Matrix stores a set of "rows" by "columns" elements of type T and provides functions that operate on the set of elements. More...

#include <matrix.h>

Detailed Description

template<class T, int rows, int columns>
class mathfu::Matrix< T, rows, columns >

Matrix stores a set of "rows" by "columns" elements of type T and provides functions that operate on the set of elements.

Template Parameters

T	type of each element in the matrix.
rows	Number of rows in the matrix.
columns	Number of columns in the matrix.

Public Member Functions
	Matrix ()
	Construct a Matrix of uninitialized values.

	Matrix (const Matrix< T, rows, columns > &m)
	Construct a Matrix from another Matrix copying each element. /. More...

	Matrix (const T &s)
	Construct a Matrix from a single float. More...

	Matrix (const T &s00, const T &s10, const T &s01, const T &s11)
	Construct a Matrix from four floats. More...

	Matrix (const T &s00, const T &s10, const T &s20, const T &s01, const T &s11, const T &s21, const T &s02, const T &s12, const T &s22)
	Create a Matrix from nine floats. More...

	Matrix (const T &s00, const T &s10, const T &s20, const T &s30, const T &s01, const T &s11, const T &s21, const T &s31, const T &s02, const T &s12, const T &s22, const T &s32)
	Creates a Matrix from twelve floats. More...

	Matrix (const T &s00, const T &s10, const T &s20, const T &s30, const T &s01, const T &s11, const T &s21, const T &s31, const T &s02, const T &s12, const T &s22, const T &s32, const T &s03, const T &s13, const T &s23, const T &s33)
	Create a Matrix from sixteen floats. More...

	Matrix (const Vector< T, 4 > &column0, const Vector< T, 4 > &column1, const Vector< T, 4 > &column2, const Vector< T, 4 > &column3)
	Create 4x4 Matrix from 4, 4 element vectors. More...

	Matrix (const T *const a)
	Create a Matrix from the first row * column elements of an array. More...

	Matrix (const VectorPacked< T, rows > *const vectors)
	Create a Matrix from an array of "columns", "rows" element packed vectors. More...

const T &	operator() (const int row, const int column) const
	Access an element of the matrix. More...

T &	operator() (const int row, const int column)
	Access an element of the Matrix. More...

const T &	operator() (const int i) const
	Access an element of the Matrix. More...

T &	operator() (const int i)
	Access an element of the Matrix. More...

const T &	operator[] (const int i) const
	Access an element of the Matrix. More...

T &	operator[] (const int i)
	Access an element of the Matrix. More...

void	Pack (VectorPacked< T, rows > *const vector) const
	Pack the matrix to an array of "rows" element vectors, one vector per matrix column. More...

Matrix< T, rows, columns >	operator- () const
	Negate this Matrix. More...

Matrix< T, rows, columns >	operator+ (const Matrix< T, rows, columns > &m) const
	Add a Matrix to this Matrix. More...

Matrix< T, rows, columns >	operator- (const Matrix< T, rows, columns > &m) const
	Subtract a Matrix from this Matrix. More...

Matrix< T, rows, columns >	operator+ (const T &s) const
	Add a scalar to each element of this Matrix. More...

Matrix< T, rows, columns >	operator- (const T &s) const
	Subtract a scalar from each element of this Matrix. More...

Matrix< T, rows, columns >	operator* (const T &s) const
	Multiply each element of this Matrix with a scalar. More...

Matrix< T, rows, columns >	operator/ (const T &s) const
	Divide each element of this Matrix with a scalar. More...

Matrix< T, rows, columns >	operator* (const Matrix< T, rows, columns > &m) const
	Multiply this Matrix with another Matrix. More...

Matrix< T, rows, columns > &	operator+= (const Matrix< T, rows, columns > &m)
	Add a Matrix to this Matrix (in-place). More...

Matrix< T, rows, columns > &	operator-= (const Matrix< T, rows, columns > &m)
	Subtract a Matrix from this Matrix (in-place). More...

Matrix< T, rows, columns > &	operator+= (const T &s)
	Add a scalar to each element of this Matrix (in-place). More...

