Matrix.h File Reference

Definitions of small fixed-size square matrix types. More...

#include <vector>
#include <Eigen/Core>
#include <Eigen/Geometry>
#include <Eigen/LU>

Go to the source code of this file.

Namespaces
	SurgSim
	Wraps glewInit() to separate the glew opengl definitions from the osg opengl definitions only imgui needs glew but we need to call glewInit() from a osg callback, using this call we avoid getting warnings about redefinitions.

Typedefs
typedef Eigen::Matrix< float, 2, 2, Eigen::RowMajor >	SurgSim::Math::Matrix22f
	A 2x2 matrix of floats. More...
typedef Eigen::Matrix< float, 3, 3, Eigen::RowMajor >	SurgSim::Math::Matrix33f
	A 3x3 matrix of floats. More...
typedef Eigen::Matrix< float, 4, 4, Eigen::RowMajor >	SurgSim::Math::Matrix44f
	A 4x4 matrix of floats. More...
typedef Eigen::Matrix< double, 2, 2, Eigen::RowMajor >	SurgSim::Math::Matrix22d
	A 2x2 matrix of doubles. More...
typedef Eigen::Matrix< double, 3, 3, Eigen::RowMajor >	SurgSim::Math::Matrix33d
	A 3x3 matrix of doubles. More...
typedef Eigen::Matrix< double, 4, 4, Eigen::RowMajor >	SurgSim::Math::Matrix44d
	A 4x4 matrix of doubles. More...
typedef Eigen::Matrix< double, 6, 6, Eigen::RowMajor >	SurgSim::Math::Matrix66d
	A 6x6 matrix of doubles. More...
typedef Eigen::DiagonalMatrix< double, Eigen::Dynamic >	SurgSim::Math::DiagonalMatrix
	A dynamic size diagonal matrix.
typedef Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >	SurgSim::Math::Matrix
	A dynamic size matrix.

Functions
template<typename T , int VOpt>
Eigen::Matrix< T, 3, 3 >	SurgSim::Math::makeRotationMatrix (const T &angle, const Eigen::Matrix< T, 3, 1, VOpt > &axis)
	Create a rotation matrix corresponding to the specified angle (in radians) and axis. More...
template<typename T , int VOpt>
Eigen::Matrix< T, 3, 3 >	SurgSim::Math::makeSkewSymmetricMatrix (const Eigen::Matrix< T, 3, 1, VOpt > &vector)
	Create a skew-symmetric matrix corresponding to the specified vector. More...
template<typename T , int MOpt>
Eigen::Matrix< T, 3, 1 >	SurgSim::Math::skew (const Eigen::Matrix< T, 3, 3, MOpt > &matrix)
	Extract the unique vector from the skew-symmetric part of a given matrix. More...
template<typename T , int MOpt, int VOpt>
void	SurgSim::Math::computeAngleAndAxis (const Eigen::Matrix< T, 3, 3, MOpt > &matrix, T *angle, Eigen::Matrix< T, 3, 1, VOpt > *axis)
	Get the angle (in radians) and axis corresponding to a rotation matrix. More...
template<typename T , int MOpt>
T	SurgSim::Math::computeAngle (const Eigen::Matrix< T, 3, 3, MOpt > &matrix)
	Get the angle corresponding to a quaternion's rotation, in radians. More...
template<class Matrix , class SubMatrix >
void	SurgSim::Math::addSubMatrix (const SubMatrix &subMatrix, size_t blockIdRow, size_t blockIdCol, size_t blockSizeRow, size_t blockSizeCol, Matrix *matrix)
	Helper method to add a sub-matrix into a matrix, for the sake of clarity. More...
template<class Matrix , class SubMatrix >
void	SurgSim::Math::addSubMatrix (const SubMatrix &subMatrix, const std::vector< size_t > &blockIds, size_t blockSize, Matrix *matrix)
	Helper method to add a sub-matrix made of squared-blocks into a matrix, for the sake of clarity. More...
template<class Matrix , class SubMatrix >
void	SurgSim::Math::setSubMatrix (const SubMatrix &subMatrix, size_t blockIdRow, size_t blockIdCol, size_t blockSizeRow, size_t blockSizeCol, Matrix *matrix)
	Helper method to set a sub-matrix into a matrix, for the sake of clarity. More...
template<class Matrix >
Eigen::Block< Matrix >	SurgSim::Math::getSubMatrix (Matrix &matrix, size_t blockIdRow, size_t blockIdCol, size_t blockSizeRow, size_t blockSizeCol)
	Helper method to access a sub-matrix from a matrix, for the sake of clarity. More...
template<class Derived >
void	SurgSim::Math::zeroRow (size_t row, Eigen::DenseBase< Derived > *matrix)
	Helper method to zero a row of a matrix. More...
template<class Derived >
void	SurgSim::Math::zeroColumn (size_t column, Eigen::DenseBase< Derived > *matrix)
	Helper method to zero a column of a matrix. More...

