Matrix Functions¶

Functions that operate on matrices

Warning

doxygenfunction: Unable to resolve multiple matches for function “extractScaling” with arguments (const Matrix44<T>& mat, Vec3<T>& scl, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::extractScaling(const Matrix33<T>&, Vec2<T>&, bool)
- template <class T>
  bool Imath::extractScaling(const Matrix44<T>&, Vec3<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “sansScaling” with arguments (const Matrix44<T>& mat, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  Matrix33<T> Imath::sansScaling(const Matrix33<T>&, bool)
- template <class T>
  Matrix44<T> Imath::sansScaling(const Matrix44<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “removeScaling” with arguments (Matrix44<T>& mat, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::removeScaling(Matrix33<T>&, bool)
- template <class T>
  bool Imath::removeScaling(Matrix44<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “extractScalingAndShear” with arguments (const Matrix44<T>& mat, Vec3<T>& scl, Vec3<T>& shr, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::extractScalingAndShear(const Matrix33<T>&, Vec2<T>&, T&, bool)
- template <class T>
  bool Imath::extractScalingAndShear(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “sansScalingAndShear” with arguments (const Matrix44<T>& mat, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  Matrix33<T> Imath::sansScalingAndShear(const Matrix33<T>&, bool)
- template <class T>
  Matrix44<T> Imath::sansScalingAndShear(const Matrix44<T>&, bool)
- template <class T>
  void Imath::sansScalingAndShear(Matrix44<T>&, const Matrix44<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “sansScalingAndShear” with arguments (Matrix44<T>& result, const Matrix44<T>& mat, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  Matrix33<T> Imath::sansScalingAndShear(const Matrix33<T>&, bool)
- template <class T>
  Matrix44<T> Imath::sansScalingAndShear(const Matrix44<T>&, bool)
- template <class T>
  void Imath::sansScalingAndShear(Matrix44<T>&, const Matrix44<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “removeScalingAndShear” with arguments (Matrix44<T>& mat, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::removeScalingAndShear(Matrix33<T>&, bool)
- template <class T>
  bool Imath::removeScalingAndShear(Matrix44<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “extractAndRemoveScalingAndShear” with arguments (Matrix44<T>& mat, Vec3<T>& scl, Vec3<T>& shr, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::extractAndRemoveScalingAndShear(Matrix33<T>&, Vec2<T>&, T&, bool)
- template <class T>
  bool Imath::extractAndRemoveScalingAndShear(Matrix44<T>&, Vec3<T>&, Vec3<T>&, bool)

template <class T> void Imath::extractEulerXYZ(const Matrix44<T> &mat, Vec3<T> &rot)¶

Extract the rotation from the given 4x4 matrix in the form of XYZ euler angles.

Parameters

mat: The input matrix
rot: The extracted XYZ euler angle vector

template <class T> void Imath::extractEulerZYX(const Matrix44<T> &mat, Vec3<T> &rot)¶

Extract the rotation from the given 4x4 matrix in the form of ZYX euler angles.

Parameters

mat: The input matrix
rot: The extracted ZYX euler angle vector

template <class T> Quat<T> Imath::extractQuat(const Matrix44<T> &mat)¶

Extract the rotation from the given 4x4 matrix in the form of a quaternion.

Return

The extracted quaternion

Parameters

mat: The input matrix

Warning

doxygenfunction: Unable to resolve multiple matches for function “extractSHRT” with arguments (const Matrix44<T>& mat, Vec3<T>& s, Vec3<T>& h, Vec3<T>& r, Vec3<T>& t, bool exc, typename Euler<T>::Order rOrder) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::extractSHRT(const Matrix33<T>&, Vec2<T>&, T&, T&, Vec2<T>&, bool)
- template <class T>
  bool Imath::extractSHRT(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, Euler<T>&, Vec3<T>&, bool)
- template <class T>
  bool Imath::extractSHRT(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, bool)
- template <class T>
  bool Imath::extractSHRT(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, bool, typename Euler<T>::Order)

Warning

doxygenfunction: Unable to resolve multiple matches for function “extractSHRT” with arguments (const Matrix44<T>& mat, Vec3<T>& s, Vec3<T>& h, Vec3<T>& r, Vec3<T>& t, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::extractSHRT(const Matrix33<T>&, Vec2<T>&, T&, T&, Vec2<T>&, bool)
- template <class T>
  bool Imath::extractSHRT(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, Euler<T>&, Vec3<T>&, bool)
- template <class T>
  bool Imath::extractSHRT(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, bool)
- template <class T>
  bool Imath::extractSHRT(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, bool, typename Euler<T>::Order)

