3x3 matrix class. More...

#include <openvdb/math/Mat3.h>

Public Types
using	value_type = T
	Data type held by the matrix. More...

using	ValueType = T

using	MyBase = Mat< 3, T >

enum	SIZE_

Public Member Functions
	Mat3 ()=default

	Mat3 (const Quat< T > &q)

template<typename Source >
	Mat3 (Source a, Source b, Source c, Source d, Source e, Source f, Source g, Source h, Source i)
	Constructor given array of elements, the ordering is in row major form: More...

template<typename Source >
	Mat3 (const Vec3< Source > &v1, const Vec3< Source > &v2, const Vec3< Source > &v3, bool rows=true)

template<typename Source >
	Mat3 (Source *a)

template<typename Source >
	Mat3 (const Mat3< Source > &m)
	Conversion constructor. More...

	Mat3 (const Mat4< T > &m)
	Conversion from Mat4 (copies top left) More...

void	setRow (int i, const Vec3< T > &v)
	Set ith row to vector v. More...

Vec3< T >	row (int i) const
	Get ith row, e.g. Vec3d v = m.row(1);. More...

void	setCol (int j, const Vec3< T > &v)
	Set jth column to vector v. More...

Vec3< T >	col (int j) const
	Get jth column, e.g. Vec3d v = m.col(0);. More...

T &	operator() (int i, int j)

T	operator() (int i, int j) const

void	setRows (const Vec3< T > &v1, const Vec3< T > &v2, const Vec3< T > &v3)
	Set the rows of this matrix to the vectors v1, v2, v3. More...

void	setColumns (const Vec3< T > &v1, const Vec3< T > &v2, const Vec3< T > &v3)
	Set the columns of this matrix to the vectors v1, v2, v3. More...

void	setSymmetric (const Vec3< T > &vdiag, const Vec3< T > &vtri)
	Set diagonal and symmetric triangular components. More...

void	setSkew (const Vec3< T > &v)
	Set the matrix as cross product of the given vector. More...

void	setToRotation (const Quat< T > &q)
	Set this matrix to the rotation matrix specified by the quaternion. More...

void	setToRotation (const Vec3< T > &axis, T angle)
	Set this matrix to the rotation specified by axis and angle. More...

void	setZero ()
	Set this matrix to zero. More...

void	setIdentity ()
	Set this matrix to identity. More...

template<typename Source >
const Mat3 &	operator= (const Mat3< Source > &m)
	Assignment operator. More...

bool	eq (const Mat3 &m, T eps=1.0e-8) const
	Return `true` if this matrix is equivalent to m within a tolerance of eps. More...

Mat3< T >	operator- () const
	Negation operator, for e.g. m1 = -m2;. More...

template<typename S >
const Mat3< T > &	operator*= (S scalar)
	Multiplication operator, e.g. M = scalar * M;. More...

template<typename S >
const Mat3< T > &	operator+= (const Mat3< S > &m1)
	Add each element of the given matrix to the corresponding element of this matrix. More...

template<typename S >
const Mat3< T > &	operator-= (const Mat3< S > &m1)
	Subtract each element of the given matrix from the corresponding element of this matrix. More...

template<typename S >
const Mat3< T > &	operator*= (const Mat3< S > &m1)
	Multiply this matrix by the given matrix. More...

Mat3	cofactor () const
	Return the cofactor matrix of this matrix. More...

Mat3	adjoint () const
	Return the adjoint of this matrix, i.e., the transpose of its cofactor. More...

Mat3	transpose () const
	returns transpose of this More...

Mat3	inverse (T tolerance=0) const

T	det () const
	Determinant of matrix. More...

T	trace () const
	Trace of matrix. More...