Detailed Description

Definitions of small fixed-size square matrix types.

Typedef Documentation

Matrix22d

typedef Eigen::Matrix<double, 2, 2, Eigen::RowMajor> SurgSim::Math::Matrix22d

A 2x2 matrix of doubles.

This type (and any structs that contain it) can be safely allocated via new.

Matrix22f

typedef Eigen::Matrix<float, 2, 2, Eigen::RowMajor> SurgSim::Math::Matrix22f

A 2x2 matrix of floats.

This type (and any structs that contain it) can be safely allocated via new.

Matrix33d

typedef Eigen::Matrix<double, 3, 3, Eigen::RowMajor> SurgSim::Math::Matrix33d

A 3x3 matrix of doubles.

This type (and any structs that contain it) can be safely allocated via new.

Matrix33f

typedef Eigen::Matrix<float, 3, 3, Eigen::RowMajor> SurgSim::Math::Matrix33f

A 3x3 matrix of floats.

This type (and any structs that contain it) can be safely allocated via new.

Matrix44d

typedef Eigen::Matrix<double, 4, 4, Eigen::RowMajor> SurgSim::Math::Matrix44d

A 4x4 matrix of doubles.

This type (and any structs that contain it) can be safely allocated via new.

Matrix44f

typedef Eigen::Matrix<float, 4, 4, Eigen::RowMajor> SurgSim::Math::Matrix44f

A 4x4 matrix of floats.

This type (and any structs that contain it) can be safely allocated via new.

Matrix66d

typedef Eigen::Matrix<double, 6, 6, Eigen::RowMajor> SurgSim::Math::Matrix66d

A 6x6 matrix of doubles.

This type (and any structs that contain it) can be safely allocated via new.

Function Documentation

addSubMatrix() [1/2]

template<class Matrix , class SubMatrix >

void SurgSim::Math::addSubMatrix	(	const SubMatrix &	subMatrix,
		size_t	blockIdRow,
		size_t	blockIdCol,
		size_t	blockSizeRow,
		size_t	blockSizeCol,
		Matrix *	matrix
	)

Helper method to add a sub-matrix into a matrix, for the sake of clarity.

Template Parameters

Matrix	The matrix type
SubMatrix	The sub-matrix type

Parameters

	subMatrix	The sub-matrix
	blockIdRow,blockIdCol	The block indices in matrix
	blockSizeRow,blockSizeCol	The block size (size of the sub-matrix)
[out]	matrix	The matrix to add the sub-matrix into

addSubMatrix() [2/2]

template<class Matrix , class SubMatrix >

void SurgSim::Math::addSubMatrix	(	const SubMatrix &	subMatrix,
		const std::vector< size_t > &	blockIds,
		size_t	blockSize,
		Matrix *	matrix
	)

Helper method to add a sub-matrix made of squared-blocks into a matrix, for the sake of clarity.

Template Parameters

Matrix	The matrix type
SubMatrix	The sub-matrix type

Parameters

	subMatrix	The sub-matrix (containing all the squared-blocks)
	blockIds	Vector of block indices (for accessing matrix) corresponding to the blocks in sub-matrix
	blockSize	The blocks size
[out]	matrix	The matrix to add the sub-matrix blocks into

computeAngle()

template<typename T , int MOpt>

T SurgSim::Math::computeAngle ( const Eigen::Matrix< T, 3, 3, MOpt > &  matrix )

inline

Get the angle corresponding to a quaternion's rotation, in radians.

If you don't care about the rotation axis, this is more efficient than computeAngleAndAxis().

Template Parameters

T	the numeric data type used for arguments and the return value. Can usually be deduced.
MOpt	the option flags (alignment etc.) used for the rotation matrix argument. Can be deduced.

Parameters

matrix

the rotation matrix to inspect.

Returns

the angle of the rotation, in radians.

computeAngleAndAxis()

template<typename T , int MOpt, int VOpt>

void SurgSim::Math::computeAngleAndAxis ( const Eigen::Matrix< T, 3, 3, MOpt > &  matrix, T *  angle, Eigen::Matrix< T, 3, 1, VOpt > *  axis  )

inline

Get the angle (in radians) and axis corresponding to a rotation matrix.