Warning

doxygenfunction: Unable to resolve multiple matches for function “extractSHRT” with arguments (const Matrix44<T>& mat, Vec3<T>& s, Vec3<T>& h, Euler<T>& r, Vec3<T>& t, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::extractSHRT(const Matrix33<T>&, Vec2<T>&, T&, T&, Vec2<T>&, bool)
- template <class T>
  bool Imath::extractSHRT(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, Euler<T>&, Vec3<T>&, bool)
- template <class T>
  bool Imath::extractSHRT(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, bool)
- template <class T>
  bool Imath::extractSHRT(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, bool, typename Euler<T>::Order)

Warning

doxygenfunction: Unable to resolve multiple matches for function “checkForZeroScaleInRow” with arguments (const T& scl, const Vec3<T>& row, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::checkForZeroScaleInRow(const T&, const Vec2<T>&, bool)
- template <class T>
  bool Imath::checkForZeroScaleInRow(const T&, const Vec3<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “outerProduct” with arguments (const Vec4<T>& a, const Vec4<T>& b) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  Matrix33<T> Imath::outerProduct(const Vec3<T>&, const Vec3<T>&)
- template <class T>
  Matrix44<T> Imath::outerProduct(const Vec4<T>&, const Vec4<T>&)

template <class T> Matrix44<T> Imath::rotationMatrix(const Vec3<T> &fromDirection, const Vec3<T> &toDirection)¶: Return a 4x4 matrix that rotates the vector fromDirection to toDirection

template <class T> Matrix44<T> Imath::rotationMatrixWithUpDir(const Vec3<T> &fromDir, const Vec3<T> &toDir, const Vec3<T> &upDir)¶

Return a 4x4 matrix that rotates the fromDir vector so that it points towards `toDir1.

You may also specify that you want the up vector to be pointing in a certain direction 1upDir`.

template <class T> void Imath::alignZAxisWithTargetDir(Matrix44<T> &result, Vec3<T> targetDir, Vec3<T> upDir)¶

Construct a 4x4 matrix that rotates the z-axis so that it points towards targetDir.

You must also specify that you want the up vector to be pointing in a certain direction upDir.

Notes: The following degenerate cases are handled: (a) when the directions given by toDir and upDir are parallel or opposite (the direction vectors must have a non-zero cross product); (b) when any of the given direction vectors have zero length

Parameters

result: The output matrix
targetDir: The target direction vector
upDir: The up direction vector

template <class T> Matrix44<T> Imath::computeLocalFrame(const Vec3<T> &p, const Vec3<T> &xDir, const Vec3<T> &normal)¶

Compute an orthonormal direct 4x4 frame from a position, an x axis direction and a normal to the y axis.

If the x axis and normal are perpendicular, then the normal will have the same direction as the z axis.

Return

The orthonormal frame

Parameters

p: The position of the frame
xDir: The x axis direction of the frame
normal: A normal to the y axis of the frame

Warning

doxygenfunction: Unable to resolve multiple matches for function “addOffset” with arguments (const Matrix44<T>& inMat, const Vec3<T>& tOffset, const Vec3<T>& rOffset, const Vec3<T>& sOffset, const Vec3<T>& ref) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  Matrix44<T> Imath::addOffset(const Matrix44<T>&, const Vec3<T>&, const Vec3<T>&, const Vec3<T>&, const Matrix44<T>&)
- template <class T>
  Matrix44<T> Imath::addOffset(const Matrix44<T>&, const Vec3<T>&, const Vec3<T>&, const Vec3<T>&, const Vec3<T>&)

template <class T> Matrix44<T> Imath::computeRSMatrix(bool keepRotateA, bool keepScaleA, const Matrix44<T> &A, const Matrix44<T> &B)¶

Compute 4x4 translate/rotate/scale matrix from A with the rotate/scale of B.