Matrix< T, rows, columns > &	operator-= (const T &s)
	Subtract a scalar from each element of this Matrix (in-place). More...

Matrix< T, rows, columns > &	operator*= (const T &s)
	Multiply each element of this Matrix with a scalar (in-place). More...

Matrix< T, rows, columns > &	operator/= (const T &s)
	Divide each element of this Matrix by a scalar (in-place). More...

Matrix< T, rows, columns > &	operator*= (const Matrix< T, rows, columns > &m)
	Multiply this Matrix with another Matrix (in-place). More...

Matrix< T, rows, columns >	Inverse () const
	Calculate the inverse of this Matrix. More...

bool	InverseWithDeterminantCheck (Matrix< T, rows, columns > *const inverse) const
	Calculate the inverse of this Matrix. More...

Matrix< T, columns, rows >	Transpose () const
	Calculate the transpose of this Matrix. More...

Vector< T, 2 >	TranslationVector2D () const
	Get the 2-dimensional translation of a 2-dimensional affine transform. More...

Vector< T, 3 >	TranslationVector3D () const
	Get the 3-dimensional translation of a 3-dimensional affine transform. More...

Static Public Member Functions
template<typename CompatibleT >
static Matrix< T, rows, columns >	FromType (const CompatibleT &compatible)
	Load from any byte-wise compatible external matrix. More...

template<typename CompatibleT >
static CompatibleT	ToType (const Matrix< T, rows, columns > &m)
	Load into any byte-wise compatible external matrix. More...

static Matrix< T, rows, columns >	OuterProduct (const Vector< T, rows > &v1, const Vector< T, columns > &v2)
	Calculate the outer product of two Vectors. More...

static Matrix< T, rows, columns >	HadamardProduct (const Matrix< T, rows, columns > &m1, const Matrix< T, rows, columns > &m2)
	Calculate the hadamard / component-wise product of two matrices. More...

static Matrix< T, rows, columns >	Identity ()
	Calculate the identity Matrix. More...

static Matrix< T, 3 >	FromTranslationVector (const Vector< T, 2 > &v)
	Create a 3x3 translation Matrix from a 2-dimensional Vector. More...

static Matrix< T, 4 >	FromTranslationVector (const Vector< T, 3 > &v)
	Create a 4x4 translation Matrix from a 3-dimensional Vector. More...

static Matrix< T, rows >	FromScaleVector (const Vector< T, rows-1 > &v)
	Create a square Matrix with the diagonal component set to v. More...

static Matrix< T, 4 >	FromRotationMatrix (const Matrix< T, 3 > &m)
	Create a 4x4 Matrix from a 3x3 rotation Matrix. More...

static Matrix< T, 3 >	ToRotationMatrix (const Matrix< T, 4 > &m)
	Extracts the 3x3 rotation Matrix from a 4x4 Matrix. More...

static Matrix< T, 4 >	FromAffineTransform (const Matrix< T, 4, 3 > &affine)
	Constructs a Matrix<float, 4> from an AffineTransform. More...

static Matrix< T, 4, 3 >	ToAffineTransform (const Matrix< T, 4 > &m)
	Converts a Matrix<float, 4> into an AffineTransform. More...

static Matrix< T, 3 >	RotationX (const Vector< T, 2 > &v)
	Create a 3x3 rotation Matrix from a 2D normalized directional Vector around the X axis. More...

static Matrix< T, 3 >	RotationY (const Vector< T, 2 > &v)
	Create a 3x3 rotation Matrix from a 2D normalized directional Vector around the Y axis. More...

static Matrix< T, 3 >	RotationZ (const Vector< T, 2 > &v)
	Create a 3x3 rotation Matrix from a 2D normalized directional Vector around the Z axis. More...

static Matrix< T, 3 >	RotationX (T angle)
	Create a 3x3 rotation Matrix from an angle (in radians) around the X axis. More...

static Matrix< T, 3 >	RotationY (T angle)
	Create a 3x3 rotation Matrix from an angle (in radians) around the Y axis. More...

static Matrix< T, 3 >	RotationZ (T angle)
	Create a 3x3 rotation Matrix from an angle (in radians) around the Z axis. More...

