Stores a 3x3 matrix of double elements. More...

#include <matrix3d.h>

Public Types
typedef double	ScalarType

Public Member Functions
	GfMatrix3d ()=default
	Default constructor. Leaves the matrix component values undefined.

	GfMatrix3d (double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)
	Constructor.

	GfMatrix3d (const double m[3][3])
	Constructor.

	GfMatrix3d (double s)
	Constructor.

	GfMatrix3d (int s)
	This explicit constructor initializes the matrix to `s` times the identity matrix.

	GfMatrix3d (const GfVec3d &v)
	Constructor.

GF_API	GfMatrix3d (const std::vector< std::vector< double > > &v)
	Constructor.

GF_API	GfMatrix3d (const std::vector< std::vector< float > > &v)
	Constructor.

GF_API	GfMatrix3d (const GfRotation &rot)
	Constructor. Initialize matrix from rotation.

GF_API	GfMatrix3d (const GfQuatd &rot)
	Constructor. Initialize matrix from a quaternion.

GF_API	GfMatrix3d (const class GfMatrix3f &m)
	This explicit constructor converts a "float" matrix to a "double" matrix.

void	SetRow (int i, const GfVec3d &v)
	Sets a row of the matrix from a Vec3.

void	SetColumn (int i, const GfVec3d &v)
	Sets a column of the matrix from a Vec3.

GfVec3d	GetRow (int i) const
	Gets a row of the matrix as a Vec3.

GfVec3d	GetColumn (int i) const
	Gets a column of the matrix as a Vec3.

GfMatrix3d &	Set (double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)
	Sets the matrix from 9 independent `double` values, specified in row-major order.

GfMatrix3d &	Set (const double m[3][3])
	Sets the matrix from a 3x3 array of `double` values, specified in row-major order.

GfMatrix3d &	SetIdentity ()
	Sets the matrix to the identity matrix.

GfMatrix3d &	SetZero ()
	Sets the matrix to zero.

GF_API GfMatrix3d &	SetDiagonal (double s)
	Sets the matrix to s times the identity matrix.

GF_API GfMatrix3d &	SetDiagonal (const GfVec3d &)
	Sets the matrix to have diagonal (`v[0], v[1], v[2]`).

GF_API double *	Get (double m[3][3]) const
	Fills a 3x3 array of `double` values with the values in the matrix, specified in row-major order.

double *	data ()
	Returns raw access to components of matrix as an array of `double` values.

const double *	data () const
	Returns const raw access to components of matrix as an array of `double` values.

double *	GetArray ()
	Returns vector components as an array of `double` values.

const double *	GetArray () const
	Returns vector components as a const array of `double` values.

double *	operator[] (int i)
	Accesses an indexed row i of the matrix as an array of 3 `double` values so that standard indexing (such as `m[0][1]`) works correctly.

const double *	operator[] (int i) const
	Accesses an indexed row i of the matrix as an array of 3 `double` values so that standard indexing (such as `m[0][1]`) works correctly.

GF_API bool	operator== (const GfMatrix3d &m) const
	Tests for element-wise matrix equality.

GF_API bool	operator== (const GfMatrix3f &m) const
	Tests for element-wise matrix equality.

bool	operator!= (const GfMatrix3d &m) const
	Tests for element-wise matrix inequality.

bool	operator!= (const GfMatrix3f &m) const
	Tests for element-wise matrix inequality.

GF_API GfMatrix3d	GetTranspose () const
	Returns the transpose of the matrix.

GF_API GfMatrix3d	GetInverse (double *det=NULL, double eps=0) const
	Returns the inverse of the matrix, or FLT_MAX * SetIdentity() if the matrix is singular.

GF_API double	GetDeterminant () const
	Returns the determinant of the matrix.

GF_API bool	Orthonormalize (bool issueWarning=true)
	Makes the matrix orthonormal in place.

GF_API GfMatrix3d	GetOrthonormalized (bool issueWarning=true) const
	Returns an orthonormalized copy of the matrix.

