The btMatrix3x3 class implements a 3x3 rotation matrix, to perform linear algebra in combination with btQuaternion, btTransform and btVector3. More...

#include <btMatrix3x3.h>

Collaboration diagram for btMatrix3x3:

[legend]

Public Member Functions
	btMatrix3x3 ()
	No initializaion constructor. More...

	btMatrix3x3 (const btQuaternion &q)
	Constructor from Quaternion. More...

	btMatrix3x3 (const btScalar &xx, const btScalar &xy, const btScalar &xz, const btScalar &yx, const btScalar &yy, const btScalar &yz, const btScalar &zx, const btScalar &zy, const btScalar &zz)
	Constructor with row major formatting. More...

	btMatrix3x3 (const btMatrix3x3 &other)
	Copy constructor. More...

btMatrix3x3 &	operator= (const btMatrix3x3 &other)
	Assignment Operator. More...

	btMatrix3x3 (const btVector3 &v0, const btVector3 &v1, const btVector3 &v2)

btVector3	getColumn (int i) const
	Get a column of the matrix as a vector. More...

const btVector3 &	getRow (int i) const
	Get a row of the matrix as a vector. More...

btVector3 &	operator[] (int i)
	Get a mutable reference to a row of the matrix as a vector. More...

const btVector3 &	operator[] (int i) const
	Get a const reference to a row of the matrix as a vector. More...

btMatrix3x3 &	operator*= (const btMatrix3x3 &m)
	Multiply by the target matrix on the right. More...

btMatrix3x3 &	operator+= (const btMatrix3x3 &m)
	Adds by the target matrix on the right. More...

btMatrix3x3 &	operator-= (const btMatrix3x3 &m)
	Substractss by the target matrix on the right. More...

void	setFromOpenGLSubMatrix (const btScalar *m)
	Set from the rotational part of a 4x4 OpenGL matrix. More...

void	setValue (const btScalar &xx, const btScalar &xy, const btScalar &xz, const btScalar &yx, const btScalar &yy, const btScalar &yz, const btScalar &zx, const btScalar &zy, const btScalar &zz)
	Set the values of the matrix explicitly (row major) More...

void	setRotation (const btQuaternion &q)
	Set the matrix from a quaternion. More...

void	setEulerYPR (const btScalar &yaw, const btScalar &pitch, const btScalar &roll)
	Set the matrix from euler angles using YPR around YXZ respectively. More...

void	setEulerZYX (btScalar eulerX, btScalar eulerY, btScalar eulerZ)
	Set the matrix from euler angles YPR around ZYX axes. More...

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

void	setZero ()
	Set the matrix to the identity. More...

void	getOpenGLSubMatrix (btScalar *m) const
	Fill the rotational part of an OpenGL matrix and clear the shear/perspective. More...

void	getRotation (btQuaternion &q) const
	Get the matrix represented as a quaternion. More...

void	getEulerYPR (btScalar &yaw, btScalar &pitch, btScalar &roll) const
	Get the matrix represented as euler angles around YXZ, roundtrip with setEulerYPR. More...

void	getEulerZYX (btScalar &yaw, btScalar &pitch, btScalar &roll, unsigned int solution_number=1) const
	Get the matrix represented as euler angles around ZYX. More...

btMatrix3x3	scaled (const btVector3 &s) const
	Create a scaled copy of the matrix. More...

btScalar	determinant () const
	Return the determinant of the matrix. More...

btMatrix3x3	adjoint () const
	Return the adjoint of the matrix. More...

btMatrix3x3	absolute () const
	Return the matrix with all values non negative. More...

btMatrix3x3	transpose () const
	Return the transpose of the matrix. More...

btMatrix3x3	inverse () const
	Return the inverse of the matrix. More...

btVector3	solve33 (const btVector3 &b) const
	Solve A * x = b, where b is a column vector. More...

