4x4 -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< 4, T >

enum	SIZE_

Public Member Functions
	Mat4 ()=default
	Trivial constructor, the matrix is NOT initialized. More...

template<typename Source >
	Mat4 (Source *a)
	Constructor given array of elements, the ordering is in row major form: More...

template<typename Source >
	Mat4 (Source a, Source b, Source c, Source d, Source e, Source f, Source g, Source h, Source i, Source j, Source k, Source l, Source m, Source n, Source o, Source p)
	Constructor given array of elements, the ordering is in row major form: More...

template<typename Source >
	Mat4 (const Vec4< Source > &v1, const Vec4< Source > &v2, const Vec4< Source > &v3, const Vec4< Source > &v4, bool rows=true)

template<typename Source >
	Mat4 (const Mat4< Source > &m)
	Conversion constructor. More...

void	setRow (int i, const Vec4< T > &v)
	Set ith row to vector v. More...

Vec4< T >	row (int i) const
	Get ith row, e.g. Vec4f v = m.row(1);. More...

void	setCol (int j, const Vec4< T > &v)
	Set jth column to vector v. More...

Vec4< T >	col (int j) const
	Get jth column, e.g. Vec4f v = m.col(0);. More...

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

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

void	setRows (const Vec4< T > &v1, const Vec4< T > &v2, const Vec4< T > &v3, const Vec4< T > &v4)
	Set the rows of this matrix to the vectors v1, v2, v3, v4. More...

void	setColumns (const Vec4< T > &v1, const Vec4< T > &v2, const Vec4< T > &v3, const Vec4< T > &v4)
	Set the columns of this matrix to the vectors v1, v2, v3, v4. More...

void	setZero ()

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

void	setMat3 (const Mat3< T > &m)
	Set upper left to a Mat3. More...

Mat3< T >	getMat3 () const

Vec3< T >	getTranslation () const
	Return the translation component. More...

void	setTranslation (const Vec3< T > &t)

template<typename Source >
const Mat4 &	operator= (const Mat4< Source > &m)
	Assignment operator. More...

bool	eq (const Mat4 &m, T eps=1.0e-8) const
	Return `true` if this matrix is equivalent to m within a tolerance of eps. More...

Mat4< T >	operator- () const
	Negation operator, for e.g. m1 = -m2;. More...

template<typename S >
const Mat4< T > &	operator*= (S scalar)
	Multiply each element of this matrix by scalar. More...

template<typename S >
const Mat4< T > &	operator+= (const Mat4< S > &m1)
	Add each element of the given matrix to the corresponding element of this matrix. More...

template<typename S >
const Mat4< T > &	operator-= (const Mat4< S > &m1)
	Subtract each element of the given matrix from the corresponding element of this matrix. More...

template<typename S >
const Mat4< T > &	operator*= (const Mat4< S > &m1)
	Multiply this matrix by the given matrix. More...

Mat4	transpose () const

Mat4	inverse (T tolerance=0) const

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

template<typename T0 >
void	setToTranslation (const Vec3< T0 > &v)
	Sets the matrix to a matrix that translates by v. More...

template<typename T0 >
void	preTranslate (const Vec3< T0 > &tr)
	Left multiples by the specified translation, i.e. Trans * (*this) More...

template<typename T0 >
void	postTranslate (const Vec3< T0 > &tr)
	Right multiplies by the specified translation matrix, i.e. (this) Trans. More...

template<typename T0 >
void	setToScale (const Vec3< T0 > &v)
	Sets the matrix to a matrix that scales by v. More...

template<typename T0 >
void	preScale (const Vec3< T0 > &v)

template<typename T0 >
void	postScale (const Vec3< T0 > &v)

void	setToRotation (Axis axis, T angle)
	Sets the matrix to a rotation about the given axis. More...

void	setToRotation (const Vec3< T > &axis, T angle)
	Sets the matrix to a rotation about an arbitrary axis. More...

void	setToRotation (const Vec3< T > &v1, const Vec3< T > &v2)
	Sets the matrix to a rotation that maps v1 onto v2 about the cross product of v1 and v2. More...

void	preRotate (Axis axis, T angle)
	Left multiplies by a rotation clock-wiseabout the given axis into this matrix. More...

