4x4 transformation matrix More...

#include <Nimble/Matrix4.hpp>

Public Types
typedef T	type
	Data-type of the matrix.

Public Member Functions
void	clear ()
	Fills the matrix with zeroes.

Vector4T< T >	column (int i) const
	Returns the ith column vector.

template<class K >
void	copy (const K *x)
	Fills the matrix by copying values from memory.

template<class K >
void	copyTranspose (const K *x)
	Fills the matrix by copying transposed values from memory.

T *	data ()
	Returns a pointer to the first element.

const T *	data () const
	Returns a pointer to the first element.

T	get (int r, int c) const
	Gets the given matrix element.

void	identity ()
	Sets the matrix to identity.

Matrix4T< T >	inverse (bool *ok=0) const
	Returns the inverse of the matrix. More...

void	make (T x11, T x12, T x13, T x14, T x21, T x22, T x23, T x24, T x31, T x32, T x33, T x34, T x41, T x42, T x43, T x44)
	Fills the matrix with given values.

template<class K >
	Matrix4T (const K *x)
	Constructs a matrix and fills it from memory.

	Matrix4T ()
	Constructs a matrix without initializing it.

	Matrix4T (T x11, T x12, T x13, T x14, T x21, T x22, T x23, T x24, T x31, T x32, T x33, T x34, T x41, T x42, T x43, T x44)
	Constructs a matrix and fills it with given values.

	Matrix4T (const Vector4T< T > &a, const Vector4T< T > &b, const Vector4T< T > &c, const Vector4T< T > &d)
	Constructs a matrix and initializes it with given row vectors.

bool	operator!= (const Matrix4T< T > &that) const
	Compares if two matrices differ.

Matrix4T< T > &	operator*= (const Matrix4T< T > &that)
	Multiplies two matrices together.

Matrix4T< T > &	operator*= (T s)
	Multiplies the matrix with a scalar.

bool	operator== (const Matrix4T< T > &that) const
	Compares if two matrices are equal.

Vector4T< T > &	operator[] (int i)
	void setDiagonal(const Vector3T<T> &v) { m[0][0] = v[0]; m[1][1] = v[1]; m[2][2] = v[2]; m[3][3] = (T) 1.0; } More...

const Vector4T< T > &	operator[] (int i) const
	Returns the ith row. More...

Matrix4T< T >	orthoNormalize () const
	Returns an orthonormalized version of this matrix. More...

Vector3T< T >	project (const Vector4T< T > &v) const
	Apply the matrix on a 4D vector. More...

Vector3T< T >	project (const Vector3T< T > &v) const
	Apply the matrix on a 3D vector. More...

Vector2T< T >	project (const Vector2T< T > &v) const
	Apply the matrix on a 2D vector which is interpreted as [x y 0 1]. More...

Matrix3T< T >	rotation () const
	Returns the upper-left 3x3 matrix.

Vector4T< T > &	row (int i)
	Returns the ith row.

const Vector4T< T > &	row (int i) const
	Returns the ith row.

void	scalingMatrix (const Vector3T< T > &)
	Sets the matrix to a scaling matrix.

void	setColumn (int i, const Vector4T< T > &v)
	Sets the ith column vector.

void	setDiagonal (const Vector4T< T > &v)
	Sets the diagonal to given vector.

void	setRotation (const Nimble::Matrix3T< T > &that)
	Replaces the upper-left 3x3 matrix.

void	setTranslation (const Vector3T< T > &v)
	Sets the translation part of a 4x4 transformation matrix.

Vector3T< T >	translation () const
	Returns the translation part of a 4x4 matrix.

Matrix4T< T > &	transpose ()
	Transposes the matrix.

void	transpose (Matrix4T< T > &ret) const
	Make a transpose of a matrix to a given matrix.

Matrix4T< T >	transposed () const
	Returns a transposed matrix.

Matrix3T< T >	upperLeft () const
	Get the 3x3 upper-left matrix.

Matrix2T< T >	upperLeft2 () const
	Get the 2x2 upper-left matrix.