Mat3	snapBasis (Axis axis, const Vec3< T > &direction)

template<typename T0 >
Vec3< T0 >	transform (const Vec3< T0 > &v) const

template<typename T0 >
Vec3< T0 >	pretransform (const Vec3< T0 > &v) const

Mat3	timesDiagonal (const Vec3< T > &diag) const
	Treat diag as a diagonal matrix and return the product of this matrix with diag (from the right). More...

std::string	str (unsigned indentation=0) const

T *	asPointer ()
	Direct access to the internal data. More...

const T *	asPointer () const

void	write (std::ostream &os) const

void	read (std::istream &is)

T	absMax () const
	Return the maximum of the absolute of all elements in this matrix. More...

bool	isNan () const
	True if a Nan is present in this matrix. More...

bool	isInfinite () const
	True if an Inf is present in this matrix. More...

bool	isFinite () const
	True if no Nan or Inf values are present. More...

bool	isZero () const
	True if all elements are exactly zero. More...


T *	operator[] (int i)
	Array style reference to ith row. More...

const T *	operator[] (int i) const
	Array style reference to ith row. More...

Static Public Member Functions
static const Mat3< T > &	identity ()
	Predefined constant for identity matrix. More...

static const Mat3< T > &	zero ()
	Predefined constant for zero matrix. More...

static Mat3	symmetric (const Vec3< T > &vdiag, const Vec3< T > &vtri)
	Return a matrix with the prescribed diagonal and symmetric triangular components. More...

static unsigned	numRows ()

static unsigned	numColumns ()

static unsigned	numElements ()

Protected Attributes
T	mm [SIZE *SIZE]

Related Functions
(Note that these are not member functions.)
template<typename T0 , typename T1 >
bool	operator== (const Mat3< T0 > &m0, const Mat3< T1 > &m1)
	Equality operator, does exact floating point comparisons. More...

template<typename T0 , typename T1 >
bool	operator!= (const Mat3< T0 > &m0, const Mat3< T1 > &m1)
	Inequality operator, does exact floating point comparisons. More...

template<typename S , typename T >
Mat3< typename promote< S, T >::type >	operator* (S scalar, const Mat3< T > &m)
	Multiply each element of the given matrix by scalar and return the result. More...

template<typename S , typename T >
Mat3< typename promote< S, T >::type >	operator* (const Mat3< T > &m, S scalar)
	Multiply each element of the given matrix by scalar and return the result. More...

template<typename T0 , typename T1 >
Mat3< typename promote< T0, T1 >::type >	operator+ (const Mat3< T0 > &m0, const Mat3< T1 > &m1)
	Add corresponding elements of m0 and m1 and return the result. More...

template<typename T0 , typename T1 >
Mat3< typename promote< T0, T1 >::type >	operator- (const Mat3< T0 > &m0, const Mat3< T1 > &m1)
	Subtract corresponding elements of m0 and m1 and return the result. More...

template<typename T , typename MT >
Vec3< typename promote< T, MT >::type >	operator* (const Mat3< MT > &_m, const Vec3< T > &_v)
	Multiply _m by _v and return the resulting vector. More...

template<typename T , typename MT >
Vec3< typename promote< T, MT >::type >	operator* (const Vec3< T > &_v, const Mat3< MT > &_m)
	Multiply _v by _m and return the resulting vector. More...

template<typename T , typename MT >
Vec3< T > &	operator*= (Vec3< T > &_v, const Mat3< MT > &_m)
	Multiply _v by _m and replace _v with the resulting vector. More...

Detailed Description

template<typename T>
class openvdb::v11_0::math::Mat3< T >

3x3 matrix class.

Member Typedef Documentation

using MyBase = Mat<3, T>

using value_type = T

Data type held by the matrix.

using ValueType = T

Member Enumeration Documentation

enum SIZE_

inherited

Constructor & Destructor Documentation

Mat3 ( )

default

Trivial constructor, the matrix is NOT initialized

Note: destructor, copy constructor, assignment operator and move constructor are left to be defined by the compiler (default)

Mat3 ( const Quat< T > & q )

inline

Constructor given the quaternion rotation, e.g. Mat3f m(q); The quaternion is normalized and used to construct the matrix

