4x4 matrix template class More...

#include <SLMat4.h>

Public Member Functions
	SLMat4 ()
	Sets identity matrix. More...

	SLMat4 (const SLMat4 &A)
	Sets mat by other SLMat4. More...

	SLMat4 (const SLMat3f &A)
	Sets mat by other SLMat3. More...

	SLMat4 (const T *M)
	Sets mat by array. More...

	SLMat4 (T M0, T M4, T M8, T M12, T M1, T M5, T M9, T M13, T M2, T M6, T M10, T M14, T M3, T M7, T M11, T M15)

	SLMat4 (T tx, T ty, T tz)
	Sets translate matrix. More...

	SLMat4 (T degAng, T axis_x, T axis_y, T axis_z)
	Sets rotation matrix. More...

	SLMat4 (T scale_xyz)
	Sets scaling matrix. More...

	SLMat4 (const SLVec3< T > &translationVec)
	Sets translate matrix. More...

	SLMat4 (const SLVec3< T > &fromUnitVec, const SLVec3< T > &toUnitVec)
	Sets rotation matrix. More...

	SLMat4 (const SLVec3< T > &translation, const SLMat3< T > &rotation, const SLVec3< T > &scale)
	Set matrix by translation, rotation & scale. More...

void	setMatrix (const SLMat4 &A)
	Set matrix by other 4x4 matrix. More...

void	setMatrix (const SLMat3f &A)
	Set matrix by other 3x3 matrix. More...

void	setMatrix (const SLMat4 *A)
	Set matrix by other matrix pointer. More...

void	setMatrix (const T *M)
	Set matrix by float[16] array. More...

void	setMatrix (T M0, T M4, T M8, T M12, T M1, T M5, T M9, T M13, T M2, T M6, T M10, T M14, T M3, T M7, T M11, T M15)
	Set matrix by components. More...

void	setMatrix (const SLVec3< T > &translation, const SLMat3< T > &rotation, const SLVec3< T > &scale)
	Set matrix by translation, rotation & scale. More...

void	setMatrix (const int16_t i, const SLfloat value)

void	setRotation (const SLMat3< T > &rotation)
	Set 3x3 submatrix describing the rotational part. More...

void	setTranslation (const SLVec3< T > &translation)
	Set vector as submatrix describing the translational part. More...

void	m (int i, T val)

const T *	m () const

T	m (int i) const

SLMat3< T >	mat3 () const

SLMat4< T > &	operator= (const SLMat4 &A)
	assignment operator More...

SLMat4< T >	operator* (const SLMat4 &A) const
	matrix-matrix multiplication More...

SLMat4< T > &	operator*= (const SLMat4 &A)
	matrix-matrix multiplication More...

SLMat4< T >	operator+ (const SLMat4 &A) const
	matrix-matrix addition More...

SLVec3< T >	operator* (const SLVec3< T > &v) const
	SLVec3 mult w. persp div. More...

SLVec4< T >	operator* (const SLVec4< T > &v) const
	SLVec4 mult. More...

SLMat4< T >	operator* (T a) const
	scalar mult More...

SLMat4< T > &	operator*= (T a)
	scalar mult More...

SLMat4< T >	operator/ (T a) const
	scalar division More...

SLMat4< T > &	operator/= (T a)
	scalar division More...

T &	operator() (int row, int col)

const T &	operator() (int row, int col) const

SLbool	isEqual (const SLMat4 &A, SLfloat epsilon=0.01f)
	Returns true if one element of the matrix differs more than epsilon. More...

void	multiply (const SLMat4 &A)

SLVec3< T >	multVec (SLVec3< T > v) const

SLVec4< T >	multVec (SLVec4< T > v) const

void	add (const SLMat4 &A)

void	translate (T tx, T ty, T tz=0)

void	translate (const SLVec2< T > &t)

void	translate (const SLVec3< T > &t)

void	rotate (T degAng, T axisx, T axisy, T axisz)

void	rotate (T degAng, const SLVec3< T > &axis)

void	rotate (const SLVec3< T > &fromUnitVec, const SLVec3< T > &toUnitVec)

void	scale (T sxyz)

void	scale (T sx, T sy, T sz)

void	scale (const SLVec3< T > &sxyz)

void	frustum (T l, T r, T b, T t, T n, T f)
	Defines a view frustum projection matrix equivalent to glFrustum. More...