btMatrix3x3	transposeTimes (const btMatrix3x3 &m) const

btMatrix3x3	timesTranspose (const btMatrix3x3 &m) const

btScalar	tdotx (const btVector3 &v) const

btScalar	tdoty (const btVector3 &v) const

btScalar	tdotz (const btVector3 &v) const

void	extractRotation (btQuaternion &q, btScalar tolerance=1.0e-9, int maxIter=100)
	extractRotation is from "A robust method to extract the rotational part of deformations" See http://dl.acm.org/citation.cfm?doid=2994258.2994269 decomposes a matrix A in a orthogonal matrix R and a symmetric matrix S: A = R*S. More...

void	diagonalize (btMatrix3x3 &rot, btScalar threshold, int maxSteps)
	diagonalizes this matrix by the Jacobi method. More...

btScalar	cofac (int r1, int c1, int r2, int c2) const
	Calculate the matrix cofactor. More...

void	serialize (struct btMatrix3x3Data &dataOut) const

void	serializeFloat (struct btMatrix3x3FloatData &dataOut) const

void	deSerialize (const struct btMatrix3x3Data &dataIn)

void	deSerializeFloat (const struct btMatrix3x3FloatData &dataIn)

void	deSerializeDouble (const struct btMatrix3x3DoubleData &dataIn)

Static Public Member Functions
static const btMatrix3x3 &	getIdentity ()

Private Attributes
btVector3	m_el [3]
	Data storage for the matrix, each vector is a row of the matrix. More...

Detailed Description

The btMatrix3x3 class implements a 3x3 rotation matrix, to perform linear algebra in combination with btQuaternion, btTransform and btVector3.

Make sure to only include a pure orthogonal matrix without scaling.

Definition at line 48 of file btMatrix3x3.h.

Constructor & Destructor Documentation

◆ btMatrix3x3() [1/5]

btMatrix3x3::btMatrix3x3 ( )

inline

No initializaion constructor.

Definition at line 56 of file btMatrix3x3.h.

◆ btMatrix3x3() [2/5]

btMatrix3x3::btMatrix3x3 ( const btQuaternion & q )

inlineexplicit

Constructor from Quaternion.

Definition at line 61 of file btMatrix3x3.h.

◆ btMatrix3x3() [3/5]

btMatrix3x3::btMatrix3x3	(	const btScalar &	xx,
		const btScalar &	xy,
		const btScalar &	xz,
		const btScalar &	yx,
		const btScalar &	yy,
		const btScalar &	yz,
		const btScalar &	zx,
		const btScalar &	zy,
		const btScalar &	zz
	)

inline

Constructor with row major formatting.

Definition at line 70 of file btMatrix3x3.h.

◆ btMatrix3x3() [4/5]

btMatrix3x3::btMatrix3x3 ( const btMatrix3x3 & other )

inline

Copy constructor.

Definition at line 115 of file btMatrix3x3.h.

◆ btMatrix3x3() [5/5]

btMatrix3x3::btMatrix3x3	(	const btVector3 &	v0,
		const btVector3 &	v1,
		const btVector3 &	v2
	)

inline

Definition at line 131 of file btMatrix3x3.h.

Member Function Documentation

◆ absolute()

btMatrix3x3 btMatrix3x3::absolute ( ) const

inline

Return the matrix with all values non negative.

Definition at line 1028 of file btMatrix3x3.h.

◆ adjoint()

btMatrix3x3 btMatrix3x3::adjoint ( ) const

inline

Return the adjoint of the matrix.

Definition at line 1085 of file btMatrix3x3.h.

◆ cofac()

btScalar btMatrix3x3::cofac	(	int	r1,
		int	c1,
		int	r2,
		int	c2
	)		const

inline

Calculate the matrix cofactor.

Parameters

r1	The first row to use for calculating the cofactor
c1	The first column to use for calculating the cofactor
r1	The second row to use for calculating the cofactor
c1	The second column to use for calculating the cofactor See http://en.wikipedia.org/wiki/Cofactor_(linear_algebra) for more details

Definition at line 801 of file btMatrix3x3.h.