void	postRotate (Axis axis, T angle)
	Right multiplies by a rotation clock-wiseabout the given axis into this matrix. More...

void	setToShear (Axis axis0, Axis axis1, T shearby)
	Sets the matrix to a shear along axis0 by a fraction of axis1. More...

void	preShear (Axis axis0, Axis axis1, T shear)
	Left multiplies a shearing transformation into the matrix. More...

void	postShear (Axis axis0, Axis axis1, T shear)
	Right multiplies a shearing transformation into the matrix. More...

template<typename T0 >
Vec4< T0 >	transform (const Vec4< T0 > &v) const
	Transform a Vec4 by post-multiplication. More...

template<typename T0 >
Vec3< T0 >	transform (const Vec3< T0 > &v) const
	Transform a Vec3 by post-multiplication, without homogenous division. More...

template<typename T0 >
Vec4< T0 >	pretransform (const Vec4< T0 > &v) const
	Transform a Vec4 by pre-multiplication. More...

template<typename T0 >
Vec3< T0 >	pretransform (const Vec3< T0 > &v) const
	Transform a Vec3 by pre-multiplication, without homogenous division. More...

template<typename T0 >
Vec3< T0 >	transformH (const Vec3< T0 > &p) const
	Transform a Vec3 by post-multiplication, doing homogenous divison. More...

template<typename T0 >
Vec3< T0 >	pretransformH (const Vec3< T0 > &p) const
	Transform a Vec3 by pre-multiplication, doing homogenous division. More...

template<typename T0 >
Vec3< T0 >	transform3x3 (const Vec3< T0 > &v) const
	Transform a Vec3 by post-multiplication, without translation. 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 Mat4< T > &	identity ()
	Predefined constant for identity matrix. More...

static const Mat4< T > &	zero ()
	Predefined constant for zero matrix. More...

static Mat4	translation (const Vec3d &v)
	Sets the matrix to a matrix that translates by v. 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 Mat4< T0 > &m0, const Mat4< T1 > &m1)
	Equality operator, does exact floating point comparisons. More...

template<typename T0 , typename T1 >
bool	operator!= (const Mat4< T0 > &m0, const Mat4< T1 > &m1)
	Inequality operator, does exact floating point comparisons. More...

template<typename S , typename T >
Mat4< typename promote< S, T >::type >	operator* (S scalar, const Mat4< T > &m)
	Multiply each element of the given matrix by scalar and return the result. More...

template<typename S , typename T >
Mat4< typename promote< S, T >::type >	operator* (const Mat4< T > &m, S scalar)
	Multiply each element of the given matrix by scalar and return the result. More...

template<typename T , typename MT >
Vec4< typename promote< T, MT >::type >	operator* (const Mat4< MT > &_m, const Vec4< T > &_v)
	Multiply _m by _v and return the resulting vector. More...

template<typename T , typename MT >
Vec4< typename promote< T, MT >::type >	operator* (const Vec4< T > &_v, const Mat4< MT > &_m)
	Multiply _v by _m and return the resulting vector. More...

template<typename T , typename MT >
Vec3< typename promote< T, MT >::type >	operator* (const Mat4< 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 Mat4< MT > &_m)
	Multiply _v by _m and return the resulting vector. More...

template<typename T0 , typename T1 >
Mat4< typename promote< T0, T1 >::type >	operator+ (const Mat4< T0 > &m0, const Mat4< T1 > &m1)
	Add corresponding elements of m0 and m1 and return the result. More...

template<typename T0 , typename T1 >
Mat4< typename promote< T0, T1 >::type >	operator- (const Mat4< T0 > &m0, const Mat4< T1 > &m1)
	Subtract corresponding elements of m0 and m1 and return the result. More...

template<typename T0 , typename T1 >
Mat4< typename promote< T0, T1 >::type >	operator* (const Mat4< T0 > &m0, const Mat4< T1 > &m1)
	Multiply m0 by m1 and return the resulting matrix. More...

Detailed Description

template<typename T>
class openvdb::v9_0::math::Mat4< T >

4x4 -matrix class.