Return

Matrix A with tweaked rotation/scale

Parameters

keepRotateA: If true, keep rotate from matrix A, use B otherwise
keepScaleA: If true, keep scale from matrix A, use B otherwise
A: Matrix A
B: Matrix B

Warning

doxygenfunction: Unable to resolve multiple matches for function “extractScaling” with arguments (const Matrix33<T>& mat, Vec2<T>& scl, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::extractScaling(const Matrix33<T>&, Vec2<T>&, bool)
- template <class T>
  bool Imath::extractScaling(const Matrix44<T>&, Vec3<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “sansScaling” with arguments (const Matrix33<T>& mat, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  Matrix33<T> Imath::sansScaling(const Matrix33<T>&, bool)
- template <class T>
  Matrix44<T> Imath::sansScaling(const Matrix44<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “removeScaling” with arguments (Matrix33<T>& mat, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::removeScaling(Matrix33<T>&, bool)
- template <class T>
  bool Imath::removeScaling(Matrix44<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “extractScalingAndShear” with arguments (const Matrix33<T>& mat, Vec2<T>& scl, T& shr, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::extractScalingAndShear(const Matrix33<T>&, Vec2<T>&, T&, bool)
- template <class T>
  bool Imath::extractScalingAndShear(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “sansScalingAndShear” with arguments (const Matrix33<T>& mat, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  Matrix33<T> Imath::sansScalingAndShear(const Matrix33<T>&, bool)
- template <class T>
  Matrix44<T> Imath::sansScalingAndShear(const Matrix44<T>&, bool)
- template <class T>
  void Imath::sansScalingAndShear(Matrix44<T>&, const Matrix44<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “removeScalingAndShear” with arguments (Matrix33<T>& mat, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::removeScalingAndShear(Matrix33<T>&, bool)
- template <class T>
  bool Imath::removeScalingAndShear(Matrix44<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “extractAndRemoveScalingAndShear” with arguments (Matrix33<T>& mat, Vec2<T>& scl, T& shr, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::extractAndRemoveScalingAndShear(Matrix33<T>&, Vec2<T>&, T&, bool)
- template <class T>
  bool Imath::extractAndRemoveScalingAndShear(Matrix44<T>&, Vec3<T>&, Vec3<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “extractEuler” with arguments (const Matrix22<T>& mat, T& rot) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  void Imath::extractEuler(const Matrix22<T>&, T&)
- template <class T>
  void Imath::extractEuler(const Matrix33<T>&, T&)

Warning

doxygenfunction: Unable to resolve multiple matches for function “extractEuler” with arguments (const Matrix33<T>& mat, T& rot) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  void Imath::extractEuler(const Matrix22<T>&, T&)
- template <class T>
  void Imath::extractEuler(const Matrix33<T>&, T&)

Warning

doxygenfunction: Unable to resolve multiple matches for function “extractSHRT” with arguments (const Matrix33<T>& mat, Vec2<T>& s, T& h, T& r, Vec2<T>& t, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::extractSHRT(const Matrix33<T>&, Vec2<T>&, T&, T&, Vec2<T>&, bool)
- template <class T>
  bool Imath::extractSHRT(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, Euler<T>&, Vec3<T>&, bool)
- template <class T>
  bool Imath::extractSHRT(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, bool)
- template <class T>
  bool Imath::extractSHRT(const Matrix44<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, Vec3<T>&, bool, typename Euler<T>::Order)

Warning

doxygenfunction: Unable to resolve multiple matches for function “checkForZeroScaleInRow” with arguments (const T& scl, const Vec2<T>& row, bool exc) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  bool Imath::checkForZeroScaleInRow(const T&, const Vec2<T>&, bool)
- template <class T>
  bool Imath::checkForZeroScaleInRow(const T&, const Vec3<T>&, bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “outerProduct” with arguments (const Vec3<T>& a, const Vec3<T>& b) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <class T>
  Matrix33<T> Imath::outerProduct(const Vec3<T>&, const Vec3<T>&)
- template <class T>
  Matrix44<T> Imath::outerProduct(const Vec4<T>&, const Vec4<T>&)

Warning

doxygenfunction: Unable to resolve multiple matches for function “procrustesRotationAndTranslation” with arguments (const Vec3<T>* A, const Vec3<T>* B, const T* weights, const size_t numPoints, const bool doScaling) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <typename T>
  M44d Imath::procrustesRotationAndTranslation(const Vec3<T> *, const Vec3<T> *, const T *, const size_t, const bool)
- template <typename T>
  M44d Imath::procrustesRotationAndTranslation(const Vec3<T> *, const Vec3<T> *, const size_t, const bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “procrustesRotationAndTranslation” with arguments (const Vec3<T>* A, const Vec3<T>* B, const size_t numPoints, const bool doScaling) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <typename T>
  M44d Imath::procrustesRotationAndTranslation(const Vec3<T> *, const Vec3<T> *, const T *, const size_t, const bool)
- template <typename T>
  M44d Imath::procrustesRotationAndTranslation(const Vec3<T> *, const Vec3<T> *, const size_t, const bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “jacobiSVD” with arguments (const Matrix33<T>& A, Matrix33<T>& U, Vec3<T>& S, Matrix33<T>& V, const T tol, const bool forcePositiveDeterminant) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <typename T>
  void Imath::jacobiSVD(const Matrix33<T>&, Matrix33<T>&, Vec3<T>&, Matrix33<T>&, const T, const bool)
- template <typename T>
  void Imath::jacobiSVD(const Matrix44<T>&, Matrix44<T>&, Vec4<T>&, Matrix44<T>&, const T, const bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “jacobiSVD” with arguments (const Matrix44<T>& A, Matrix44<T>& U, Vec4<T>& S, Matrix44<T>& V, const T tol, const bool forcePositiveDeterminant) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <typename T>
  void Imath::jacobiSVD(const Matrix33<T>&, Matrix33<T>&, Vec3<T>&, Matrix33<T>&, const T, const bool)
- template <typename T>
  void Imath::jacobiSVD(const Matrix44<T>&, Matrix44<T>&, Vec4<T>&, Matrix44<T>&, const T, const bool)