void	perspective (T fov, T aspect, T n, T f)
	Defines a perspective projection matrix with a field of view angle. More...

void	perspectiveCenteredPP (T w, T h, T fx, T fy, T cx, T cy, T n, T f)
	Defines a projection matrix for a calibrated camera, the principle point has to be centered (from intrinsics matrix) More...

void	ortho (T l, T r, T b, T t, T n, T f)
	Defines a orthographic projection matrix with a field of view angle. More...

void	viewport (T x, T y, T ww, T wh, T n=0.0f, T f=1.0f)
	Defines the viewport matrix. More...

void	lookAt (T EyeX, T EyeY, T EyeZ, T AtX=0, T AtY=0, T AtZ=0, T UpX=0, T UpY=0, T UpZ=0)
	Defines the a view matrix as the corresponding gluLookAt function. More...

void	lookAt (const SLVec3< T > &Eye, const SLVec3< T > &At=SLVec3< T >::ZERO, const SLVec3< T > &Up=SLVec3< T >::ZERO)
	Defines the a view matrix as the corresponding gluLookAt function. More...

void	lookAt (SLVec3< T > eye, SLVec3< T > at, SLVec3< T > up, SLVec3< T > right) const
	Reads out of the matrix the look at parameters. More...

void	lightAt (T PosX, T PosY, T PosZ, T AtX=0, T AtY=0, T AtZ=0, T UpX=0, T UpY=0, T UpZ=0)
	Defines the a model matrix for light positioning. More...

void	lightAt (const SLVec3< T > &pos, const SLVec3< T > &At=SLVec3< T >::ZERO, const SLVec3< T > &Up=SLVec3< T >::ZERO)
	Defines the a model matrix for light positioning. More...

void	posAtUp (T PosX, T PosY, T PosZ, T dirAtX=0, T dirAtY=0, T dirAtZ=0, T dirUpX=0, T dirUpY=0, T dirUpZ=0)
	Same as lightAt. More...

void	posAtUp (const SLVec3< T > &pos, const SLVec3< T > &dirAt=SLVec3< T >::ZERO, const SLVec3< T > &dirUp=SLVec3< T >::ZERO)
	Same as lightAt. More...

SLVec3< T >	translation () const

SLVec3< T >	axisX () const

SLVec3< T >	axisY () const

SLVec3< T >	axisZ () const

void	translation (T tx, T ty, T tz, SLbool keepLinear=true)
	Sets the translation with or without overwriting the linear submatrix. More...

void	translation (const SLVec3< T > &t, SLbool keepLinear=true)

void	rotation (T degAng, const SLVec3< T > &axis, SLbool keepTranslation=true)
	Sets the rotation with or without overwriting the translation. More...

void	rotation (T degAng, T axisx, T axisy, T axisz, SLbool keepTranslation=true)

void	rotation (const SLVec3< T > &fromUnitVec, const SLVec3< T > &toUnitVec)

void	scaling (T sxyz, SLbool keepTrans=true)
	Sets the scaling with or without overwriting the translation. More...

void	scaling (const SLVec3< T > &sxyz, SLbool keepTrans=true)

void	scaling (T sx, T sy, T sz, SLbool keepTranslation=true)

void	fromEulerAnglesZXZ (double angle1RAD, double angle2RAD, double angle3RAD, bool keepTranslation=true)

void	fromEulerAnglesXYZ (double angle1RAD, double angle2RAD, double angle3RAD, bool keepTranslation=true)

void	toEulerAnglesZYX (T &zRotRAD, T &yRotRAD, T &xRotRAD)

void	toEulerAnglesXYZ (T &xRotRAD, T &yRotRAD, T &zRotRAD)

SLVec3< T >	toEulerAngles (int order)

void	identity ()
	Sets the identity matrix. More...

void	transpose ()
	Sets the transposed matrix by swaping around the main diagonal. More...

SLMat4< T >	transposed ()
	Returns the transposed of the matrix and leaves the itself unchanged. More...

void	invert ()
	Inverts the matrix. More...

SLMat4< T >	inverted () const
	Computes the inverse of a 4x4 non-singular matrix. More...