Template Parameters

T	the numeric data type used for arguments and the return value. Can usually be deduced.
MOpt	the option flags (alignment etc.) used for the rotation matrix argument. Can be deduced.
VOpt	the option flags (alignment etc.) used for the axis vector argument. Can be deduced.

Parameters

	matrix	the rotation matrix to inspect.
[out]	angle	the angle of the rotation, in radians.
[out]	axis	the axis of the rotation.

getSubMatrix()

template<class Matrix >

Eigen::Block<Matrix> SurgSim::Math::getSubMatrix	(	Matrix &	matrix,
		size_t	blockIdRow,
		size_t	blockIdCol,
		size_t	blockSizeRow,
		size_t	blockSizeCol
	)

Helper method to access a sub-matrix from a matrix, for the sake of clarity.

Template Parameters

Matrix

The matrix type to get the sub-matrix from

Parameters

matrix	The matrix to get the sub-matrix from
blockIdRow,blockIdCol	The block indices
blockSizeRow,blockSizeCol	The block size

Returns

The requested sub-matrix

Note

Disable cpplint warnings for use of non-const reference

Eigen has a specific type for Block that we want to return with read/write access

therefore the Matrix from which the Block is built from must not be const

makeRotationMatrix()

template<typename T , int VOpt>

Eigen::Matrix<T, 3, 3> SurgSim::Math::makeRotationMatrix ( const T &  angle, const Eigen::Matrix< T, 3, 1, VOpt > &  axis  )

inline

Create a rotation matrix corresponding to the specified angle (in radians) and axis.

Template Parameters

T	the numeric data type used for arguments and the return value. Can usually be deduced.
VOpt	the option flags (alignment etc.) used for the axis vector argument. Can be deduced.

Parameters

angle	the angle of the rotation, in radians.
axis	the axis of the rotation.

Returns

the rotation matrix.

makeSkewSymmetricMatrix()

template<typename T , int VOpt>

Eigen::Matrix<T, 3, 3> SurgSim::Math::makeSkewSymmetricMatrix ( const Eigen::Matrix< T, 3, 1, VOpt > &  vector )

inline

Create a skew-symmetric matrix corresponding to the specified vector.

Skew-symmetric matrices are particularly useful for representing a portion of the vector cross-product.

Template Parameters

T	the numeric data type used for arguments and the return value. Can usually be deduced.
VOpt	the option flags (alignment etc.) used for the vector argument. Can be deduced.

Parameters

vector

the vector to be transformed.

Returns

the skew-symmetric matrix corresponding with the vector argument.

setSubMatrix()

template<class Matrix , class SubMatrix >

void SurgSim::Math::setSubMatrix	(	const SubMatrix &	subMatrix,
		size_t	blockIdRow,
		size_t	blockIdCol,
		size_t	blockSizeRow,
		size_t	blockSizeCol,
		Matrix *	matrix
	)

Helper method to set a sub-matrix into a matrix, for the sake of clarity.

Template Parameters

Matrix	The matrix type
SubMatrix	The sub-matrix type

Parameters

	subMatrix	The sub-matrix
	blockIdRow,blockIdCol	The block indices for row and column in matrix
	blockSizeRow,blockSizeCol	The size of the sub-matrix
[out]	matrix	The matrix to set the sub-matrix into

skew()

template<typename T , int MOpt>

Eigen::Matrix<T, 3, 1> SurgSim::Math::skew ( const Eigen::Matrix< T, 3, 3, MOpt > &  matrix )

inline

Extract the unique vector from the skew-symmetric part of a given matrix.

Template Parameters

T	the numeric data type used for arguments and the return value. Can usually be deduced.
MOpt	the option flags (alignment etc.) used for the matrix argument. Can be deduced.

Parameters

matrix

the matrix to compute the skew symmetric part from.

Returns

the unique vector defining the skew-symmetric part of the matrix.

Note

For any vector u, skew(makeSkewSymmetricMatrix(u)) = u

In general, returns the vector of the skew symmetric part of matrix: (matrix - matrix^T)/2

zeroColumn()

template<class Derived >

void SurgSim::Math::zeroColumn	(	size_t	column,
		Eigen::DenseBase< Derived > *	matrix
	)

Helper method to zero a column of a matrix.

Template Parameters

Matrix

The matrix type

Parameters

	column	The column to set to zero
[in,out]	matrix	The matrix to set the zero column on.

zeroRow()

template<class Derived >

void SurgSim::Math::zeroRow	(	size_t	row,
		Eigen::DenseBase< Derived > *	matrix
	)

Helper method to zero a row of a matrix.

Template Parameters

Matrix

The matrix type

Parameters

	row	The row to set to zero
[in,out]	matrix	The matrix to set the zero row on.