static Matrix< T, 4, 4 >	Perspective (T fovy, T aspect, T znear, T zfar, T handedness=1)
	Create a 4x4 perspective Matrix. More...

static Matrix< T, 4, 4 >	Ortho (T left, T right, T bottom, T top, T znear, T zfar, T handedness=1)
	Create a 4x4 orthographic Matrix. More...

static Matrix< T, 4, 4 >	LookAt (const Vector< T, 3 > &at, const Vector< T, 3 > &eye, const Vector< T, 3 > &up, T handedness=-1)
	Create a 3-dimensional camera Matrix. More...

static Vector< T, 3 >	UnProject (const Vector< T, 3 > &window_coord, const Matrix< T, 4, 4 > &model_view, const Matrix< T, 4, 4 > &projection, const float window_width, const float window_height)
	Get the 3D position in object space from a window coordinate. More...

Static Public Attributes
static const int	kRows = rows
	Number of rows in the matrix.

static const int	kColumns = columns
	Number of columns in the matrix.

static const int	kElements = rows * columns
	Total number of elements in the matrix.

Friends
Vector< T, columns >	operator* (const Vector< T, rows > &v, const Matrix< T, rows, columns > &m)
	Multiply a Vector by a Matrix. More...

Related Functions
(Note that these are not member functions.)
template<class T , int rows, int columns>
Matrix< T, rows, columns >	operator* (const T &s, const Matrix< T, columns, rows > &m)
	Multiply each element of a Matrix by a scalar. More...

template<class T , int rows, int columns>
Vector< T, rows >	operator* (const Matrix< T, rows, columns > &m, const Vector< T, columns > &v)
	Multiply a Matrix by a Vector. More...

template<class T >
Vector< T, 3 >	operator* (const Matrix< T, 4, 4 > &m, const Vector< T, 3 > &v)
	Multiply a 4x4 Matrix by a 3-dimensional Vector. More...

Constructor & Destructor Documentation

template<class T, int rows, int columns>

mathfu::Matrix< T, rows, columns >::Matrix ( const Matrix< T, rows, columns > & m )

inline

Construct a Matrix from another Matrix copying each element. /.

Parameters

m	Matrix that the data will be copied from.

template<class T, int rows, int columns>

mathfu::Matrix< T, rows, columns >::Matrix ( const T & s )

inlineexplicit

Construct a Matrix from a single float.

Parameters

s	Scalar value used to initialize each element of the matrix.

template<class T, int rows, int columns>

mathfu::Matrix< T, rows, columns >::Matrix	(	const T &	s00,
		const T &	s10,
		const T &	s01,
		const T &	s11
	)

inline

Construct a Matrix from four floats.

Note: This method only works with a 2x2 Matrix.

Parameters

s00	Value of the first row and column.
s10	Value of the second row, first column.
s01	Value of the first row, second column.
s11	Value of the second row and column.

template<class T, int rows, int columns>

mathfu::Matrix< T, rows, columns >::Matrix	(	const T &	s00,
		const T &	s10,
		const T &	s20,
		const T &	s01,
		const T &	s11,
		const T &	s21,
		const T &	s02,
		const T &	s12,
		const T &	s22
	)

inline

Create a Matrix from nine floats.

Note: This method only works with a 3x3 Matrix.

Parameters

s00	Value of the first row and column.
s10	Value of the second row, first column.
s20	Value of the third row, first column.
s01	Value of the first row, second column.
s11	Value of the second row and column.
s21	Value of the third row, second column.
s02	Value of the first row, third column.
s12	Value of the second row, third column.
s22	Value of the third row and column.

template<class T, int rows, int columns>

mathfu::Matrix< T, rows, columns >::Matrix	(	const T &	s00,
		const T &	s10,
		const T &	s20,
		const T &	s30,
		const T &	s01,
		const T &	s11,
		const T &	s21,
		const T &	s31,
		const T &	s02,
		const T &	s12,
		const T &	s22,
		const T &	s32
	)

inline

Creates a Matrix from twelve floats.

Note: This method only works with Matrix<float, 4, 3>.