GF_API double	GetHandedness () const
	Returns the sign of the determinant of the matrix, i.e.

bool	IsRightHanded () const
	Returns true if the vectors in the matrix form a right-handed coordinate system.

bool	IsLeftHanded () const
	Returns true if the vectors in matrix form a left-handed coordinate system.

GF_API GfMatrix3d &	operator*= (const GfMatrix3d &m)
	Post-multiplies matrix m into this matrix.

GF_API GfMatrix3d &	operator*= (double)
	Multiplies the matrix by a double.

GF_API GfMatrix3d &	operator+= (const GfMatrix3d &m)
	Adds matrix m to this matrix.

GF_API GfMatrix3d &	operator-= (const GfMatrix3d &m)
	Subtracts matrix m from this matrix.

GF_API GfMatrix3d &	SetScale (double scaleFactor)
	Sets matrix to specify a uniform scaling by scaleFactor.

3D Transformation Utilities
GF_API GfMatrix3d &	SetRotate (const GfQuatd &rot)
	Sets the matrix to specify a rotation equivalent to rot.

GF_API GfMatrix3d &	SetRotate (const GfRotation &rot)
	Sets the matrix to specify a rotation equivalent to rot.

GF_API GfMatrix3d &	SetScale (const GfVec3d &scaleFactors)
	Sets the matrix to specify a nonuniform scaling in x, y, and z by the factors in vector scaleFactors.

GF_API GfRotation	ExtractRotation () const
	Returns the rotation corresponding to this matrix.

GF_API GfVec3d	DecomposeRotation (const GfVec3d &axis0, const GfVec3d &axis1, const GfVec3d &axis2) const
	Decompose the rotation corresponding to this matrix about 3 orthogonal axes.

GF_API GfQuaternion	ExtractRotationQuaternion () const
	Returns the quaternion corresponding to this matrix.

Static Public Attributes
static const size_t	numRows = 3

static const size_t	numColumns = 3

Friends
class	GfMatrix3f

size_t	hash_value (GfMatrix3d const &m)
	Hash.

GfMatrix3d	operator* (const GfMatrix3d &m1, double d)
	Returns the product of a matrix and a double.

GfMatrix3d	operator* (double d, const GfMatrix3d &m)

GF_API friend GfMatrix3d	operator- (const GfMatrix3d &m)
	Returns the unary negation of matrix m.

GfMatrix3d	operator+ (const GfMatrix3d &m1, const GfMatrix3d &m2)
	Adds matrix m2 to m1.

GfMatrix3d	operator- (const GfMatrix3d &m1, const GfMatrix3d &m2)
	Subtracts matrix m2 from m1.

GfMatrix3d	operator* (const GfMatrix3d &m1, const GfMatrix3d &m2)
	Multiplies matrix m1 by m2.

GfMatrix3d	operator/ (const GfMatrix3d &m1, const GfMatrix3d &m2)
	Divides matrix m1 by m2 (that is, `m1 * inv(m2)`).

GfVec3d	operator* (const GfMatrix3d &m, const GfVec3d &vec)
	Returns the product of a matrix m and a column vector vec.

GfVec3d	operator* (const GfVec3d &vec, const GfMatrix3d &m)
	Returns the product of row vector vec and a matrix m.

Detailed Description

Stores a 3x3 matrix of double elements.

A basic type.

Matrices are defined to be in row-major order, so matrix[i][j] indexes the element in the i th row and the j th column.

3D Transformations

Three methods, SetRotate(), SetScale(), and ExtractRotation(), interpret a GfMatrix3d as a 3D transformation. By convention, vectors are treated primarily as row vectors, implying the following:

Transformation matrices are organized to deal with row vectors, not column vectors.
Each of the Set() methods in this class completely rewrites the matrix; for example, SetRotate() yields a matrix which does nothing but rotate.
When multiplying two transformation matrices, the matrix on the left applies a more local transformation to a row vector. For example, if R represents a rotation matrix and S represents a scale matrix, the product R*S will rotate a row vector, then scale it.