Mat3	(	Source	a,
		Source	b,
		Source	c,
		Source	d,
		Source	e,
		Source	f,
		Source	g,
		Source	h,
		Source	i
	)

inline

Constructor given array of elements, the ordering is in row major form:

a b c
d e f
g h i

Mat3	(	const Vec3< Source > &	v1,
		const Vec3< Source > &	v2,
		const Vec3< Source > &	v3,
		bool	rows = `true`
	)

inline

Construct matrix from rows or columns vectors (defaults to rows for historical reasons)

Mat3 ( Source * a )

inline

Constructor given array of elements, the ordering is in row major form:
a[0] a[1] a[2]
a[3] a[4] a[5]
a[6] a[7] a[8]

Mat3 ( const Mat3< Source > & m )

inlineexplicit

Conversion constructor.

Mat3 ( const Mat4< T > & m )

inlineexplicit

Conversion from Mat4 (copies top left)

Member Function Documentation

T absMax ( ) const

inlineinherited

Return the maximum of the absolute of all elements in this matrix.

Mat3 adjoint ( ) const

inline

Return the adjoint of this matrix, i.e., the transpose of its cofactor.

T* asPointer ( )

inlineinherited

Direct access to the internal data.

const T* asPointer ( ) const

inlineinherited

Mat3 cofactor ( ) const

inline

Return the cofactor matrix of this matrix.

Vec3<T> col ( int j ) const

inline

Get jth column, e.g. Vec3d v = m.col(0);.

T det ( ) const

inline

Determinant of matrix.

bool eq	(	const Mat3< T > &	m,
		T	eps = `1.0e-8`
	)		const

inline

Return true if this matrix is equivalent to m within a tolerance of eps.

static const Mat3<T>& identity ( )

inlinestatic

Predefined constant for identity matrix.

Mat3 inverse ( T tolerance = 0 ) const

inline

returns inverse of this

Exceptions

ArithmeticError if singular

bool isFinite ( ) const

inlineinherited

True if no Nan or Inf values are present.

bool isInfinite ( ) const

inlineinherited

True if an Inf is present in this matrix.

bool isNan ( ) const

inlineinherited

True if a Nan is present in this matrix.

bool isZero ( ) const

inlineinherited

True if all elements are exactly zero.

static unsigned numColumns ( )

inlinestaticinherited

static unsigned numElements ( )

inlinestaticinherited

static unsigned numRows ( )

inlinestaticinherited

T& operator()	(	int	i,
		int	j
	)

inline

Alternative indexed reference to the elements Note that the indices are row first and column second. e.g. m(0,0) = 1;

T operator()	(	int	i,
		int	j
	)		const

inline

Alternative indexed constant reference to the elements, Note that the indices are row first and column second. e.g. float f = m(1,0);

const Mat3<T>& operator*= ( S scalar )

inline

Multiplication operator, e.g. M = scalar * M;.

Multiply each element of this matrix by scalar.

const Mat3<T>& operator*= ( const Mat3< S > & m1 )

inline

Multiply this matrix by the given matrix.

const Mat3<T>& operator+= ( const Mat3< S > & m1 )

inline

Add each element of the given matrix to the corresponding element of this matrix.

Mat3<T> operator- ( ) const

inline

Negation operator, for e.g. m1 = -m2;.

const Mat3<T>& operator-= ( const Mat3< S > & m1 )

inline

Subtract each element of the given matrix from the corresponding element of this matrix.

const Mat3& operator= ( const Mat3< Source > & m )

inline

Assignment operator.

T* operator[] ( int i )

inlineinherited

Array style reference to ith row.

const T* operator[] ( int i ) const

inlineinherited

Array style reference to ith row.