Parameters

s00	Value of the first row and column.
s10	Value of the second row, first column.
s20	Value of the third row, first column.
s30	Value of the fourth row, first column.
s01	Value of the first row, second column.
s11	Value of the second row and column.
s21	Value of the third row, second column.
s31	Value of the fourth row, second column.
s02	Value of the first row, third column.
s12	Value of the second row, third column.
s22	Value of the third row and column.
s32	Value of the fourth row, third column.

template<class T, int rows, int columns>

mathfu::Matrix< T, rows, columns >::Matrix	(	const T &	s00,
		const T &	s10,
		const T &	s20,
		const T &	s30,
		const T &	s01,
		const T &	s11,
		const T &	s21,
		const T &	s31,
		const T &	s02,
		const T &	s12,
		const T &	s22,
		const T &	s32,
		const T &	s03,
		const T &	s13,
		const T &	s23,
		const T &	s33
	)

inline

Create a Matrix from sixteen floats.

Note: This method only works with a 4x4 Matrix.

Parameters

s00	Value of the first row and column.
s10	Value of the second row, first column.
s20	Value of the third row, first column.
s30	Value of the fourth row, first column.
s01	Value of the first row, second column.
s11	Value of the second row and column.
s21	Value of the third row, second column.
s31	Value of the fourth row, second column.
s02	Value of the first row, third column.
s12	Value of the second row, third column.
s22	Value of the third row and column.
s32	Value of the fourth row, third column.
s03	Value of the first row, fourth column.
s13	Value of the second row, fourth column.
s23	Value of the third row, fourth column.
s33	Value of the fourth row and column.

template<class T, int rows, int columns>

mathfu::Matrix< T, rows, columns >::Matrix	(	const Vector< T, 4 > &	column0,
		const Vector< T, 4 > &	column1,
		const Vector< T, 4 > &	column2,
		const Vector< T, 4 > &	column3
	)

inline

Create 4x4 Matrix from 4, 4 element vectors.

Note: This method only works with a 4x4 Matrix.

Parameters

column0	Vector used for the first column.
column1	Vector used for the second column.
column2	Vector used for the third column.
column3	Vector used for the fourth column.

template<class T, int rows, int columns>

mathfu::Matrix< T, rows, columns >::Matrix ( const T *const a )

inlineexplicit

Create a Matrix from the first row * column elements of an array.

Parameters

a	Array of values that the matrix will be iniitlized to.

template<class T, int rows, int columns>

mathfu::Matrix< T, rows, columns >::Matrix ( const VectorPacked< T, rows > *const vectors )

inlineexplicit

Create a Matrix from an array of "columns", "rows" element packed vectors.

Parameters

vectors Array of "columns", "rows" element packed vectors.

Member Function Documentation

template<class T, int rows, int columns>

static Matrix<T, 4> mathfu::Matrix< T, rows, columns >::FromAffineTransform ( const Matrix< T, 4, 3 > & affine )

inlinestatic

Constructs a Matrix<float, 4> from an AffineTransform.

Parameters

affine An AffineTransform reference to be used to construct a Matrix<float, 4> by adding in the 'w' row of [0, 0, 0, 1].

template<class T, int rows, int columns>

static Matrix<T, 4> mathfu::Matrix< T, rows, columns >::FromRotationMatrix ( const Matrix< T, 3 > & m )

inlinestatic

Create a 4x4 Matrix from a 3x3 rotation Matrix.

This Matrix will have an empty or zero translation component.

Parameters

m	3x3 rotation Matrix.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

static Matrix<T, rows> mathfu::Matrix< T, rows, columns >::FromScaleVector ( const Vector< T, rows-1 > & v )

inlinestatic

Create a square Matrix with the diagonal component set to v.

This is an affine transform matrix, so the dimension of the vector is one less than the dimension of the matrix.

Parameters

v	Vector containing components for scaling.

Returns: Matrix with v along the diagonal, and 1 in the bottom right.

template<class T, int rows, int columns>

static Matrix<T, 3> mathfu::Matrix< T, rows, columns >::FromTranslationVector ( const Vector< T, 2 > & v )

inlinestatic

Create a 3x3 translation Matrix from a 2-dimensional Vector.

This matrix will have an empty or zero rotation component.