Definition at line 64 of file matrix3d.h.

Member Typedef Documentation

◆ ScalarType

typedef double ScalarType

Definition at line 67 of file matrix3d.h.

Constructor & Destructor Documentation

◆ GfMatrix3d() [1/11]

GfMatrix3d ( )

default

Default constructor. Leaves the matrix component values undefined.

◆ GfMatrix3d() [2/11]

GfMatrix3d	(	double	m00,
		double	m01,
		double	m02,
		double	m10,
		double	m11,
		double	m12,
		double	m20,
		double	m21,
		double	m22
	)

inline

Constructor.

Initializes the matrix from 9 independent double values, specified in row-major order. For example, parameter m10 specifies the value in row 1 and column 0.

Definition at line 78 of file matrix3d.h.

◆ GfMatrix3d() [3/11]

GfMatrix3d ( const double m[3][3] )

inline

Constructor.

Initializes the matrix from a 3x3 array of double values, specified in row-major order.

Definition at line 88 of file matrix3d.h.

◆ GfMatrix3d() [4/11]

GfMatrix3d ( double s )

inlineexplicit

Constructor.

Explicitly initializes the matrix to s times the identity matrix.

Definition at line 94 of file matrix3d.h.

◆ GfMatrix3d() [5/11]

GfMatrix3d ( int s )

inlineexplicit

This explicit constructor initializes the matrix to s times the identity matrix.

Definition at line 100 of file matrix3d.h.

◆ GfMatrix3d() [6/11]

GfMatrix3d ( const GfVec3d & v )

inlineexplicit

Constructor.

Explicitly initializes the matrix to diagonal form, with the i th element on the diagonal set to v[i].

Definition at line 106 of file matrix3d.h.

◆ GfMatrix3d() [7/11]

GF_API GfMatrix3d ( const std::vector< std::vector< double > > & v )

explicit

Constructor.

Initialize the matrix from a vector of vectors of double. The vector is expected to be 3x3. If it is too big, only the first 3 rows and/or columns will be used. If it is too small, uninitialized elements will be filled in with the corresponding elements from an identity matrix.

◆ GfMatrix3d() [8/11]

GF_API GfMatrix3d ( const std::vector< std::vector< float > > & v )

explicit

Constructor.

Initialize the matrix from a vector of vectors of float. The vector is expected to be 3x3. If it is too big, only the first 3 rows and/or columns will be used. If it is too small, uninitialized elements will be filled in with the corresponding elements from an identity matrix.

◆ GfMatrix3d() [9/11]

GF_API GfMatrix3d ( const GfRotation & rot )

Constructor. Initialize matrix from rotation.

◆ GfMatrix3d() [10/11]

GF_API GfMatrix3d ( const GfQuatd & rot )

explicit

Constructor. Initialize matrix from a quaternion.

◆ GfMatrix3d() [11/11]

GF_API GfMatrix3d ( const class GfMatrix3f & m )

explicit

This explicit constructor converts a "float" matrix to a "double" matrix.

Member Function Documentation

◆ data() [1/2]

double * data ( )

inline

Returns raw access to components of matrix as an array of double values.

Components are in row-major order.

Definition at line 216 of file matrix3d.h.

◆ data() [2/2]

const double * data ( ) const

inline

Returns const raw access to components of matrix as an array of double values.

Components are in row-major order.

Definition at line 222 of file matrix3d.h.

◆ DecomposeRotation()

GF_API GfVec3d DecomposeRotation	(	const GfVec3d &	axis0,
		const GfVec3d &	axis1,
		const GfVec3d &	axis2
	)		const

Decompose the rotation corresponding to this matrix about 3 orthogonal axes.

If the axes are not orthogonal, warnings will be spewed.

This is a convenience method that is equivalent to calling ExtractRotation().Decompose().

◆ ExtractRotation()

GF_API GfRotation ExtractRotation ( ) const

Returns the rotation corresponding to this matrix.

This works well only if the matrix represents a rotation.

