OpenVDB: openvdb/math/Mat.h File Reference

OpenVDB 12.1.0

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Mat.h File Reference
`#include "Math.h"`
`#include <openvdb/Exceptions.h>`
`#include <algorithm>`
`#include <cmath>`
`#include <iostream>`
`#include <string>`

Go to the source code of this file.

## Classes
class | Mat< SIZE, T >

## Namespaces
namespace | openvdb
namespace | openvdb::v12_1
namespace | openvdb::v12_1::math

## Functions
template<class MatType>
MatType | rotation (const Quat< typename MatType::value_type > &q, typename MatType::value_type eps=static_cast< typename MatType::value_type >(1.0e-8))
| Return the rotation matrix specified by the given quaternion.
template<class MatType>
MatType | rotation (Axis axis, typename MatType::value_type angle)
| Return a matrix for rotation by angle radians about the given axis.
template<class MatType>
MatType | rotation (const Vec3< typename MatType::value_type > &_axis, typename MatType::value_type angle)
| Return a matrix for rotation by angle radians about the given axis.
template<class MatType>
Vec3< typename MatType::value_type > | eulerAngles (const MatType &mat, RotationOrder rotationOrder, typename MatType::value_type eps=static_cast< typename MatType::value_type >(1.0e-8))
| Return the Euler angles composing the given rotation matrix.
template<typename MatType, typename ValueType1, typename ValueType2>
MatType | rotation (const Vec3< ValueType1 > &_v1, const Vec3< ValueType2 > &_v2, typename MatType::value_type eps=static_cast< typename MatType::value_type >(1.0e-8))
| Return a rotation matrix that maps v1 onto v2 about the cross product of v1 and v2.
template<class MatType>
MatType | scale (const Vec3< typename MatType::value_type > &s)
| Return a matrix that scales by s.
template<class MatType>
Vec3< typename MatType::value_type > | getScale (const MatType &mat)
| Return a Vec3 representing the lengths of the passed matrix's upper 3×3's rows.
template<class MatType>
MatType | unit (const MatType &mat, typename MatType::value_type eps=1.0e-8)
| Return a copy of the given matrix with its upper 3×3 rows normalized.
template<class MatType>
MatType | unit (const MatType &in, typename MatType::value_type eps, Vec3< typename MatType::value_type > &scaling)
| Return a copy of the given matrix with its upper 3×3 rows normalized, and return the length of each of these rows in scaling.
template<class MatType>
MatType | shear (Axis axis0, Axis axis1, typename MatType::value_type shear)
| Set the matrix to a shear along axis0 by a fraction of axis1.
template<class MatType>
MatType | skew (const Vec3< typename MatType::value_type > &skew)
| Return a matrix as the cross product of the given vector.
template<class MatType>
MatType | aim (const Vec3< typename MatType::value_type > &direction, const Vec3< typename MatType::value_type > &vertical)
| Return an orientation matrix such that z points along direction, and y is along the direction / vertical plane.
template<class MatType>
MatType | snapMatBasis (const MatType &source, Axis axis, const Vec3< typename MatType::value_type > &direction)
| This function snaps a specific axis to a specific direction, preserving scaling.
template<class MatType>
MatType & | padMat4 (MatType &dest)
| Write 0s along Mat4's last row and column, and a 1 on its diagonal.
template<typename MatType>
void | sqrtSolve (const MatType &aA, MatType &aB, double aTol=0.01)
| Solve for A=B*B, given A.
template<typename MatType>
void | powSolve (const MatType &aA, MatType &aB, double aPower, double aTol=0.01)
template<typename MatType>
bool | isIdentity (const MatType &m)
| Determine if a matrix is an identity matrix.
template<typename MatType>
bool | isInvertible (const MatType &m)
| Determine if a matrix is invertible.
template<typename MatType>
bool | isSymmetric (const MatType &m)
| Determine if a matrix is symmetric.
template<typename MatType>
bool | isUnitary (const MatType &m)
| Determine if a matrix is unitary (i.e., rotation or reflection).
template<typename MatType>
bool | isDiagonal (const MatType &mat)
| Determine if a matrix is diagonal.
template<typename MatType>
MatType::ValueType | lInfinityNorm (const MatType &matrix)
| Return the L∞ norm of an N×N matrix.
template<typename MatType>
MatType::ValueType | lOneNorm (const MatType &matrix)
| Return the L1 norm of an N×N matrix.
template<typename MatType>
bool | polarDecomposition (const MatType &input, MatType &unitary, MatType &positive_hermitian, unsigned int MAX_ITERATIONS=100)
| Decompose an invertible 3×3 matrix into a unitary matrix followed by a symmetric matrix (positive semi-definite Hermitian), i.e., M = U * S.
template<unsigned SIZE, typename T>
bool | cwiseLessThan (const Mat< SIZE, T > &m0, const Mat< SIZE, T > &m1)
template<unsigned SIZE, typename T>
bool | cwiseGreaterThan (const Mat< SIZE, T > &m0, const Mat< SIZE, T > &m1)

## Detailed Description

Author
  Joshua Schpok