◆ deSerialize()

void btMatrix3x3::deSerialize ( const struct btMatrix3x3Data & dataIn )

inline

Definition at line 1413 of file btMatrix3x3.h.

◆ deSerializeDouble()

void btMatrix3x3::deSerializeDouble ( const struct btMatrix3x3DoubleData & dataIn )

inline

Definition at line 1425 of file btMatrix3x3.h.

◆ deSerializeFloat()

void btMatrix3x3::deSerializeFloat ( const struct btMatrix3x3FloatData & dataIn )

inline

Definition at line 1419 of file btMatrix3x3.h.

◆ determinant()

btScalar btMatrix3x3::determinant ( ) const

inline

Return the determinant of the matrix.

Definition at line 1022 of file btMatrix3x3.h.

◆ diagonalize()

void btMatrix3x3::diagonalize	(	btMatrix3x3 &	rot,
		btScalar	threshold,
		int	maxSteps
	)

inline

diagonalizes this matrix by the Jacobi method.

Parameters

rot	stores the rotation from the coordinate system in which the matrix is diagonal to the original coordinate system, i.e., old_this = rot * new_this * rot^T.
threshold	See iteration
iteration	The iteration stops when all off-diagonal elements are less than the threshold multiplied by the sum of the absolute values of the diagonal, or when maxSteps have been executed.

Note that this matrix is assumed to be symmetric.

Definition at line 716 of file btMatrix3x3.h.

◆ extractRotation()

void btMatrix3x3::extractRotation	(	btQuaternion &	q,
		btScalar	tolerance = `1.0e-9`,
		int	maxIter = `100`
	)

inline

extractRotation is from "A robust method to extract the rotational part of deformations" See http://dl.acm.org/citation.cfm?doid=2994258.2994269 decomposes a matrix A in a orthogonal matrix R and a symmetric matrix S: A = R*S.

note that R can include both rotation and scaling.

Definition at line 688 of file btMatrix3x3.h.

◆ getColumn()

btVector3 btMatrix3x3::getColumn ( int i ) const

inline

Get a column of the matrix as a vector.

Parameters

i	Column number 0 indexed

Definition at line 142 of file btMatrix3x3.h.

◆ getEulerYPR()

void btMatrix3x3::getEulerYPR	(	btScalar &	yaw,
		btScalar &	pitch,
		btScalar &	roll
	)		const

inline

Get the matrix represented as euler angles around YXZ, roundtrip with setEulerYPR.

Parameters

yaw	Yaw around Y axis
pitch	Pitch around X axis
roll	around Z axis

Definition at line 526 of file btMatrix3x3.h.

◆ getEulerZYX()

void btMatrix3x3::getEulerZYX	(	btScalar &	yaw,
		btScalar &	pitch,
		btScalar &	roll,
		unsigned int	solution_number = `1`
	)		const

inline

Get the matrix represented as euler angles around ZYX.

Parameters

yaw	Yaw around Z axis
pitch	Pitch around Y axis
roll	around X axis
solution_number	Which solution of two possible solutions ( 1 or 2) are possible values

Definition at line 553 of file btMatrix3x3.h.

◆ getIdentity()

static const btMatrix3x3 & btMatrix3x3::getIdentity ( )

inlinestatic

Definition at line 350 of file btMatrix3x3.h.

◆ getOpenGLSubMatrix()

void btMatrix3x3::getOpenGLSubMatrix ( btScalar * m ) const

inline

Fill the rotational part of an OpenGL matrix and clear the shear/perspective.

Parameters

m	The array to be filled

Definition at line 367 of file btMatrix3x3.h.

◆ getRotation()

void btMatrix3x3::getRotation ( btQuaternion & q ) const

inline

Get the matrix represented as a quaternion.

Parameters

q	The quaternion which will be set

Definition at line 420 of file btMatrix3x3.h.

◆ getRow()

const btVector3 & btMatrix3x3::getRow ( int i ) const

inline

Get a row of the matrix as a vector.