SLMat3< T >	inverseTransposed ()

T	trace () const

void	compose (SLVec3f trans, SLVec3f rotEulerRAD, SLVec3f scale)

void	decompose (SLVec3f &trans, SLVec4f &rotQuat, SLVec3f &scale)

void	decompose (SLVec3f &trans, SLMat3f &rotMat, SLVec3f &scale)

void	decompose (SLVec3f &trans, SLVec3f &rotEulerRAD, SLVec3f &scale)

void	print (const SLchar *str=nullptr) const

SLstring	toString () const

Static Public Member Functions
static void	swap (T &a, T &b)

Private Attributes
T	_m [16]
	The 16 elements of the matrix. More...

Detailed Description

template<class T>
class SLMat4< T >

4x4 matrix template class

Implements a 4 by 4 matrix template class. An array of 16 floats or double is used instead of a 2D array [4][4] to be compliant with OpenGL. The index layout is as follows:

     | 0  4  8 12 |
     | 1  5  9 13 |
 M = | 2  6 10 14 |
     | 3  7 11 15 |

Vectors are interpreted as column vectors when applying matrix multiplications. This means a vector is as a single column, 4-row matrix. The result is that the transformations implemented by the matrices happens right-to-left e.g. if vector V is to be transformed by M1 then M2 then M3, the calculation would be M3 * M2 * M1 * V. 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. The use of column vectors and right-to-left ordering is the standard in most mathematical texts, and is the same as used in OpenGL. It is, however, the opposite of Direct3D, which has inexplicably chosen to differ from the accepted standard and uses row vectors and left-to-right matrix multiplication.

Constructor & Destructor Documentation

◆ SLMat4() [1/11]

template<class T >

SLMat4< T >::SLMat4

Sets identity matrix.

◆ SLMat4() [2/11]

template<class T >

SLMat4< T >::SLMat4 ( const SLMat4< T > & A )

Sets mat by other SLMat4.

◆ SLMat4() [3/11]

template<class T >

SLMat4< T >::SLMat4 ( const SLMat3f & A )

Sets mat by other SLMat3.

◆ SLMat4() [4/11]

template<class T >

SLMat4< T >::SLMat4 ( const T * M )

Sets mat by array.

◆ SLMat4() [5/11]

template<class T >

SLMat4< T >::SLMat4	(	T	M0,
		T	M4,
		T	M8,
		T	M12,
		T	M1,
		T	M5,
		T	M9,
		T	M13,
		T	M2,
		T	M6,
		T	M10,
		T	M14,
		T	M3,
		T	M7,
		T	M11,
		T	M15
	)

◆ SLMat4() [6/11]

template<class T >

SLMat4< T >::SLMat4	(	T	tx,
		T	ty,
		T	tz
	)

Sets translate matrix.

◆ SLMat4() [7/11]

template<class T >

SLMat4< T >::SLMat4	(	T	degAng,
		T	axis_x,
		T	axis_y,
		T	axis_z
	)

explicit

Sets rotation matrix.

◆ SLMat4() [8/11]

template<class T >

SLMat4< T >::SLMat4 ( T scale_xyz )

explicit

Sets scaling matrix.

◆ SLMat4() [9/11]

template<class T >

SLMat4< T >::SLMat4 ( const SLVec3< T > & translationVec )

explicit

Sets translate matrix.

◆ SLMat4() [10/11]

template<class T >

SLMat4< T >::SLMat4	(	const SLVec3< T > &	fromUnitVec,
		const SLVec3< T > &	toUnitVec
	)

Sets rotation matrix.

◆ SLMat4() [11/11]

template<class T >

SLMat4< T >::SLMat4	(	const SLVec3< T > &	translation,
		const SLMat3< T > &	rotation,
		const SLVec3< T > &	scale
	)

Set matrix by translation, rotation & scale.

Member Function Documentation

◆ add()

template<class T >

void SLMat4< T >::add ( const SLMat4< T > & A )

Adds the matrix to an other matrix A.