Static Public Member Functions
static int	columns ()
	Returns the number of columns (4)

static Matrix4T< T >	makeRotation (T radians, const Vector3T< T > &axis)
	Create a rotation matrix. More...

static Matrix4T< T >	makeScale (const Vector3T< T > &v)
	Create a non-uniform scaling matrix. More...

static Matrix4T< T >	makeTranslation (const Vector2T< T > &v)

static Matrix4T< T >	makeTranslation (const Vector3T< T > &v)
	Create a translation matrix. More...

static Matrix4T< T >	makeTranslation (T x, T y, T z)
	Create a translation matrix. More...

static Matrix4T< T >	makeUniformScale (const T &s)
	Create a uniform scaling matrix. More...

static Matrix4T< T >	ortho3D (T left, T right, T bottom, T top, T nearPlane, T farPlane)
	Creates an orthogonal projection matrix in 3D This function works in a way similar to glOrtho (http://lmb.informatik.uni-freiburg.de/people/reisert/opengl/doc/glOrtho.html). More...

static Matrix4T< T >	orthogonalProjection (T left, T right, T bottom, T top, T nearPlane, T farPlane)
	Creates an orthogonal projection matrix. More...

static Matrix4T< T >	perspectiveProjection (T fovY, T aspect, T nearPlane, T farPlane)
	Creates a perspective projection matrix. More...

static int	rows ()
	Returns the number of rows (4)

static Matrix4T< T >	simpleProjection (T width, T height, T fovy=Nimble::Math::PI *0.5)
	Creates a new WPCV-matrix (window-projection-camera-view -matrix) Camera is positioned so that 0,0,0 is mapped to 0,0,0 and w,h,0 is mapped to w,h,0. More...

static Matrix4T< T >	transformation (T angle, const Vector3T< T > &axis, const Vector3T< T > &scale, const Vector3T< T > &translation)
	Returns a 3d transformation matrix that does scale, rotate & translation (in this order) More...

Static Public Attributes
static const Matrix4T< T >	IDENTITY
	Identity matrix. More...

Detailed Description

template<class T>
class Nimble::Matrix4T< T >

4x4 transformation matrix

This class is a row-major 4x4 matrix. The matrix functions (rotations etc.) assume right-handed coordinate system.

Examples:: AdvancedRenderingExample.cpp, and Widget3DExample.cpp.

Member Function Documentation

template<class T >

Matrix4T< T > Nimble::Matrix4T< T >::inverse ( bool * ok = 0 ) const

inline

Returns the inverse of the matrix.

Inverts the matrix.

The boolean argument is set to true or false depending on how well the operation went.

Parameters

[out] ok (optional) false if the inversion fails, otherwise true

Returns: Inverse matrix

Examples:: PositionalSoundsExample.cpp, and Widget3DExample.cpp.

template<class T >

static Matrix4T<T> Nimble::Matrix4T< T >::makeRotation	(	T	radians,
		const Vector3T< T > &	axis
	)

inlinestatic

Create a rotation matrix.

Parameters

radians	angle in radians
axis	axis to rotate around

Returns: New rotation matrix

Examples:: Widget3DExample.cpp.

template<class T >

static Matrix4T<T> Nimble::Matrix4T< T >::makeScale ( const Vector3T< T > & v )

inlinestatic

Create a non-uniform scaling matrix.

Parameters

v	XYZ scaling factors

Returns: new Scaling matrix

template<class T >

static Matrix4T<T> Nimble::Matrix4T< T >::makeTranslation ( const Vector3T< T > & v )

inlinestatic

Create a translation matrix.

Parameters

v	Translation vector

Returns: New translation matrix

template<class T >

static Matrix4T<T> Nimble::Matrix4T< T >::makeTranslation	(	T	x,
		T	y,
		T	z
	)

inlinestatic

Create a translation matrix.

Parameters

x	Tranlation along X-axis
y	Tranlation along Y-axis
z	Tranlation along Z-axis

Returns: New translation matrix

template<class T >

static Matrix4T<T> Nimble::Matrix4T< T >::makeUniformScale ( const T & s )

inlinestatic

Create a uniform scaling matrix.

Parameters

s	Scaling factor

Returns: new Scaling matrix

template<class T >

Vector4T<T>& Nimble::Matrix4T< T >::operator[] ( int i )

inline

void setDiagonal(const Vector3T<T> &v) { m[0][0] = v[0]; m[1][1] = v[1]; m[2][2] = v[2]; m[3][3] = (T) 1.0; }

Returns the ith row

Parameters

i	row number

Returns: Reference to the row

template<class T >

const Vector4T<T>& Nimble::Matrix4T< T >::operator[] ( int i ) const

inline

Returns the ith row.

