A class that represents a 3x3 matrix. More...

#include <omMatrix3D.h>

Public Member Functions
	MatrixND ()
	Create a 3x3 matrix with all elements equal to zero. More...

	MatrixND (const VectorND< T, 3 > &column1, const VectorND< T, 3 > &column2, const VectorND< T, 3 > &column3)
	Create a 3x3 matrix from three column vectors. More...

	MatrixND (T a, T b, T c, T d, T e, T f, T g, T h, T i)
	Create a 3x3 matrix with elements specified in row-major order. More...

	MatrixND (const T array[9])
	Create a 3x3 matrix from a pointer to an array of elements in column-major order. More...

template<typename U >
	MatrixND (const MatrixND< U, 2, 2 > &other)
	Create an identity matrx with the specified 2x2 matrix in the upper-left corner. More...

template<typename U >
	MatrixND (const MatrixND< U, 3, 3 > &other)
	Create a copy of the specified 3x3 matrix with different template parameter type. More...

T *	toArrayColumnMajor ()
	Return a pointer to the matrix's elements in colunn-major order. More...

const T *	toArrayColumnMajor () const
	Return a pointer to the matrix's elements in colunn-major order. More...

void	toArrayRowMajor (T *outputArray) const
	Place the elements of the matrix at the location specified in row-major order. More...

VectorND< T, 3 > &	getColumn (Index columnIndex)
	Get the column at the specified index in the matrix. More...

const VectorND< T, 3 > &	getColumn (Index columnIndex) const
	Get the column at the specified index in the matrix. More...

VectorND< T, 3 > &	operator() (Index columnIndex)
	Get the column at the specified index in the matrix. More...

const VectorND< T, 3 > &	operator() (Index columnIndex) const
	Get the column at the specified index in the matrix. More...

VectorND< T, 3 > &	operator[] (Index columnIndex)
	Get the column at the specified index in the matrix. More...

const VectorND< T, 3 > &	operator[] (Index columnIndex) const
	Get the column at the specified index in the matrix. More...

VectorND< T, 3 >	getRow (Index rowIndex) const
	Get the row at the specified index in the matrix. More...

T &	get (Index columnIndex, Index rowIndex)
	Get the element at the specified (column, row) index in the matrix. More...

const T &	get (Index columnIndex, Index rowIndex) const
	Get the element at the specified (column, row) index in the matrix. More...

T &	operator() (Index columnIndex, Index rowIndex)
	Get the element at the specified (column, row) index in the matrix. More...

const T &	operator() (Index columnIndex, Index rowIndex) const
	Get the element at the specified (column, row) index in the matrix. More...

void	set (Index rowIndex, Index columnIndex, T value)
	Set the element in the matrix at the specified (row, column) index. More...

void	setColumn (Index columnIndex, const VectorND< T, 3 > &newColumn)
	Set the column in the matrix at the specified index. More...

void	setRow (Index rowIndex, const VectorND< T, 3 > &newRow)
	Set the row in the matrix at the specified index. More...

VectorND< T, 3 >	getDiagonal () const
	Return the diagonal vector of this matrix. More...

MatrixND< T, 2, 2 >	getXY () const
	Return the upper-left 2x2 submatrix of this matrix. More...

T	getDeterminant () const
	Return the determinant of this matrix. More...

MatrixND	invert (T threshold=0) const
	Return the inverse of this matrix, or the zero matrix if the matrix has no inverse. More...

Bool	invert (MatrixND &inverse, T threshold=0) const
	Compute the inverse of this matrix, returning the result in the output parameter. More...

MatrixND	orthonormalize () const
	Return the orthonormalization of this matrix. More...

MatrixND	transpose () const
	Return the transposition of this matrix. More...

Bool	operator== (const MatrixND &m) const
	Compare two matrices component-wise for equality. More...

Bool	operator!= (const MatrixND &m) const
	Compare two matrices component-wise for inequality. More...

MatrixND	operator- () const
	Negate every element of this matrix and return the resulting matrix. More...

MatrixND	operator+ () const
	'Positivate' every element of this matrix, returning a copy of the original matrix. More...

MatrixND	operator+ (const MatrixND &matrix) const
	Add this matrix to another and return the resulting matrix. More...

MatrixND	operator+ (const T &value) const
	Add a scalar to the elements of this matrix and return the resulting matrix. More...

MatrixND	operator- (const MatrixND &matrix) const
	Subtract a matrix from this matrix and return the resulting matrix. More...

MatrixND	operator- (const T &value) const
	Subtract a scalar from the elements of this matrix and return the resulting matrix. More...

MatrixND	operator* (const MatrixND &matrix) const
	Multiply a matrix by this matrix and return the result. More...

VectorND< T, 3 >	operator* (const VectorND< T, 3 > &vector) const
	Multiply a vector/point by this matrix and return the result. More...

MatrixND	operator* (const T &value) const
	Multiply the elements of this matrix by a scalar and return the resulting matrix. More...

MatrixND	operator/ (const T &value) const
	Divide the elements of this matrix by a scalar and return the resulting matrix. More...