Parameters

v	Vector of size 2.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

static Matrix<T, 4> mathfu::Matrix< T, rows, columns >::FromTranslationVector ( const Vector< T, 3 > & v )

inlinestatic

Create a 4x4 translation Matrix from a 3-dimensional Vector.

This matrix will have an empty or zero rotation component.

Parameters

v	The vector of size 3.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

template<typename CompatibleT >

static Matrix<T, rows, columns> mathfu::Matrix< T, rows, columns >::FromType ( const CompatibleT & compatible )

inlinestatic

Load from any byte-wise compatible external matrix.

Format should be columns vectors, each holding rows values of type T.

Use this for safe conversion from external matrix classes. Often, external libraries will have their own matrix types that are, byte-for-byte, exactly the same as mathfu::Matrix. This function allows you to load a mathfu::Matrix from those external types, without potential aliasing bugs that are caused by casting.

Note: If your external type gives you access to a T*, then you can equivalently use the Matrix(const T*) constructor.

Parameters

compatible reference to a byte-wise compatible matrix structure; array of columns x rows Ts.

Returns: compatible loaded as a mathfu::Matrix.

template<class T, int rows, int columns>

static Matrix<T, rows, columns> mathfu::Matrix< T, rows, columns >::HadamardProduct	(	const Matrix< T, rows, columns > &	m1,
		const Matrix< T, rows, columns > &	m2
	)

inlinestatic

Calculate the hadamard / component-wise product of two matrices.

Parameters

m1	First Matrix.
m2	Second Matrix.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

static Matrix<T, rows, columns> mathfu::Matrix< T, rows, columns >::Identity ( )

inlinestatic

Calculate the identity Matrix.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

Matrix<T, rows, columns> mathfu::Matrix< T, rows, columns >::Inverse ( ) const

inline

Calculate the inverse of this Matrix.

This calculates the inverse Matrix such that (m * m).Inverse() is the identity.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

bool mathfu::Matrix< T, rows, columns >::InverseWithDeterminantCheck ( Matrix< T, rows, columns > *const inverse ) const

inline

Calculate the inverse of this Matrix.

This calculates the inverse Matrix such that (m * m).Inverse() is the identity. By contrast to Inverse() this returns whether the matrix is invertible.

The invertible check simply compares the calculated determinant with Constants<T>::GetDeterminantThreshold() to roughly determine whether the matrix is invertible. This simple check works in common cases but will fail for corner cases where the matrix is a combination of huge and tiny values that can't be accurately represented by the floating point datatype T. More extensive checks (relative to the input values) are possible but far more expensive, complicated and difficult to test.

Returns: Whether the matrix is invertible.

template<class T, int rows, int columns>

static Matrix<T, 4, 4> mathfu::Matrix< T, rows, columns >::LookAt	(	const Vector< T, 3 > &	at,
		const Vector< T, 3 > &	eye,
		const Vector< T, 3 > &	up,
		T	handedness = `-1`
	)

inlinestatic

Create a 3-dimensional camera Matrix.

Parameters

at	The look-at target of the camera.
eye	The position of the camera.
up	The up vector in the world, for example (0, 1, 0) if the y-axis is up.
handedness	1.0f for RH, -1.0f for LH.

Returns: 3-dimensional camera Matrix. TODO: Change default handedness to +1 so that it matches Perspective().

template<class T, int rows, int columns>

const T& mathfu::Matrix< T, rows, columns >::operator()	(	const int	row,
		const int	column
	)		const

inline

Access an element of the matrix.

Parameters

row	Index of the row to access.
column	Index of the column to access.

Returns: Const reference to the element.

template<class T, int rows, int columns>

T& mathfu::Matrix< T, rows, columns >::operator()	(	const int	row,
		const int	column
	)

inline

Access an element of the Matrix.

Parameters

row	Index of the row to access.
column	Index of the column to access.

Returns: Reference to the data that can be modified by the caller.

template<class T, int rows, int columns>

const T& mathfu::Matrix< T, rows, columns >::operator() ( const int i ) const

inline

Access an element of the Matrix.

Parameters

i	Index of the element to access in flattened memory. Where the column accessed is i / rows and the row is i % rows.

