This reference page is linked to from the following overview topics: Math and Geometry Utilities.

Detailed Description

This class represents a 4x4 transformation matrix.

Definition at line 1062 of file math.h.

#include <math.h>

Public Member Functions
	Matrix (void)
	Construct a matrix without initializing its elements. The values stored in the matrix are undefined.
	Matrix (const Matrix &m)
	Matrix (float f11, float f12, float f13, float f14, float f21, float f22, float f23, float f24, float f31, float f32, float f33, float f34, float f41, float f42, float f43, float f44)
	Construct the matrix by passing all the 16 values.
	Matrix (const double *pMatrix)
	Construct a matrix from an array of double values. At least 16 values should be contained in the array.
float &	operator() (int iRow, int iColumn)
	Returns a reference to a specific element in the matrix.
float	operator() (int iRow, int iColumn) const
	Returns the value of a specific element in the matrix.
	operator const float * (void) const
	Returns a pointer to the matrix data as a pointer to float values.
	operator float * (void)
	Returns a pointer to the constant matrix data as a pointer to float values.
Matrix &	SetIdentity (void)
	Sets this matrix to be the identity matrix.
bool	IsIdentity (void) const
	Return true if the matrix is the identity matrix.
bool	IsRigid (void) const
	Returns true if the transformation represented by the matrix is rigid (contains only translation and rotation, not scale).
Matrix &	operator*= (float)
	Multiplies the matrix with a scalar value.
Matrix	operator* (const Matrix &m) const
	Multiplies two matrices.
Matrix	operator* (float) const
	Returns the multiplication of a matrix and a scalar.
Matrix	operator+ (const Matrix &) const
	Returns the sum of two matrices.
Matrix &	operator*= (const Matrix &m)
	Multiplies the matrix with another matrix.
bool	operator== (const Matrix &m) const
	Return true if the two matrices are identical.
void	SetRow (int iRowIndex, const Vector &vValue)
	Sets the values in a row of the matrix.
Matrix &	Transpose (void)
	Transposes the matrix and returns it.
Matrix &	Invert (void)
	Inverts the matrix and returns it.
Matrix &	FromEuler (const Vector &vAngles)
	Creates a rotation matrix from the given euler values stored in the vector and returns it.
Vector	ToEuler (void) const
	Converts a rotation matrix to euler values returns them in a vector.
Matrix &	FromAxisAngle (const Vector &vAxis, float fAngle)
	Calculates a rotation matrix from an axis and angle and returns it.
Vector	Transform (const Vector &v, float fW=1.0f) const
	Transforms a vector by the matrix and returns the result.
Vector	ProjectedTransform (const Vector &v, float fW=1.0f) const
	Transforms a point (represented by a Vector) by the matrix and returns the result.
Vector	Transform (const Vector &v, float fW, float &fRW) const
	Transforms a point (represented by a Vector) by the matrix, and returns all four homogeneous coordinates.
Vector	TransformDirection (const Vector &v) const
	Transform a direction vector by the matrix.
Public Attributes
union {
float m_fData [16]
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
}
double m_fAlignDummy [8]
__m128 m_vAlignDummy [4]
};

Constructor & Destructor Documentation

Matrix ( void ) [inline]

Construct a matrix without initializing its elements. The values stored in the matrix are undefined.

Definition at line 1067 of file math.h.

{};

Matrix ( const Matrix & m ) [inline]

Definition at line 1069 of file math.h.

                              :
        _11(m._11), _12(m._12), _13(m._13), _14(m._14), 
        _21(m._21), _22(m._22), _23(m._23), _24(m._24), 
        _31(m._31), _32(m._32), _33(m._33), _34(m._34), 
        _41(m._41), _42(m._42), _43(m._43), _44(m._44) {};

Matrix	(	float	f11,
		float	f12,
		float	f13,
		float	f14,
		float	f21,
		float	f22,
		float	f23,
		float	f24,
		float	f31,
		float	f32,
		float	f33,
		float	f34,
		float	f41,
		float	f42,
		float	f43,
		float	f44
	)		`[inline]`

Construct the matrix by passing all the 16 values.

Definition at line 1076 of file math.h.

                                                         :
        _11(f11), _12(f12), _13(f13), _14(f14), 
        _21(f21), _22(f22), _23(f23), _24(f24), 
        _31(f31), _32(f32), _33(f33), _34(f34), 
        _41(f41), _42(f42), _43(f43), _44(f44) {};

Matrix ( const double * pMatrix )

Construct a matrix from an array of double values. At least 16 values should be contained in the array.

Member Function Documentation

float& operator()	(	int	iRow,
		int	iColumn
	)		`[inline]`

Returns a reference to a specific element in the matrix.

Definition at line 1089 of file math.h.

    { 
        return m_fData[iRow*4+iColumn]; 
    };

float operator()	(	int	iRow,
		int	iColumn
	)		const `[inline]`

Returns the value of a specific element in the matrix.

Definition at line 1095 of file math.h.

