Class encapsulating a standard 4x4 homogeneous matrix. More...

#include <ParaMatrix4.h>

Public Member Functions
	Matrix4 ()
	Default constructor. More...

	Matrix4 (float m00, float m01, float m02, float m03, float m10, float m11, float m12, float m13, float m20, float m21, float m22, float m23, float m30, float m31, float m32, float m33)

	Matrix4 (const Matrix3 &m3x3)
	Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling 3x3 matrix.

	Matrix4 (const DeviceMatrix &mat)

	Matrix4 (const QMatrix &mat2DAffine)
	convert from 2d affine matrix. More...

	Matrix4 (const Quaternion &rot)
	Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling Quaternion.

void	identity ()
	make this identity

float *	operator[] (size_t iRow)

const float *const	operator[] (size_t iRow) const

Matrix4	operator* (const Matrix4 &m2) const
	Matrix4 concatenation using '*'.

Matrix4	Multiply4x3 (const Matrix4 &m2) const
	we will assume both matrix are row-major affine matrix. More...

void	*operator=** (const Matrix4 &m2)

Vector3	operator* (const Vector3 &v) const
	Vector transformation using '*'. More...

Vector4	operator* (const Vector4 &v) const

Plane	operator* (const Plane &p) const

Matrix4	operator+ (const Matrix4 &m2) const
	Matrix4 addition.

Matrix4 &	operator+= (const Matrix4 &m2)

Matrix4	operator- (const Matrix4 &m2) const
	Matrix4 subtraction.

Matrix4 &	operator-= (const Matrix4 &m2)

bool	operator== (const Matrix4 &m2) const
	Tests 2 matrices for equality.

bool	operator!= (const Matrix4 &m2) const
	Tests 2 matrices for inequality.

void	operator= (const Matrix3 &mat3)
	Assignment from 3x3 matrix.

Matrix4	transpose (void) const

void	offsetTrans (const Vector3 &v)

void	setTrans (const Vector3 &v)
	Sets the translation transformation part of the matrix.

Vector3	getTrans () const
	Extracts the translation transformation part of the matrix.

void	makeTrans (const Vector3 &v)
	Builds a translation matrix.

void	makeTrans (float tx, float ty, float tz)

void	setScale (const Vector3 &v)
	Sets the scale part of the matrix.

void	makeScale (float s_x, float s_y, float s_z)
	Gets a scale matrix - variation for not using a vector.

void	makeScale (const Vector3 &v)

void	extract3x3Matrix (Matrix3 &m3x3) const
	Extracts the rotation / scaling part of the Matrix4 as a 3x3 matrix. More...

bool	hasScale () const
	Determines if this matrix involves a scaling. More...

bool	hasNegativeScale () const
	Determines if this matrix involves a negative scaling. More...

Quaternion	extractQuaternion () const
	Extracts the rotation / scaling part as a quaternion from the Matrix4.

Matrix4	operator* (float scalar) const

Matrix4	adjoint () const

float	determinant () const

Matrix4	inverse () const

void	invert ()

Matrix4	InvertPRMatrix () const
	Inverts a PR matrix. More...

void	makeTransform (const Vector3 &position, const Vector3 &scale, const Quaternion &orientation)
	Building a Matrix4 from orientation / scale / position. More...

void	makeRot (const Quaternion &orientation, const Vector3 &origin)
	make rotation matrix

void	makeInverseTransform (const Vector3 &position, const Vector3 &scale, const Quaternion &orientation)
	Building an inverse Matrix4 from orientation / scale / position. More...

bool	isAffine (void) const
	Check whether or not the matrix is affine row-major matrix. More...

bool	isAffineColumnMajor (void) const

Vector3	transformAffine (const Vector3 &v) const
	Column vector: 3-D Vector transformation specially for affine matrix. More...

Vector4	transformAffine (const Vector4 &v) const
	Column vector: 4-D Vector transformation specially for affine matrix. More...

void	RemoveScaling (float Tolerance=SMALL_NUMBER)

Matrix4	GetMatrixWithoutScale (float Tolerance=SMALL_NUMBER) const

Vector3	ExtractScaling (float Tolerance=SMALL_NUMBER)
	Remove any scaling from this matrix (ie magnitude of each row is 1) and return the 3D scale vector that was initially present. More...

Vector3	GetScaleVector (float Tolerance=SMALL_NUMBER) const
	return a 3D scale vector calculated from this matrix (where each component is the magnitude of a row vector). More...

float	GetScaleByAxis (int axis, float Tolerance=SMALL_NUMBER) const

Matrix4	RemoveTranslation () const

DeviceMatrix_ptr	GetPointer ()

const DeviceMatrix_ptr	GetConstPointer () const

Public Attributes
union {
struct {
float _11

float _12

float _13

float _14

float _21

float _22

float _23

float _24

float _31

float _32

float _33

float _34

float _41

float _42

float _43

float _44

}

float m [4][4]

float _m [16]

};
	The matrix entries, indexed by [row][col].

Static Public Attributes
static const Matrix4	ZERO

static const Matrix4	IDENTITY

static const Matrix4	CLIPSPACE2DTOIMAGESPACE
	Useful little matrix which takes 2D clipspace {-1, 1} to {0,1} and inverts the Y. More...

Friends
std::ostream &	operator<< (std::ostream &o, const Matrix4 &m)
	Function for writing to a stream.

Detailed Description

Class encapsulating a standard 4x4 homogeneous matrix.

Remarks: ParaEngine uses row vectors when applying matrix multiplications, This means a vector is represented as a single row, 4-column matrix. This has the effect that the transformations implemented by the matrices happens left-to-right e.g. if vector V is to be transformed by M1 then M2 then M3, the calculation would be V * M1 * M2 * M3 . The order that matrices are concatenated is vital since matrix multiplication is not commutative, i.e. you can get a different result if you concatenate in the wrong order. But it is fine to use this class in a column-major math, the math are the same.