Returns: Reference to the data that can be modified by the caller.

template<class T, int rows, int columns>

T& mathfu::Matrix< T, rows, columns >::operator() ( const int i )

inline

Access an element of the Matrix.

Parameters

i	Index of the element to access in flattened memory. Where the column accessed is i / rows and the row is i % rows.

Returns: Reference to the data that can be modified by the caller.

template<class T, int rows, int columns>

Matrix<T, rows, columns> mathfu::Matrix< T, rows, columns >::operator* ( const T & s ) const

inline

Multiply each element of this Matrix with a scalar.

Parameters

s	Scalar to multiply with this Matrix.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

Matrix<T, rows, columns> mathfu::Matrix< T, rows, columns >::operator* ( const Matrix< T, rows, columns > & m ) const

inline

Multiply this Matrix with another Matrix.

Parameters

m	Matrix to multiply with this Matrix.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

Matrix<T, rows, columns>& mathfu::Matrix< T, rows, columns >::operator*= ( const T & s )

inline

Multiply each element of this Matrix with a scalar (in-place).

Parameters

s	Scalar to multiply with each element of this Matrix.

Returns: Reference to this class.

template<class T, int rows, int columns>

Matrix<T, rows, columns>& mathfu::Matrix< T, rows, columns >::operator*= ( const Matrix< T, rows, columns > & m )

inline

Multiply this Matrix with another Matrix (in-place).

Parameters

m	Matrix to multiply with this Matrix.

Returns: Reference to this class.

template<class T, int rows, int columns>

Matrix<T, rows, columns> mathfu::Matrix< T, rows, columns >::operator+ ( const Matrix< T, rows, columns > & m ) const

inline

Add a Matrix to this Matrix.

Parameters

m	Matrix to add to this Matrix.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

Matrix<T, rows, columns> mathfu::Matrix< T, rows, columns >::operator+ ( const T & s ) const

inline

Add a scalar to each element of this Matrix.

Parameters

s	Scalar to add to this Matrix.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

Matrix<T, rows, columns>& mathfu::Matrix< T, rows, columns >::operator+= ( const Matrix< T, rows, columns > & m )

inline

Add a Matrix to this Matrix (in-place).

Parameters

m	Matrix to add to this Matrix.

Returns: Reference to this class.

template<class T, int rows, int columns>

Matrix<T, rows, columns>& mathfu::Matrix< T, rows, columns >::operator+= ( const T & s )

inline

Add a scalar to each element of this Matrix (in-place).

Parameters

s	Scalar to add to each element of this Matrix.

Returns: Reference to this class.

template<class T, int rows, int columns>

Matrix<T, rows, columns> mathfu::Matrix< T, rows, columns >::operator- ( ) const

inline

Negate this Matrix.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

Matrix<T, rows, columns> mathfu::Matrix< T, rows, columns >::operator- ( const Matrix< T, rows, columns > & m ) const

inline

Subtract a Matrix from this Matrix.

Parameters

m	Matrix to subtract from this Matrix.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

Matrix<T, rows, columns> mathfu::Matrix< T, rows, columns >::operator- ( const T & s ) const

inline

Subtract a scalar from each element of this Matrix.

Parameters

s	Scalar to subtract from this matrix.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

Matrix<T, rows, columns>& mathfu::Matrix< T, rows, columns >::operator-= ( const Matrix< T, rows, columns > & m )

inline

Subtract a Matrix from this Matrix (in-place).

Parameters

m	Matrix to subtract from this Matrix.

Returns: Reference to this class.

template<class T, int rows, int columns>

Matrix<T, rows, columns>& mathfu::Matrix< T, rows, columns >::operator-= ( const T & s )

inline

Subtract a scalar from each element of this Matrix (in-place).

Parameters

s	Scalar to subtract from each element of this Matrix.

Returns: Reference to this class.

template<class T, int rows, int columns>

Matrix<T, rows, columns> mathfu::Matrix< T, rows, columns >::operator/ ( const T & s ) const

inline

Divide each element of this Matrix with a scalar.