For good results, consider calling Orthonormalize() before calling this method.

◆ ExtractRotationQuaternion()

GF_API GfQuaternion ExtractRotationQuaternion ( ) const

Returns the quaternion corresponding to this matrix.

This works well only if the matrix represents a rotation.

For good results, consider calling Orthonormalize() before calling this method.

◆ Get()

GF_API double * Get ( double m[3][3] ) const

Fills a 3x3 array of double values with the values in the matrix, specified in row-major order.

◆ GetArray() [1/2]

double * GetArray ( )

inline

Returns vector components as an array of double values.

Definition at line 227 of file matrix3d.h.

◆ GetArray() [2/2]

const double * GetArray ( ) const

inline

Returns vector components as a const array of double values.

Definition at line 232 of file matrix3d.h.

◆ GetColumn()

GfVec3d GetColumn ( int i ) const

inline

Gets a column of the matrix as a Vec3.

Definition at line 160 of file matrix3d.h.

◆ GetDeterminant()

GF_API double GetDeterminant ( ) const

Returns the determinant of the matrix.

◆ GetHandedness()

GF_API double GetHandedness ( ) const

Returns the sign of the determinant of the matrix, i.e.

1 for a right-handed matrix, -1 for a left-handed matrix, and 0 for a singular matrix.

◆ GetInverse()

GF_API GfMatrix3d GetInverse	(	double *	det = `NULL`,
		double	eps = `0`
	)		const

Returns the inverse of the matrix, or FLT_MAX * SetIdentity() if the matrix is singular.

(FLT_MAX is the largest value a float can have, as defined by the system.) The matrix is considered singular if the determinant is less than or equal to the optional parameter eps. If det is non-null, *det is set to the determinant.

◆ GetOrthonormalized()

GF_API GfMatrix3d GetOrthonormalized ( bool issueWarning = true ) const

Returns an orthonormalized copy of the matrix.

◆ GetRow()

GfVec3d GetRow ( int i ) const

inline

Gets a row of the matrix as a Vec3.

Definition at line 155 of file matrix3d.h.

◆ GetTranspose()

GF_API GfMatrix3d GetTranspose ( ) const

Returns the transpose of the matrix.

◆ IsLeftHanded()

bool IsLeftHanded ( ) const

inline

Returns true if the vectors in matrix form a left-handed coordinate system.

Definition at line 328 of file matrix3d.h.

◆ IsRightHanded()

bool IsRightHanded ( ) const

inline

Returns true if the vectors in the matrix form a right-handed coordinate system.

Definition at line 322 of file matrix3d.h.

◆ operator!=() [1/2]

bool operator!= ( const GfMatrix3d & m ) const

inline

Tests for element-wise matrix inequality.

All elements must match exactly for matrices to be considered equal.

Definition at line 273 of file matrix3d.h.

◆ operator!=() [2/2]

bool operator!= ( const GfMatrix3f & m ) const

inline

Tests for element-wise matrix inequality.

All elements must match exactly for matrices to be considered equal.

Definition at line 279 of file matrix3d.h.

◆ operator*=() [1/2]

GF_API GfMatrix3d & operator*= ( const GfMatrix3d & m )

Post-multiplies matrix m into this matrix.

◆ operator*=() [2/2]

GF_API GfMatrix3d & operator*= ( double )

Multiplies the matrix by a double.

◆ operator+=()

GF_API GfMatrix3d & operator+= ( const GfMatrix3d & m )

Adds matrix m to this matrix.

◆ operator-=()

GF_API GfMatrix3d & operator-= ( const GfMatrix3d & m )

Subtracts matrix m from this matrix.

◆ operator==() [1/2]

GF_API bool operator== ( const GfMatrix3d & m ) const

Tests for element-wise matrix equality.

All elements must match exactly for matrices to be considered equal.

◆ operator==() [2/2]

GF_API bool operator== ( const GfMatrix3f & m ) const

Tests for element-wise matrix equality.

All elements must match exactly for matrices to be considered equal.