Parameters

i	Row number 0 indexed

Definition at line 149 of file btMatrix3x3.h.

◆ inverse()

btMatrix3x3 btMatrix3x3::inverse ( ) const

inline

Return the inverse of the matrix.

Definition at line 1093 of file btMatrix3x3.h.

◆ operator*=()

btMatrix3x3 & btMatrix3x3::operator*= ( const btMatrix3x3 & m )

inline

Multiply by the target matrix on the right.

Parameters

m	Rotation matrix to be applied Equivilant to this = this * m

Definition at line 818 of file btMatrix3x3.h.

◆ operator+=()

btMatrix3x3 & btMatrix3x3::operator+= ( const btMatrix3x3 & m )

inline

Adds by the target matrix on the right.

Parameters

m	matrix to be applied Equivilant to this = this + m

Definition at line 908 of file btMatrix3x3.h.

◆ operator-=()

btMatrix3x3 & btMatrix3x3::operator-= ( const btMatrix3x3 & m )

inline

Substractss by the target matrix on the right.

Parameters

m	matrix to be applied Equivilant to this = this - m

Definition at line 1000 of file btMatrix3x3.h.

◆ operator=()

btMatrix3x3 & btMatrix3x3::operator= ( const btMatrix3x3 & other )

inline

Assignment Operator.

Definition at line 123 of file btMatrix3x3.h.

◆ operator[]() [1/2]

btVector3 & btMatrix3x3::operator[] ( int i )

inline

Get a mutable reference to a row of the matrix as a vector.

Parameters

i	Row number 0 indexed

Definition at line 157 of file btMatrix3x3.h.

◆ operator[]() [2/2]

const btVector3 & btMatrix3x3::operator[] ( int i ) const

inline

Get a const reference to a row of the matrix as a vector.

Parameters

i	Row number 0 indexed

Definition at line 165 of file btMatrix3x3.h.

◆ scaled()

btMatrix3x3 btMatrix3x3::scaled ( const btVector3 & s ) const

inline

Create a scaled copy of the matrix.

Parameters

s	Scaling vector The elements of the vector will scale each column

Definition at line 622 of file btMatrix3x3.h.

◆ serialize()

void btMatrix3x3::serialize ( struct btMatrix3x3Data & dataOut ) const

inline

Definition at line 1401 of file btMatrix3x3.h.

◆ serializeFloat()

void btMatrix3x3::serializeFloat ( struct btMatrix3x3FloatData & dataOut ) const

inline

Definition at line 1407 of file btMatrix3x3.h.

◆ setEulerYPR()

void btMatrix3x3::setEulerYPR	(	const btScalar &	yaw,
		const btScalar &	pitch,
		const btScalar &	roll
	)

inline

Set the matrix from euler angles using YPR around YXZ respectively.

Parameters

yaw	Yaw about Y axis
pitch	Pitch about X axis
roll	Roll about Z axis

Definition at line 289 of file btMatrix3x3.h.

◆ setEulerZYX()

void btMatrix3x3::setEulerZYX	(	btScalar	eulerX,
		btScalar	eulerY,
		btScalar	eulerZ
	)

inline

Set the matrix from euler angles YPR around ZYX axes.

Parameters

eulerX	Roll about X axis
eulerY	Pitch around Y axis
eulerZ	Yaw about Z axis

These angles are used to produce a rotation matrix. The euler angles are applied in ZYX order. I.e a vector is first rotated about X then Y and then Z

Definition at line 303 of file btMatrix3x3.h.

◆ setFromOpenGLSubMatrix()

void btMatrix3x3::setFromOpenGLSubMatrix ( const btScalar * m )

inline

Set from the rotational part of a 4x4 OpenGL matrix.

Parameters

m	A pointer to the beginning of the array of scalars

Definition at line 188 of file btMatrix3x3.h.

◆ setIdentity()

void btMatrix3x3::setIdentity ( )

inline

Set the matrix to the identity.