MatrixND &	operator+= (const MatrixND &matrix)
	Add the elements of another matrix to this matrix. More...

MatrixND &	operator+= (const T &value)
	Add a scalar value to the elements of this matrix. More...

MatrixND &	operator-= (const MatrixND &matrix)
	Subtract the elements of another matrix from this matrix. More...

MatrixND &	operator-= (const T &value)
	Subtract a scalar value from the elements of this matrix. More...

MatrixND &	operator*= (const T &value)
	Multiply the elements of this matrix by a scalar value. More...

MatrixND &	operator/= (const T &value)
	Divide the elements of this matrix by a scalar value. More...

data::String	toString () const
	Convert this 3x3 matrix into a human-readable string representation. More...

	operator data::String () const
	Convert this 3x3 matrix into a human-readable string representation. More...

Static Public Member Functions
static MatrixND	skewSymmetric (const VectorND< T, 3 > &vector)
	Return a skew-symmetric matrix using the elements of the specified vector. More...

static MatrixND	planeBasis (const VectorND< T, 3 > &normal)
	Return an orthogonal matrix defining a basis for the coordinate frame of a plane with the specified normal. More...

static MatrixND	rotateX (T xAngle)
	Create a 3x3 rotation matrix about the X-axis with the angle in radians. More...

static MatrixND	rotateY (T yAngle)
	Create a 3x3 rotation matrix about the Y-axis with the angle in radians. More...

static MatrixND	rotateZ (T zAngle)
	Create a 3x3 rotation matrix about the Z-axis with the angle in radians. More...

static MatrixND	rotateXDegrees (T xAngle)
	Create a 3x3 rotation matrix about the X-axis with the angle in degrees. More...

static MatrixND	rotateYDegrees (T yAngle)
	Create a 3x3 rotation matrix about the Y-axis with the angle in degrees. More...

static MatrixND	rotateZDegrees (T zAngle)
	Create a 3x3 rotation matrix about the Z-axis with the angle in degrees. More...

static MatrixND	rotateXYZ (T xAngle, T yAngle, T zAngle)
	Create a 3x3 rotation matrix from Euler angles in the XYZ order. More...

static MatrixND	rotateXYZ (const VectorND< T, 3 > &angle)
	Create a 3x3 rotation matrix from Euler angles in the XYZ order. More...

static MatrixND	rotateXZY (T xAngle, T yAngle, T zAngle)
	Create a 3x3 rotation matrix from Euler angles in the XZY order. More...

static MatrixND	rotateXZY (const VectorND< T, 3 > &angle)
	Create a 3x3 rotation matrix from Euler angles in the XZY order. More...

static MatrixND	rotateYXZ (T xAngle, T yAngle, T zAngle)
	Create a 3x3 rotation matrix from Euler angles in the YXZ order. More...

static MatrixND	rotateYXZ (const VectorND< T, 3 > &angle)
	Create a 3x3 rotation matrix from Euler angles in the YXZ order. More...

static MatrixND	rotateYZX (T xAngle, T yAngle, T zAngle)
	Create a 3x3 rotation matrix from Euler angles in the YZX order. More...

static MatrixND	rotateYZX (const VectorND< T, 3 > &angle)
	Create a 3x3 rotation matrix from Euler angles in the YZX order. More...

static MatrixND	rotateZXY (T xAngle, T yAngle, T zAngle)
	Create a 3x3 rotation matrix from Euler angles in the ZXY order. More...

static MatrixND	rotateZXY (const VectorND< T, 3 > &angle)
	Create a 3x3 rotation matrix from Euler angles in the ZXY order. More...

static MatrixND	rotateZYX (T xAngle, T yAngle, T zAngle)
	Create a 3x3 rotation matrix from Euler angles in the ZYX order. More...

static MatrixND	rotateZYX (const VectorND< T, 3 > &angle)
	Create a 3x3 rotation matrix from Euler angles in the ZYX order. More...

Public Attributes
VectorND< T, 3 >	x
	The first column vector of the matrix. More...

VectorND< T, 3 >	y
	The second column vector of the matrix. More...

VectorND< T, 3 >	z
	The third column vector of the matrix. More...

Static Public Attributes
static const MatrixND	ZERO
	Constant matrix with all elements equal to zero. More...

static const MatrixND	IDENTITY
	Constant matrix with diagonal elements equal to one and all others equal to zero. More...

Detailed Description

template<typename T>
class om::math::MatrixND< T, 3, 3 >

A class that represents a 3x3 matrix.

Elements in the matrix are stored in column-major order.