    { 
        return m_fData[iRow*4+iColumn]; 
    };

operator const float * ( void ) const [inline]

Returns a pointer to the matrix data as a pointer to float values.

Do not delete this pointer.

Definition at line 1102 of file math.h.

{ return m_fData; };

operator float * ( void ) [inline]

Returns a pointer to the constant matrix data as a pointer to float values.

Definition at line 1106 of file math.h.

{ return m_fData; };

Matrix& SetIdentity ( void )

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Sets this matrix to be the identity matrix.

bool IsIdentity ( void ) const

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Return true if the matrix is the identity matrix.

bool IsRigid ( void ) const

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Returns true if the transformation represented by the matrix is rigid (contains only translation and rotation, not scale).

Matrix& operator*= ( float )

Multiplies the matrix with a scalar value.

Matrix operator* ( const Matrix & m ) const

Multiplies two matrices.

Matrix operator* ( float ) const

Returns the multiplication of a matrix and a scalar.

Matrix operator+ ( const Matrix & ) const

Returns the sum of two matrices.

Matrix& operator*= ( const Matrix & m )

Multiplies the matrix with another matrix.

bool operator== ( const Matrix & m ) const

Return true if the two matrices are identical.

void SetRow	(	int	iRowIndex,
		const Vector &	vValue
	)

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Sets the values in a row of the matrix.

The last value in the row remains unchanged.

Matrix& Transpose ( void )

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Transposes the matrix and returns it.

Matrix& Invert ( void )

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Inverts the matrix and returns it.

Matrix& FromEuler ( const Vector & vAngles )

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Creates a rotation matrix from the given euler values stored in the vector and returns it.

Vector ToEuler ( void ) const

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Converts a rotation matrix to euler values returns them in a vector.

Matrix& FromAxisAngle	(	const Vector &	vAxis,
		float	fAngle
	)

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Calculates a rotation matrix from an axis and angle and returns it.

Vector Transform	(	const Vector &	v,
		float	fW = `1.0f`
	)		const `[inline]`

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Transforms a vector by the matrix and returns the result.

The fourth component of the vector (if you are using homogeneous coordinates) can be passed in the fW parameter.

Parameters:

[in]	v	A Vector containing the x, y, z components of the point
[in]	fW	The w component of the point

Definition at line 1158 of file math.h.

    {
        return Vector( 
            v.m_fX*_11+v.m_fY*_21+v.m_fZ*_31+fW*_41,
            v.m_fX*_12+v.m_fY*_22+v.m_fZ*_32+fW*_42,
            v.m_fX*_13+v.m_fY*_23+v.m_fZ*_33+fW*_43 );
    };

Vector ProjectedTransform	(	const Vector &	v,
		float	fW = `1.0f`
	)		const `[inline]`

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Transforms a point (represented by a Vector) by the matrix and returns the result.

This point is assumed to be represented in homogenous coordinates, with a fourth (W) value. After the transformation the result vector will be divided by the resulting W component.

Parameters:

[in]	v	A Vector containing the x, y, z components of the point
[in]	fW	The w component of the point

Definition at line 1173 of file math.h.

    {
        float fRW = v.m_fX*_14+v.m_fY*_24+v.m_fZ*_34+fW*_44;
        return (1/fRW)*Vector( 
            v.m_fX*_11+v.m_fY*_21+v.m_fZ*_31+fW*_41,
            v.m_fX*_12+v.m_fY*_22+v.m_fZ*_32+fW*_42,
            v.m_fX*_13+v.m_fY*_23+v.m_fZ*_33+fW*_43 );
    };

Vector Transform	(	const Vector &	v,
		float	fW,
		float &	fRW
	)		const `[inline]`

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Transforms a point (represented by a Vector) by the matrix, and returns all four homogeneous coordinates.

Since Vectors only hold 3 coordinates, the W coordinate is passed in and out through parameters.

Parameters:

[in]	v	A Vector containing the x, y, z components of the point
[in]	fW	The w component of the point
[out]	fRW	The w component of the transformed point

Definition at line 1191 of file math.h.

    {
        fRW = v.m_fX*_14+v.m_fY*_24+v.m_fZ*_34+fW*_44;
        return Vector( 
            v.m_fX*_11+v.m_fY*_21+v.m_fZ*_31+fW*_41,
            v.m_fX*_12+v.m_fY*_22+v.m_fZ*_32+fW*_42,
            v.m_fX*_13+v.m_fY*_23+v.m_fZ*_33+fW*_43 );
    };

Vector TransformDirection ( const Vector & v ) const [inline]

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Transform a direction vector by the matrix.

Vector transformation is different than point transformation, in that it ignores the last row (translation) of the matrix during the transformation.

Definition at line 1208 of file math.h.

    {
        return Vector( 
            v.m_fX*_11+v.m_fY*_21+v.m_fZ*_31,
            v.m_fX*_12+v.m_fY*_22+v.m_fZ*_32,
            v.m_fX*_13+v.m_fY*_23+v.m_fZ*_33 );
    };