Definition at line 323 of file btMatrix3x3.h.

◆ setRotation()

void btMatrix3x3::setRotation ( const btQuaternion & q )

inline

Set the matrix from a quaternion.

Parameters

q	The Quaternion to match

Definition at line 215 of file btMatrix3x3.h.

◆ setValue()

void btMatrix3x3::setValue	(	const btScalar &	xx,
		const btScalar &	xy,
		const btScalar &	xz,
		const btScalar &	yx,
		const btScalar &	yy,
		const btScalar &	yz,
		const btScalar &	zx,
		const btScalar &	zy,
		const btScalar &	zz
	)

inline

Set the values of the matrix explicitly (row major)

Parameters

xx	Top left
xy	Top Middle
xz	Top Right
yx	Middle Left
yy	Middle Middle
yz	Middle Right
zx	Bottom Left
zy	Bottom Middle
zz	Bottom Right

Definition at line 204 of file btMatrix3x3.h.

◆ setZero()

void btMatrix3x3::setZero ( )

inline

Set the matrix to the identity.

Definition at line 337 of file btMatrix3x3.h.

◆ solve33()

btVector3 btMatrix3x3::solve33 ( const btVector3 & b ) const

inline

Solve A * x = b, where b is a column vector.

This is more efficient than computing the inverse in one-shot cases. Solve33 is from Box2d, thanks to Erin Catto,

Definition at line 648 of file btMatrix3x3.h.

◆ tdotx()

btScalar btMatrix3x3::tdotx ( const btVector3 & v ) const

inline

Definition at line 669 of file btMatrix3x3.h.

◆ tdoty()

btScalar btMatrix3x3::tdoty ( const btVector3 & v ) const

inline

Definition at line 673 of file btMatrix3x3.h.

◆ tdotz()

btScalar btMatrix3x3::tdotz ( const btVector3 & v ) const

inline

Definition at line 677 of file btMatrix3x3.h.

◆ timesTranspose()

btMatrix3x3 btMatrix3x3::timesTranspose ( const btMatrix3x3 & m ) const

inline

Definition at line 1162 of file btMatrix3x3.h.

◆ transpose()

btMatrix3x3 btMatrix3x3::transpose ( ) const

inline

Return the transpose of the matrix.

Definition at line 1049 of file btMatrix3x3.h.

◆ transposeTimes()

btMatrix3x3 btMatrix3x3::transposeTimes ( const btMatrix3x3 & m ) const

inline

Definition at line 1106 of file btMatrix3x3.h.

Member Data Documentation

◆ m_el

btVector3 btMatrix3x3::m_el[3]

private

Data storage for the matrix, each vector is a row of the matrix.

Definition at line 52 of file btMatrix3x3.h.

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

btMatrix3x3.h

Public Member Functions

Static Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ btMatrix3x3() [1/5]

◆ btMatrix3x3() [2/5]

◆ btMatrix3x3() [3/5]

◆ btMatrix3x3() [4/5]

◆ btMatrix3x3() [5/5]

Member Function Documentation

◆ absolute()

◆ adjoint()

◆ cofac()

◆ deSerialize()

◆ deSerializeDouble()

◆ deSerializeFloat()

◆ determinant()

◆ diagonalize()

◆ extractRotation()

◆ getColumn()

◆ getEulerYPR()

◆ getEulerZYX()

◆ getIdentity()

◆ getOpenGLSubMatrix()

◆ getRotation()

◆ getRow()

◆ inverse()

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator=()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ scaled()

◆ serialize()

◆ serializeFloat()

◆ setEulerYPR()

◆ setEulerZYX()

◆ setFromOpenGLSubMatrix()

◆ setIdentity()

◆ setRotation()

◆ setValue()

◆ setZero()

◆ solve33()

◆ tdotx()

◆ tdoty()

◆ tdotz()

◆ timesTranspose()

◆ transpose()

◆ transposeTimes()

Member Data Documentation

◆ m_el