◆ operator[]() [1/2]

double * operator[] ( int i )

inline

Accesses an indexed row i of the matrix as an array of 3 double values so that standard indexing (such as m[0][1]) works correctly.

Definition at line 239 of file matrix3d.h.

◆ operator[]() [2/2]

const double * operator[] ( int i ) const

inline

Accesses an indexed row i of the matrix as an array of 3 double values so that standard indexing (such as m[0][1]) works correctly.

Definition at line 244 of file matrix3d.h.

◆ Orthonormalize()

GF_API bool Orthonormalize ( bool issueWarning = true )

Makes the matrix orthonormal in place.

This is an iterative method that is much more stable than the previous cross/cross method. If the iterative method does not converge, a warning is issued.

Returns true if the iteration converged, false otherwise. Leaves any translation part of the matrix unchanged. If issueWarning is true, this method will issue a warning if the iteration does not converge, otherwise it will be silent.

◆ Set() [1/2]

GfMatrix3d & Set ( const double m[3][3] )

inline

Sets the matrix from a 3x3 array of double values, specified in row-major order.

Definition at line 178 of file matrix3d.h.

◆ Set() [2/2]

GfMatrix3d & Set	(	double	m00,
		double	m01,
		double	m02,
		double	m10,
		double	m11,
		double	m12,
		double	m20,
		double	m21,
		double	m22
	)

inline

Sets the matrix from 9 independent double values, specified in row-major order.

For example, parameter m10 specifies the value in row 1 and column 0.

Definition at line 167 of file matrix3d.h.

◆ SetColumn()

void SetColumn	(	int	i,
		const GfVec3d &	v
	)

inline

Sets a column of the matrix from a Vec3.

Definition at line 148 of file matrix3d.h.

◆ SetDiagonal() [1/2]

GF_API GfMatrix3d & SetDiagonal ( const GfVec3d & )

Sets the matrix to have diagonal (v[0], v[1], v[2]).

◆ SetDiagonal() [2/2]

GF_API GfMatrix3d & SetDiagonal ( double s )

Sets the matrix to s times the identity matrix.

◆ SetIdentity()

GfMatrix3d & SetIdentity ( )

inline

Sets the matrix to the identity matrix.

Definition at line 192 of file matrix3d.h.

◆ SetRotate() [1/2]

GF_API GfMatrix3d & SetRotate ( const GfQuatd & rot )

Sets the matrix to specify a rotation equivalent to rot.

◆ SetRotate() [2/2]

GF_API GfMatrix3d & SetRotate ( const GfRotation & rot )

Sets the matrix to specify a rotation equivalent to rot.

◆ SetRow()

void SetRow	(	int	i,
		const GfVec3d &	v
	)

inline

Sets a row of the matrix from a Vec3.

Definition at line 141 of file matrix3d.h.

◆ SetScale() [1/2]

GF_API GfMatrix3d & SetScale ( const GfVec3d & scaleFactors )

Sets the matrix to specify a nonuniform scaling in x, y, and z by the factors in vector scaleFactors.

◆ SetScale() [2/2]

GF_API GfMatrix3d & SetScale ( double scaleFactor )

Sets matrix to specify a uniform scaling by scaleFactor.

◆ SetZero()

GfMatrix3d & SetZero ( )

inline

Sets the matrix to zero.

Definition at line 197 of file matrix3d.h.

Friends And Related Function Documentation

◆ GfMatrix3f

friend class GfMatrix3f

friend

Definition at line 470 of file matrix3d.h.

◆ hash_value

size_t hash_value ( GfMatrix3d const & m )

friend

Hash.

Definition at line 247 of file matrix3d.h.

◆ operator* [1/5]

GfVec3d operator*	(	const GfMatrix3d &	m,
		const GfVec3d &	vec
	)

friend

Returns the product of a matrix m and a column vector vec.

Definition at line 397 of file matrix3d.h.

◆ operator* [2/5]

GfMatrix3d operator*	(	const GfMatrix3d &	m1,
		const GfMatrix3d &	m2
	)

friend

Multiplies matrix m1 by m2.