Warning

doxygenfunction: Unable to resolve multiple matches for function “jacobiEigenSolver” with arguments (Matrix33<T>& A, Vec3<T>& S, Matrix33<T>& V, const T tol) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <typename T>
  void Imath::jacobiEigenSolver(Matrix33<T>&, Vec3<T>&, Matrix33<T>&)
- template <typename T>
  void Imath::jacobiEigenSolver(Matrix33<T>&, Vec3<T>&, Matrix33<T>&, const T)
- template <typename T>
  void Imath::jacobiEigenSolver(Matrix44<T>&, Vec4<T>&, Matrix44<T>&)
- template <typename T>
  void Imath::jacobiEigenSolver(Matrix44<T>&, Vec4<T>&, Matrix44<T>&, const T)

Warning

doxygenfunction: Unable to resolve multiple matches for function “jacobiEigenSolver” with arguments (Matrix33<T>& A, Vec3<T>& S, Matrix33<T>& V) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <typename T>
  void Imath::jacobiEigenSolver(Matrix33<T>&, Vec3<T>&, Matrix33<T>&)
- template <typename T>
  void Imath::jacobiEigenSolver(Matrix33<T>&, Vec3<T>&, Matrix33<T>&, const T)
- template <typename T>
  void Imath::jacobiEigenSolver(Matrix44<T>&, Vec4<T>&, Matrix44<T>&)
- template <typename T>
  void Imath::jacobiEigenSolver(Matrix44<T>&, Vec4<T>&, Matrix44<T>&, const T)

Warning

doxygenfunction: Unable to resolve multiple matches for function “jacobiEigenSolver” with arguments (Matrix44<T>& A, Vec4<T>& S, Matrix44<T>& V, const T tol) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <typename T>
  void Imath::jacobiEigenSolver(Matrix33<T>&, Vec3<T>&, Matrix33<T>&)
- template <typename T>
  void Imath::jacobiEigenSolver(Matrix33<T>&, Vec3<T>&, Matrix33<T>&, const T)
- template <typename T>
  void Imath::jacobiEigenSolver(Matrix44<T>&, Vec4<T>&, Matrix44<T>&)
- template <typename T>
  void Imath::jacobiEigenSolver(Matrix44<T>&, Vec4<T>&, Matrix44<T>&, const T)

Warning

doxygenfunction: Unable to resolve multiple matches for function “jacobiEigenSolver” with arguments (Matrix44<T>& A, Vec4<T>& S, Matrix44<T>& V) in doxygen xml output for project “Imath” from directory: doxyxml/. Potential matches:

- template <typename T>
  void Imath::jacobiEigenSolver(Matrix33<T>&, Vec3<T>&, Matrix33<T>&)
- template <typename T>
  void Imath::jacobiEigenSolver(Matrix33<T>&, Vec3<T>&, Matrix33<T>&, const T)
- template <typename T>
  void Imath::jacobiEigenSolver(Matrix44<T>&, Vec4<T>&, Matrix44<T>&)
- template <typename T>
  void Imath::jacobiEigenSolver(Matrix44<T>&, Vec4<T>&, Matrix44<T>&, const T)

template <typename TM, typename TV> void Imath::maxEigenVector(TM &A, TV &S)¶: Compute a eigenvector corresponding to the abs max eigenvalue of a real symmetric matrix using Jacobi transformation.

template <typename TM, typename TV> void Imath::minEigenVector(TM &A, TV &S)¶: Compute a eigenvector corresponding to the abs min eigenvalue of a real symmetric matrix using Jacobi transformation.

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