[k][k])) + 1.0);
659      q[3] = (mat[j][k] - mat[k][j]) * s;
660      q[j] = (mat[i][j] + mat[j][i]) * s;
661      q[k] = (mat[i][k] + mat[k][i]) * s;
674 extractSHRT (const Matrix44<T> &mat,
684     rot = mat;
690     t.x = mat[3][0];
691     t.y = mat[3][1];
692     t.z = mat[3][2];
706 extractSHRT (const Matrix44<T> &mat,
713     return extractSHRT(mat, s, h, r, t, exc, Imath::Euler<T>::XYZ);
718 extractSHRT (const Matrix44<T> &mat,
725     return extractSHRT (mat, s, h, r, t, exc, r.order ());
842     Matrix44<T> mat ( row[0][0],  row[0][1],  row[0][2],  0,
847     return mat;
859 extractScaling (const Matrix33<T> &mat, Vec2<T> &scl, bool exc)
862     Matrix33<T> M (mat);
873 sansScaling (const Matrix33<T> &mat, bool exc)
880     if (! extractSHRT (mat, scl, shr, rot, tran, exc))
881 	return mat;
895 removeScaling (Matrix33<T> &mat, bool exc)
902     if (! extractSHRT (mat, scl, shr, rot, tran, exc))
905     mat.makeIdentity ();
906     mat.translate (tran);
907     mat.rotate (rot);
908     mat.shear (shr);
916 extractScalingAndShear (const Matrix33<T> &mat, Vec2<T> &scl, T &shr, bool exc)
918     Matrix33<T> M (mat);
929 sansScalingAndShear (const Matrix33<T> &mat, bool exc)
933     Matrix33<T> M (mat);
936 	return mat;
944 removeScalingAndShear (Matrix33<T> &mat, bool exc)
949     if (! extractAndRemoveScalingAndShear (mat, scl, shr, exc))
957 extractAndRemoveScalingAndShear (Matrix33<T> &mat,
962     row[0] = Vec2<T> (mat[0][0], mat[0][1]);
963     row[1] = Vec2<T> (mat[1][0], mat[1][1]);
1018     // At this point, the upper 2x2 matrix in mat is orthonormal.
1031     // The upper 2x2 matrix in mat is now a rotation matrix.
1034 	mat[i][0] = row[i][0];
1035 	mat[i][1] = row[i][1];
1046 extractEuler (const Matrix33<T> &mat, T &rot)
1052     Vec2<T> i (mat[0][0], mat[0][1]);
1053     Vec2<T> j (mat[1][0], mat[1][1]);
1068 extractSHRT (const Matrix33<T> &mat,
1077     rot = mat;
1083     t.x = mat[2][0];
1084     t.y = mat[2][1];