Member Typedef Documentation

using MyBase = Mat<4, T>

using value_type = T

Data type held by the matrix.

using ValueType = T

Member Enumeration Documentation

enum SIZE_

inherited

Constructor & Destructor Documentation

Mat4 ( )

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)

Mat4 ( 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] a[9]  a[10] a[11]
a[12] a[13] a[14] a[15]

Mat4	(	Source	a,
		Source	b,
		Source	c,
		Source	d,
		Source	e,
		Source	f,
		Source	g,
		Source	h,
		Source	i,
		Source	j,
		Source	k,
		Source	l,
		Source	m,
		Source	n,
		Source	o,
		Source	p
	)

inline

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

a b c d
e f g h
i j k l
m n o p

Mat4	(	const Vec4< Source > &	v1,
		const Vec4< Source > &	v2,
		const Vec4< Source > &	v3,
		const Vec4< Source > &	v4,
		bool	rows = `true`
	)

inline

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

Mat4 ( const Mat4< Source > & m )

inlineexplicit

Conversion constructor.

Member Function Documentation

T absMax ( ) const

inlineinherited

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

T* asPointer ( )

inlineinherited

Direct access to the internal data.

const T* asPointer ( ) const

inlineinherited

Vec4<T> col ( int j ) const

inline

Get jth column, e.g. Vec4f v = m.col(0);.

T det ( ) const

inline

Determinant of matrix.

bool eq	(	const Mat4< T > &	m,
		T	eps = `1.0e-8`
	)		const

inline

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

Mat3<T> getMat3 ( ) const

inline

Vec3<T> getTranslation ( ) const

inline

Return the translation component.

static const Mat4<T>& identity ( )

inlinestatic

Predefined constant for identity matrix.

Mat4 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 Mat4<T>& operator*= ( S scalar )

inline

Multiply each element of this matrix by scalar.

const Mat4<T>& operator*= ( const Mat4< S > & m1 )

inline

Multiply this matrix by the given matrix.

const Mat4<T>& operator+= ( const Mat4< S > & m1 )

inline

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

Mat4<T> operator- ( ) const

inline

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

const Mat4<T>& operator-= ( const Mat4< S > & m1 )

inline

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

const Mat4& operator= ( const Mat4< 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.

void postRotate	(	Axis	axis,
		T	angle
	)

inline

Right multiplies by a rotation clock-wiseabout the given axis into this matrix.

Parameters

axis	The axis (one of X, Y, Z) of rotation.
angle	The clock-wise rotation angle, in radians.

void postScale ( const Vec3< T0 > & v )

inline

void postShear	(	Axis	axis0,
		Axis	axis1,
		T	shear
	)

inline

Right multiplies a shearing transformation into the matrix.

See also: setToShear

void postTranslate ( const Vec3< T0 > & tr )

inline

Right multiplies by the specified translation matrix, i.e. (*this) * Trans.

void preRotate	(	Axis	axis,
		T	angle
	)

inline

Left multiplies by a rotation clock-wiseabout the given axis into this matrix.

Parameters

axis	The axis (one of X, Y, Z) of rotation.
angle	The clock-wise rotation angle, in radians.

void preScale ( const Vec3< T0 > & v )

inline

void preShear	(	Axis	axis0,
		Axis	axis1,
		T	shear
	)

inline

Left multiplies a shearing transformation into the matrix.

See also: setToShear

Vec4<T0> pretransform ( const Vec4< T0 > & v ) const

inline

Transform a Vec4 by pre-multiplication.

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

inline

Transform a Vec3 by pre-multiplication, without homogenous division.

Vec3<T0> pretransformH ( const Vec3< T0 > & p ) const

inline

Transform a Vec3 by pre-multiplication, doing homogenous division.

void preTranslate ( const Vec3< T0 > & tr )

inline

Left multiples by the specified translation, i.e. Trans * (*this)

void read ( std::istream & is )

inlineinherited

Vec4<T> row ( int i ) const

inline

Get ith row, e.g. Vec4f v = m.row(1);.

void setCol	(	int	j,
		const Vec4< T > &	v
	)

inline

Set jth column to vector v.