Parameters

i	row number

Returns: Const reference to the row

template<class T >

Matrix4T< T > Nimble::Matrix4T< T >::ortho3D	(	T	left,
		T	right,
		T	bottom,
		T	top,
		T	nearPlane,
		T	farPlane
	)

static

Creates an orthogonal projection matrix in 3D This function works in a way similar to glOrtho (http://lmb.informatik.uni-freiburg.de/people/reisert/opengl/doc/glOrtho.html).

Parameters

left	left clipping plane
right	right clipping plane
bottom	bottom clipping plane
top	top clipping plane
nearPlane	near clipping plane
farPlane	far clipping plane

Returns: orthogonal projection matrix

template<class T >

static Matrix4T<T> Nimble::Matrix4T< T >::orthogonalProjection	(	T	left,
		T	right,
		T	bottom,
		T	top,
		T	nearPlane,
		T	farPlane
	)

inlinestatic

Creates an orthogonal projection matrix.

Parameters

left	Left clip plane location
right	Right clip plane location
bottom	Bottom clip plane location
top	Top clip plane location
nearPlane	Near clip plane location
farPlane	Far clip plane location

Returns: New projection matrix

template<class T >

Matrix4T<T> Nimble::Matrix4T< T >::orthoNormalize ( ) const

inline

Returns an orthonormalized version of this matrix.

Returns: Normalized matrix

template<class T >

static Matrix4T<T> Nimble::Matrix4T< T >::perspectiveProjection	(	T	fovY,
		T	aspect,
		T	nearPlane,
		T	farPlane
	)

inlinestatic

Creates a perspective projection matrix.

Parameters

fovY	field of view in degress in the Y direction
aspect	aspect ratio (width / height)
nearPlane	distance to the near clipping plane, always positive
farPlane	distance to the far clipping plane, always positive

Returns: New projection matrix

Examples:: Widget3DExample.cpp.

template<class T >

Vector3T<T> Nimble::Matrix4T< T >::project ( const Vector4T< T > & v ) const

inline

Apply the matrix on a 4D vector.

Parameters

v	homogenous 3D vector

Returns: projected 3D vector

template<class T >

Vector3T<T> Nimble::Matrix4T< T >::project ( const Vector3T< T > & v ) const

inline

Apply the matrix on a 3D vector.

Parameters

v 3D vector

Returns: transformed 3D vector

template<class T >

Vector2T<T> Nimble::Matrix4T< T >::project ( const Vector2T< T > & v ) const

inline

Apply the matrix on a 2D vector which is interpreted as [x y 0 1].

Parameters

v 2D vector

Returns: transformed 2D vector

template<class T >

static Matrix4T<T> Nimble::Matrix4T< T >::simpleProjection	(	T	width,
		T	height,
		T	fovy = `Nimble::Math::PI*0.5`
	)

inlinestatic

Creates a new WPCV-matrix (window-projection-camera-view -matrix) Camera is positioned so that 0,0,0 is mapped to 0,0,0 and w,h,0 is mapped to w,h,0.

The projection matrix doesn't have the third row, no depth information, so no near/far values needed. (0,0,0) is lower left bottom, (w,h,0) is in right top, z increases towards the camera

Parameters

width	Width of the viewport
height	Height of the viewport
fovy	Field of view in y-direction in radians

Returns: New projection matrix

template<typename T >

Matrix4T< T > Nimble::Matrix4T< T >::transformation	(	T	angle,
		const Vector3T< T > &	axis,
		const Vector3T< T > &	scale,
		const Vector3T< T > &	translation
	)

inlinestatic

Returns a 3d transformation matrix that does scale, rotate & translation (in this order)

Parameters

angle	rotation angle (counter-clockwise)
axis	rotation axis (normalized)
scale	3D scale
translation	3D translation

Returns: New transformation matrix

Member Data Documentation

template<class T >

const Matrix4T< T > Nimble::Matrix4T< T >::IDENTITY

static

Identity matrix.

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

template<class T> class Nimble::Matrix4T< T >

Member Function Documentation

Member Data Documentation

template<class T>
class Nimble::Matrix4T< T >