Parameters

s	Scalar to divide this Matrix with.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

Matrix<T, rows, columns>& mathfu::Matrix< T, rows, columns >::operator/= ( const T & s )

inline

Divide each element of this Matrix by a scalar (in-place).

Parameters

s	Scalar to divide this Matrix by.

Returns: Reference to this class.

template<class T, int rows, int columns>

const T& mathfu::Matrix< T, rows, columns >::operator[] ( const int i ) const

inline

Access an element of the Matrix.

Parameters

i	Index of the element to access in flattened memory. Where the column accessed is i / rows and the row is i % rows.

Returns: Const reference to the data.

template<class T, int rows, int columns>

T& mathfu::Matrix< T, rows, columns >::operator[] ( const int i )

inline

Access an element of the Matrix.

Parameters

i	Index of the element to access in flattened memory. Where the column accessed is i / rows and the row is i % rows.

Returns: Reference to the data that can be modified by the caller.

template<class T, int rows, int columns>

static Matrix<T, 4, 4> mathfu::Matrix< T, rows, columns >::Ortho	(	T	left,
		T	right,
		T	bottom,
		T	top,
		T	znear,
		T	zfar,
		T	handedness = `1`
	)

inlinestatic

Create a 4x4 orthographic Matrix.

Parameters

left	Left extent.
right	Right extent.
bottom	Bottom extent.
top	Top extent.
znear	Near plane location.
zfar	Far plane location.
handedness	1.0f for RH, -1.0f for LH

Returns: 4x4 orthographic Matrix.

template<class T, int rows, int columns>

static Matrix<T, rows, columns> mathfu::Matrix< T, rows, columns >::OuterProduct	(	const Vector< T, rows > &	v1,
		const Vector< T, columns > &	v2
	)

inlinestatic

Calculate the outer product of two Vectors.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

void mathfu::Matrix< T, rows, columns >::Pack ( VectorPacked< T, rows > *const vector ) const

inline

Pack the matrix to an array of "rows" element vectors, one vector per matrix column.

Parameters

vector Array of "columns" entries to write to.

template<class T, int rows, int columns>

static Matrix<T, 4, 4> mathfu::Matrix< T, rows, columns >::Perspective	(	T	fovy,
		T	aspect,
		T	znear,
		T	zfar,
		T	handedness = `1`
	)

inlinestatic

Create a 4x4 perspective Matrix.

Parameters

fovy	Field of view.
aspect	Aspect ratio.
znear	Near plane location.
zfar	Far plane location.
handedness	1.0f for RH, -1.0f for LH

Returns: 4x4 perspective Matrix.

template<class T, int rows, int columns>

static Matrix<T, 3> mathfu::Matrix< T, rows, columns >::RotationX ( const Vector< T, 2 > & v )

inlinestatic

Create a 3x3 rotation Matrix from a 2D normalized directional Vector around the X axis.

Parameters

v	2D normalized directional Vector.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

static Matrix<T, 3> mathfu::Matrix< T, rows, columns >::RotationX ( T angle )

inlinestatic

Create a 3x3 rotation Matrix from an angle (in radians) around the X axis.

Parameters

angle Angle (in radians).

Returns: Matrix containing the result.

template<class T, int rows, int columns>

static Matrix<T, 3> mathfu::Matrix< T, rows, columns >::RotationY ( const Vector< T, 2 > & v )

inlinestatic

Create a 3x3 rotation Matrix from a 2D normalized directional Vector around the Y axis.

Parameters

v	2D normalized directional Vector.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

static Matrix<T, 3> mathfu::Matrix< T, rows, columns >::RotationY ( T angle )

inlinestatic

Create a 3x3 rotation Matrix from an angle (in radians) around the Y axis.

Parameters

angle Angle (in radians).

Returns: Matrix containing the result.

template<class T, int rows, int columns>

static Matrix<T, 3> mathfu::Matrix< T, rows, columns >::RotationZ ( const Vector< T, 2 > & v )

inlinestatic

Create a 3x3 rotation Matrix from a 2D normalized directional Vector around the Z axis.

Parameters

v	2D normalized directional Vector.