Constructor & Destructor Documentation

template<typename T >

om::math::MatrixND< T, 3, 3 >::MatrixND ( )

inline

Create a 3x3 matrix with all elements equal to zero.

template<typename T >

om::math::MatrixND< T, 3, 3 >::MatrixND	(	const VectorND< T, 3 > &	column1,
		const VectorND< T, 3 > &	column2,
		const VectorND< T, 3 > &	column3
	)

inline

Create a 3x3 matrix from three column vectors.

template<typename T >

om::math::MatrixND< T, 3, 3 >::MatrixND	(	T	a,
		T	b,
		T	c,
		T	d,
		T	e,
		T	f,
		T	g,
		T	h,
		T	i
	)

inline

Create a 3x3 matrix with elements specified in row-major order.

template<typename T >

om::math::MatrixND< T, 3, 3 >::MatrixND ( const T array[9] )

inlineexplicit

Create a 3x3 matrix from a pointer to an array of elements in column-major order.

template<typename T >

template<typename U >

om::math::MatrixND< T, 3, 3 >::MatrixND ( const MatrixND< U, 2, 2 > & other )

inlineexplicit

Create an identity matrx with the specified 2x2 matrix in the upper-left corner.

template<typename T >

template<typename U >

om::math::MatrixND< T, 3, 3 >::MatrixND ( const MatrixND< U, 3, 3 > & other )

inline

Create a copy of the specified 3x3 matrix with different template parameter type.

Member Function Documentation

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::skewSymmetric ( const VectorND< T, 3 > & vector )

inlinestatic

Return a skew-symmetric matrix using the elements of the specified vector.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::planeBasis ( const VectorND< T, 3 > & normal )

inlinestatic

Return an orthogonal matrix defining a basis for the coordinate frame of a plane with the specified normal.

The normal becomes the z-column of the resulting matrix, and X and Y columns are generated robustly from the input normal vector. The normal vector must have non-zero length.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateX ( T xAngle )

inlinestatic

Create a 3x3 rotation matrix about the X-axis with the angle in radians.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateY ( T yAngle )

inlinestatic

Create a 3x3 rotation matrix about the Y-axis with the angle in radians.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateZ ( T zAngle )

inlinestatic

Create a 3x3 rotation matrix about the Z-axis with the angle in radians.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateXDegrees ( T xAngle )

inlinestatic

Create a 3x3 rotation matrix about the X-axis with the angle in degrees.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateYDegrees ( T yAngle )

inlinestatic

Create a 3x3 rotation matrix about the Y-axis with the angle in degrees.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateZDegrees ( T zAngle )

inlinestatic

Create a 3x3 rotation matrix about the Z-axis with the angle in degrees.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateXYZ	(	T	xAngle,
		T	yAngle,
		T	zAngle
	)

inlinestatic

Create a 3x3 rotation matrix from Euler angles in the XYZ order.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateXYZ ( const VectorND< T, 3 > & angle )

inlinestatic

Create a 3x3 rotation matrix from Euler angles in the XYZ order.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateXZY	(	T	xAngle,
		T	yAngle,
		T	zAngle
	)

inlinestatic

Create a 3x3 rotation matrix from Euler angles in the XZY order.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateXZY ( const VectorND< T, 3 > & angle )

inlinestatic

Create a 3x3 rotation matrix from Euler angles in the XZY order.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateYXZ	(	T	xAngle,
		T	yAngle,
		T	zAngle
	)

inlinestatic

Create a 3x3 rotation matrix from Euler angles in the YXZ order.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateYXZ ( const VectorND< T, 3 > & angle )

inlinestatic

Create a 3x3 rotation matrix from Euler angles in the YXZ order.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateYZX	(	T	xAngle,
		T	yAngle,
		T	zAngle
	)

inlinestatic

Create a 3x3 rotation matrix from Euler angles in the YZX order.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateYZX ( const VectorND< T, 3 > & angle )

inlinestatic

Create a 3x3 rotation matrix from Euler angles in the YZX order.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateZXY	(	T	xAngle,
		T	yAngle,
		T	zAngle
	)

inlinestatic

Create a 3x3 rotation matrix from Euler angles in the ZXY order.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateZXY ( const VectorND< T, 3 > & angle )

inlinestatic

Create a 3x3 rotation matrix from Euler angles in the ZXY order.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateZYX	(	T	xAngle,
		T	yAngle,
		T	zAngle
	)

inlinestatic

Create a 3x3 rotation matrix from Euler angles in the ZYX order.

template<typename T >

static MatrixND om::math::MatrixND< T, 3, 3 >::rotateZYX ( const VectorND< T, 3 > & angle )

inlinestatic

Create a 3x3 rotation matrix from Euler angles in the ZYX order.

template<typename T >

T* om::math::MatrixND< T, 3, 3 >::toArrayColumnMajor ( )

inline

Return a pointer to the matrix's elements in colunn-major order.

Since matrix elements are stored in column-major order, no allocation is performed and the elements are accessed directly.

template<typename T >

const T* om::math::MatrixND< T, 3, 3 >::toArrayColumnMajor ( ) const

inline

Return a pointer to the matrix's elements in colunn-major order.

Since matrix elements are stored in column-major order, no allocation is performed and the elements are accessed directly.

template<typename T >

void om::math::MatrixND< T, 3, 3 >::toArrayRowMajor ( T * outputArray ) const

inline

Place the elements of the matrix at the location specified in row-major order.

The output array must be at least 9 elements long.

template<typename T >

VectorND<T,3>& om::math::MatrixND< T, 3, 3 >::getColumn ( Index columnIndex )

inline