Vec3<T0> pretransform ( const Vec3< T0 > & v ) const

inline

Return the transformed vector by transpose of this matrix. This function is equivalent to pre-multiplying the matrix.

void read ( std::istream & is )

inlineinherited

Vec3<T> row ( int i ) const

inline

Get ith row, e.g. Vec3d v = m.row(1);.

void setCol	(	int	j,
		const Vec3< T > &	v
	)

inline

Set jth column to vector v.

void setColumns	(	const Vec3< T > &	v1,
		const Vec3< T > &	v2,
		const Vec3< T > &	v3
	)

inline

Set the columns of this matrix to the vectors v1, v2, v3.

void setIdentity ( )

inline

Set this matrix to identity.

void setRow	(	int	i,
		const Vec3< T > &	v
	)

inline

Set ith row to vector v.

void setRows	(	const Vec3< T > &	v1,
		const Vec3< T > &	v2,
		const Vec3< T > &	v3
	)

inline

Set the rows of this matrix to the vectors v1, v2, v3.

void setSkew ( const Vec3< T > & v )

inline

Set the matrix as cross product of the given vector.

void setSymmetric	(	const Vec3< T > &	vdiag,
		const Vec3< T > &	vtri
	)

inline

Set diagonal and symmetric triangular components.

void setToRotation ( const Quat< T > & q )

inline

Set this matrix to the rotation matrix specified by the quaternion.

The quaternion is normalized and used to construct the matrix. Note that the matrix is transposed to match post-multiplication semantics.

void setToRotation	(	const Vec3< T > &	axis,
		T	angle
	)

inline

Set this matrix to the rotation specified by axis and angle.

The axis must be unit vector

void setZero ( )

inline

Set this matrix to zero.

Mat3 snapBasis	(	Axis	axis,
		const Vec3< T > &	direction
	)

inline

This function snaps a specific axis to a specific direction, preserving scaling. It does this using minimum energy, thus posing a unique solution if basis & direction arent parralel. Direction need not be unit.

std::string str ( unsigned indentation = 0 ) const

inlineinherited

Returns: string representation of matrix Since output is multiline, optional indentation argument prefixes each newline with that much white space. It does not indent the first line, since you might be calling this inline:

cout << "matrix: " << mat.str(7)

matrix: [[1 2] [3 4]]

static Mat3 symmetric	(	const Vec3< T > &	vdiag,
		const Vec3< T > &	vtri
	)

inlinestatic

Return a matrix with the prescribed diagonal and symmetric triangular components.

Mat3 timesDiagonal ( const Vec3< T > & diag ) const

inline

Treat diag as a diagonal matrix and return the product of this matrix with diag (from the right).

T trace ( ) const

inline

Trace of matrix.

Vec3<T0> transform ( const Vec3< T0 > & v ) const

inline

Return the transformed vector by this matrix. This function is equivalent to post-multiplying the matrix.

Mat3 transpose ( ) const

inline

returns transpose of this

void write ( std::ostream & os ) const

inlineinherited

static const Mat3<T>& zero ( )

inlinestatic

Predefined constant for zero matrix.

Friends And Related Function Documentation

bool operator!=	(	const Mat3< T0 > &	m0,
		const Mat3< T1 > &	m1
	)

Mat3< typename promote< S, T >::type > operator*	(	S	scalar,
		const Mat3< T > &	m
	)

Mat3< typename promote< S, T >::type > operator*	(	const Mat3< T > &	m,
		S	scalar
	)

Vec3< typename promote< T, MT >::type > operator*	(	const Mat3< MT > &	_m,
		const Vec3< T > &	_v
	)

Vec3< typename promote< T, MT >::type > operator*	(	const Vec3< T > &	_v,
		const Mat3< MT > &	_m
	)

Vec3< T > & operator*=	(	Vec3< T > &	_v,
		const Mat3< MT > &	_m
	)

Mat3< typename promote< T0, T1 >::type > operator+	(	const Mat3< T0 > &	m0,
		const Mat3< T1 > &	m1
	)

Mat3< typename promote< T0, T1 >::type > operator-	(	const Mat3< T0 > &	m0,
		const Mat3< T1 > &	m1
	)

bool operator==	(	const Mat3< T0 > &	m0,
		const Mat3< T1 > &	m1
	)

Member Data Documentation

T mm[SIZE *SIZE]

protectedinherited

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Related Functions

Detailed Description

template<typename T> class openvdb::v11_0::math::Mat3< T >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<typename T>
class openvdb::v11_0::math::Mat3< T >