Returns: Matrix containing the result.

template<class T, int rows, int columns>

static Matrix<T, 3> mathfu::Matrix< T, rows, columns >::RotationZ ( T angle )

inlinestatic

Create a 3x3 rotation Matrix from an angle (in radians) around the Z axis.

Parameters

angle Angle (in radians).

Returns: Matrix containing the result.

template<class T, int rows, int columns>

static Matrix<T, 4, 3> mathfu::Matrix< T, rows, columns >::ToAffineTransform ( const Matrix< T, 4 > & m )

inlinestatic

Converts a Matrix<float, 4> into an AffineTransform.

Parameters

m	A Matrix<float, 4> reference to be converted into an AffineTransform by dropping the fixed 'w' row.

Returns: Returns an AffineTransform that contains the essential transformation data from the Matrix<float, 4>.

template<class T, int rows, int columns>

static Matrix<T, 3> mathfu::Matrix< T, rows, columns >::ToRotationMatrix ( const Matrix< T, 4 > & m )

inlinestatic

Extracts the 3x3 rotation Matrix from a 4x4 Matrix.

This resulting Matrix will contain the upper-left 3x3 sub-matrix of the input Matrix.

Parameters

m	4x4 Matrix.

Returns: rotation Matrix containing the result.

template<class T, int rows, int columns>

template<typename CompatibleT >

static CompatibleT mathfu::Matrix< T, rows, columns >::ToType ( const Matrix< T, rows, columns > & m )

inlinestatic

Load into any byte-wise compatible external matrix.

Format should be columns vectors, each holding rows values of type T.

Use this for safe conversion to external matrix classes. Often, external libraries will have their own matrix types that are, byte-for-byte, exactly the same as mathfu::Matrix. This function allows you to load an external type from a mathfu::Matrix, without potential aliasing bugs that are caused by casting.

Parameters

m	reference to mathfu::Matrix to convert.

Returns: CompatibleT loaded from m.

template<class T, int rows, int columns>

Vector<T, 2> mathfu::Matrix< T, rows, columns >::TranslationVector2D ( ) const

inline

Get the 2-dimensional translation of a 2-dimensional affine transform.

Note: 2-dimensional affine transforms are represented by 3x3 matrices.

Returns: Vector with the first two components of column 2 of this Matrix.

template<class T, int rows, int columns>

Vector<T, 3> mathfu::Matrix< T, rows, columns >::TranslationVector3D ( ) const

inline

Get the 3-dimensional translation of a 3-dimensional affine transform.

Note: 3-dimensional affine transforms are represented by 4x4 matrices.

Returns: Vector with the first three components of column 3.

template<class T, int rows, int columns>

Matrix<T, columns, rows> mathfu::Matrix< T, rows, columns >::Transpose ( ) const

inline

Calculate the transpose of this Matrix.

Returns: The transpose of the specified Matrix.

template<class T, int rows, int columns>

static Vector<T, 3> mathfu::Matrix< T, rows, columns >::UnProject	(	const Vector< T, 3 > &	window_coord,
		const Matrix< T, 4, 4 > &	model_view,
		const Matrix< T, 4, 4 > &	projection,
		const float	window_width,
		const float	window_height
	)

inlinestatic

Get the 3D position in object space from a window coordinate.

Parameters

window_coord	The window coordinate. The z value is for depth. A window coordinate on the near plane will have 0 as the z value. And a window coordinate on the far plane will have 1 as the z value. z value should be with in [0, 1] here.
model_view	The Model View matrix.
projection	The projection matrix.
window_width	Width of the window.
window_height	Height of the window.

Returns: the mapped 3D position in object space.

Friends And Related Function Documentation

template<class T, int rows, int columns>

Vector<T, columns> operator*	(	const Vector< T, rows > &	v,
		const Matrix< T, rows, columns > &	m
	)

friend

Multiply a Vector by a Matrix.

Parameters

v	Vector to multiply.
m	Matrix to multiply.

Returns: Matrix containing the result.

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

matrix.h

Detailed Description

template<class T, int rows, int columns> class mathfu::Matrix< T, rows, columns >

Public Member Functions

Static Public Member Functions

Static Public Attributes

Friends

Related Functions

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

template<class T, int rows, int columns>
class mathfu::Matrix< T, rows, columns >