: ParaEngine deals with the differences between D3D and OpenGL etc. internally when operating through different render systems.

: matrix is indexed first by row and then by column.

Constructor & Destructor Documentation

§ Matrix4() [1/2]

ParaEngine::Matrix4::Matrix4 ( )

inline

Default constructor.

Note: It does NOT initialize the matrix for efficiency.

§ Matrix4() [2/2]

ParaEngine::Matrix4::Matrix4 ( const QMatrix & mat2DAffine )

convert from 2d affine matrix.

Member Function Documentation

§ extract3x3Matrix()

void ParaEngine::Matrix4::extract3x3Matrix ( Matrix3 & m3x3 ) const

inline

Extracts the rotation / scaling part of the Matrix4 as a 3x3 matrix.

Parameters

m3x3	Destination Matrix3

§ ExtractScaling()

ParaEngine::Vector3 ParaEngine::Matrix4::ExtractScaling ( float Tolerance = SMALL_NUMBER )

Remove any scaling from this matrix (ie magnitude of each row is 1) and return the 3D scale vector that was initially present.

§ GetScaleByAxis()

float ParaEngine::Matrix4::GetScaleByAxis	(	int	axis,
		float	Tolerance = `SMALL_NUMBER`
	)		const

Parameters

axis	0,1,2 for x,y,z

§ GetScaleVector()

ParaEngine::Vector3 ParaEngine::Matrix4::GetScaleVector ( float Tolerance = SMALL_NUMBER ) const

return a 3D scale vector calculated from this matrix (where each component is the magnitude of a row vector).

§ hasNegativeScale()

bool ParaEngine::Matrix4::hasNegativeScale ( ) const

inline

Determines if this matrix involves a negative scaling.

§ hasScale()

bool ParaEngine::Matrix4::hasScale ( ) const

Determines if this matrix involves a scaling.

§ InvertPRMatrix()

Matrix4 ParaEngine::Matrix4::InvertPRMatrix ( ) const

Inverts a PR matrix.

(which only contains a rotation and a translation) This is faster and less subject to FPU errors than the generic inversion code.

Parameters

dest	[out] destination matrix

§ isAffine()

bool ParaEngine::Matrix4::isAffine ( void ) const

inline

Check whether or not the matrix is affine row-major matrix.

Remarks: An affine matrix is a 4x4 matrix with column 3 equal to (0, 0, 0, 1), e.g. no projective coefficients.

§ makeInverseTransform()

void ParaEngine::Matrix4::makeInverseTransform	(	const Vector3 &	position,
		const Vector3 &	scale,
		const Quaternion &	orientation
	)

Building an inverse Matrix4 from orientation / scale / position.

Remarks: As makeTransform except it build the inverse given the same data as makeTransform, so performing -translation, -rotate, 1/scale in that order.

§ makeTransform()

void ParaEngine::Matrix4::makeTransform	(	const Vector3 &	position,
		const Vector3 &	scale,
		const Quaternion &	orientation
	)

Building a Matrix4 from orientation / scale / position.

Remarks: Transform is performed in the order scale, rotate, translation, i.e. translation is independent of orientation axes, scale does not affect size of translation, rotation and scaling are always centered on the origin.

§ Multiply4x3()

ParaEngine::Matrix4 ParaEngine::Matrix4::Multiply4x3 ( const Matrix4 & m2 ) const

we will assume both matrix are row-major affine matrix.

column 3 is (0,0,0,1)

§ operator*()

Vector3 ParaEngine::Matrix4::operator* ( const Vector3 & v ) const

inline

Vector transformation using '*'.

Remarks: Transforms the given 3-D vector by the matrix, projecting the result back into w = 1.

Note: This means that the initial w is considered to be 1.0, and then all the tree elements of the resulting 3-D vector are divided by the resulting w.

§ transformAffine() [1/2]

Vector3 ParaEngine::Matrix4::transformAffine ( const Vector3 & v ) const

inline

Column vector: 3-D Vector transformation specially for affine matrix.

Remarks: Transforms the given 3-D vector by the matrix, projecting the result back into w = 1.

Note: The matrix must be an affine matrix.

See also: Matrix4::isAffine.

§ transformAffine() [2/2]

Vector4 ParaEngine::Matrix4::transformAffine ( const Vector4 & v ) const

inline

Column vector: 4-D Vector transformation specially for affine matrix.

Note: The matrix must be an affine matrix.

See also: Matrix4::isAffine.

Member Data Documentation

§ CLIPSPACE2DTOIMAGESPACE

const Matrix4 ParaEngine::Matrix4::CLIPSPACE2DTOIMAGESPACE

static

Useful little matrix which takes 2D clipspace {-1, 1} to {0,1} and inverts the Y.

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

Client/trunk/ParaEngineClient/math/ParaMatrix4.h
Client/trunk/ParaEngineClient/math/ParaMatrix4.cpp

Public Member Functions

Public Attributes

Static Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

§ Matrix4() [1/2]

§ Matrix4() [2/2]

Member Function Documentation

§ extract3x3Matrix()

§ ExtractScaling()

§ GetScaleByAxis()

§ GetScaleVector()

§ hasNegativeScale()

§ hasScale()

§ InvertPRMatrix()

§ isAffine()

§ makeInverseTransform()

§ makeTransform()

§ Multiply4x3()

§ operator*()

§ transformAffine() [1/2]

§ transformAffine() [2/2]

Member Data Documentation

§ CLIPSPACE2DTOIMAGESPACE