Definition at line 383 of file matrix3d.h.

◆ operator* [3/5]

GfMatrix3d operator*	(	const GfMatrix3d &	m1,
		double	d
	)

friend

Returns the product of a matrix and a double.

Definition at line 341 of file matrix3d.h.

◆ operator* [4/5]

GfVec3d operator*	(	const GfVec3d &	vec,
		const GfMatrix3d &	m
	)

friend

Returns the product of row vector vec and a matrix m.

Definition at line 404 of file matrix3d.h.

◆ operator* [5/5]

GfMatrix3d operator*	(	double	d,
		const GfMatrix3d &	m
	)

friend

Definition at line 349 of file matrix3d.h.

◆ operator+

GfMatrix3d operator+	(	const GfMatrix3d &	m1,
		const GfMatrix3d &	m2
	)

friend

Adds matrix m2 to m1.

Definition at line 367 of file matrix3d.h.

◆ operator- [1/2]

GF_API friend GfMatrix3d operator- ( const GfMatrix3d & m )

friend

Returns the unary negation of matrix m.

◆ operator- [2/2]

GfMatrix3d operator-	(	const GfMatrix3d &	m1,
		const GfMatrix3d &	m2
	)

friend

Subtracts matrix m2 from m1.

Definition at line 375 of file matrix3d.h.

◆ operator/

GfMatrix3d operator/	(	const GfMatrix3d &	m1,
		const GfMatrix3d &	m2
	)

friend

Divides matrix m1 by m2 (that is, m1 * inv(m2)).

Definition at line 391 of file matrix3d.h.

Member Data Documentation

◆ numColumns

const size_t numColumns = 3

static

Definition at line 70 of file matrix3d.h.

◆ numRows

const size_t numRows = 3

static

Definition at line 69 of file matrix3d.h.

The documentation for this class was generated from the following file:

pxr/base/gf/matrix3d.h

Public Types

Public Member Functions

Static Public Attributes

Friends

Detailed Description

3D Transformations

Member Typedef Documentation

◆ ScalarType

Constructor & Destructor Documentation

◆ GfMatrix3d() [1/11]

◆ GfMatrix3d() [2/11]

◆ GfMatrix3d() [3/11]

◆ GfMatrix3d() [4/11]

◆ GfMatrix3d() [5/11]

◆ GfMatrix3d() [6/11]

◆ GfMatrix3d() [7/11]

◆ GfMatrix3d() [8/11]

◆ GfMatrix3d() [9/11]

◆ GfMatrix3d() [10/11]

◆ GfMatrix3d() [11/11]

Member Function Documentation

◆ data() [1/2]

◆ data() [2/2]

◆ DecomposeRotation()

◆ ExtractRotation()

◆ ExtractRotationQuaternion()

◆ Get()

◆ GetArray() [1/2]

◆ GetArray() [2/2]

◆ GetColumn()

◆ GetDeterminant()

◆ GetHandedness()

◆ GetInverse()

◆ GetOrthonormalized()

◆ GetRow()

◆ GetTranspose()

◆ IsLeftHanded()

◆ IsRightHanded()

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+=()

◆ operator-=()

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ Orthonormalize()

◆ Set() [1/2]

◆ Set() [2/2]

◆ SetColumn()

◆ SetDiagonal() [1/2]

◆ SetDiagonal() [2/2]

◆ SetIdentity()

◆ SetRotate() [1/2]

◆ SetRotate() [2/2]

◆ SetRow()

◆ SetScale() [1/2]

◆ SetScale() [2/2]

◆ SetZero()

Friends And Related Function Documentation

◆ GfMatrix3f

◆ hash_value

◆ operator* [1/5]

◆ operator* [2/5]

◆ operator* [3/5]

◆ operator* [4/5]

◆ operator* [5/5]

◆ operator+

◆ operator- [1/2]

◆ operator- [2/2]

◆ operator/

Member Data Documentation

◆ numColumns

◆ numRows