void setColumns	(	const Vec4< T > &	v1,
		const Vec4< T > &	v2,
		const Vec4< T > &	v3,
		const Vec4< T > &	v4
	)

inline

Set the columns of this matrix to the vectors v1, v2, v3, v4.

void setIdentity ( )

inline

Set this matrix to identity.

void setMat3 ( const Mat3< T > & m )

inline

Set upper left to a Mat3.

void setRow	(	int	i,
		const Vec4< T > &	v
	)

inline

Set ith row to vector v.

void setRows	(	const Vec4< T > &	v1,
		const Vec4< T > &	v2,
		const Vec4< T > &	v3,
		const Vec4< T > &	v4
	)

inline

Set the rows of this matrix to the vectors v1, v2, v3, v4.

void setToRotation	(	Axis	axis,
		T	angle
	)

inline

Sets the matrix to a rotation about the given axis.

Parameters

axis	The axis (one of X, Y, Z) to rotate about.
angle	The rotation angle, in radians.

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

inline

Sets the matrix to a rotation about an arbitrary axis.

Parameters

axis	The axis of rotation (cannot be zero-length)
angle	The rotation angle, in radians.

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

inline

Sets the matrix to a rotation that maps v1 onto v2 about the cross product of v1 and v2.

void setToScale ( const Vec3< T0 > & v )

inline

Sets the matrix to a matrix that scales by v.

void setToShear	(	Axis	axis0,
		Axis	axis1,
		T	shearby
	)

inline

Sets the matrix to a shear along axis0 by a fraction of axis1.

Parameters

axis0	The fixed axis of the shear.
axis1	The shear axis.
shearby	The shear factor.

void setToTranslation ( const Vec3< T0 > & v )

inline

Sets the matrix to a matrix that translates by v.

void setTranslation ( const Vec3< T > & t )

inline

void setZero ( )

inline

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]]

Vec4<T0> transform ( const Vec4< T0 > & v ) const

inline

Transform a Vec4 by post-multiplication.

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

inline

Transform a Vec3 by post-multiplication, without homogenous division.

Vec3<T0> transform3x3 ( const Vec3< T0 > & v ) const

inline

Transform a Vec3 by post-multiplication, without translation.

Vec3<T0> transformH ( const Vec3< T0 > & p ) const

inline

Transform a Vec3 by post-multiplication, doing homogenous divison.

static Mat4 translation ( const Vec3d & v )

inlinestatic

Sets the matrix to a matrix that translates by v.

Mat4 transpose ( ) const

inline

Returns: transpose of this

void write ( std::ostream & os ) const

inlineinherited

static const Mat4<T>& zero ( )

inlinestatic

Predefined constant for zero matrix.

Friends And Related Function Documentation

bool operator!=	(	const Mat4< T0 > &	m0,
		const Mat4< T1 > &	m1
	)

Mat4< typename promote< S, T >::type > operator*	(	S	scalar,
		const Mat4< T > &	m
	)

Mat4< typename promote< S, T >::type > operator*	(	const Mat4< T > &	m,
		S	scalar
	)

Vec4< typename promote< T, MT >::type > operator*	(	const Mat4< MT > &	_m,
		const Vec4< T > &	_v
	)

Vec4< typename promote< T, MT >::type > operator*	(	const Vec4< T > &	_v,
		const Mat4< MT > &	_m
	)

Vec3< typename promote< T, MT >::type > operator*	(	const Mat4< MT > &	_m,
		const Vec3< T > &	_v
	)

Vec3< typename promote< T, MT >::type > operator*	(	const Vec3< T > &	_v,
		const Mat4< MT > &	_m
	)

Mat4< typename promote< T0, T1 >::type > operator*	(	const Mat4< T0 > &	m0,
		const Mat4< T1 > &	m1
	)

Mat4< typename promote< T0, T1 >::type > operator+	(	const Mat4< T0 > &	m0,
		const Mat4< T1 > &	m1
	)

Mat4< typename promote< T0, T1 >::type > operator-	(	const Mat4< T0 > &	m0,
		const Mat4< T1 > &	m1
	)

bool operator==	(	const Mat4< T0 > &	m0,
		const Mat4< 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::v9_0::math::Mat4< 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::v9_0::math::Mat4< T >