◆ axisX()

template<class T >

SLVec3< T > SLMat4< T >::axisX ( ) const

inline

◆ axisY()

template<class T >

SLVec3< T > SLMat4< T >::axisY ( ) const

inline

◆ axisZ()

template<class T >

SLVec3< T > SLMat4< T >::axisZ ( ) const

inline

◆ compose()

template<class T >

void SLMat4< T >::compose	(	SLVec3f	trans,
		SLVec3f	rotEulerRAD,
		SLVec3f	scale
	)

Composes the matrix from a translation vector, a rotation Euler angle vector and the scaling factors.

◆ decompose() [1/3]

template<class T >

void SLMat4< T >::decompose	(	SLVec3f &	trans,
		SLMat3f &	rotMat,
		SLVec3f &	scale
	)

Decomposes the matrix into a translation vector, a 3x3 rotation matrix and the scaling factors using polar decomposition introduced by Ken Shoemake. See the paper in lib-SLExternal/Shoemake/polar-decomp.pdf

◆ decompose() [2/3]

template<class T >

void SLMat4< T >::decompose	(	SLVec3f &	trans,
		SLVec3f &	rotEulerRAD,
		SLVec3f &	scale
	)

Decomposes the matrix into a translation vector, a rotation Euler angle vector and the scaling factors using polar decomposition introduced by Ken Shoemake. See the paper in lib-SLExternal/Shoemake/polar-decomp.pdf

◆ decompose() [3/3]

template<class T >

void SLMat4< T >::decompose	(	SLVec3f &	trans,
		SLVec4f &	rotQuat,
		SLVec3f &	scale
	)

Decomposes the matrix into a translation vector, a rotation quaternion and the scaling factors using polar decomposition introduced by Ken Shoemake. See the paper in lib-SLExternal/Shoemake/polar-decomp.pdf

◆ fromEulerAnglesXYZ()

template<class T >

void SLMat4< T >::fromEulerAnglesXYZ	(	double	angle1RAD,
		double	angle2RAD,
		double	angle3RAD,
		bool	keepTranslation = `true`
	)

Sets the linear 3x3 submatrix as a rotation matrix from the 3 euler angles in radians around the z-axis, y-axis & x-axis. By default the translation components are set to 0. See: http://en.wikipedia.org/wiki/Euler_angles

◆ fromEulerAnglesZXZ()

template<class T >

void SLMat4< T >::fromEulerAnglesZXZ	(	double	angle1RAD,
		double	angle2RAD,
		double	angle3RAD,
		bool	keepTranslation = `true`
	)

Sets the linear 3x3 submatrix as a rotation matrix from the 3 euler angles in radians around the z-axis, x-axis & z-axis. By default the translation components are set to 0. See: http://en.wikipedia.org/wiki/Euler_angles

◆ frustum()

template<class T >

void SLMat4< T >::frustum	(	T	l,
		T	r,
		T	b,
		T	t,
		T	n,
		T	f
	)

Defines a view frustum projection matrix equivalent to glFrustum.

Defines a view frustum projection matrix equivalent to OpenGL's glFrustum.

The view frustum is the truncated view pyramid of a central projection that is defined with the folowing parameters:

Parameters

l	Distance from the center of projection (COP) to the left border on the near clipping plane.
r	Distance from the COP to the right border on the near clipping plane.
b	Distance from the COP to the bottom border on the near clipping plane.
t	Distance from the COP to the top border on the near clipping plane.
n	Distance from the eye to near clipping plane of the view frustum.
f	Distance from the eye to far clipping plane of the view frustum.

◆ identity()

template<class T >

void SLMat4< T >::identity

Sets the identity matrix.

◆ inverseTransposed()

template<class T >

SLMat3< T > SLMat4< T >::inverseTransposed

Computes the inverse transposed matrix of the upper left 3x3 matrix for the transformation of vertex normals.

◆ invert()

template<class T >

void SLMat4< T >::invert

Inverts the matrix.

◆ inverted()

template<class T >

SLMat4< T > SLMat4< T >::inverted

Computes the inverse of a 4x4 non-singular matrix.

◆ isEqual()

template<class T >

SLbool SLMat4< T >::isEqual	(	const SLMat4< T > &	A,
		SLfloat	epsilon = `0.01f`
	)

Returns true if one element of the matrix differs more than epsilon.

◆ lightAt() [1/2]

template<class T >

void SLMat4< T >::lightAt	(	const SLVec3< T > &	pos,
		const SLVec3< T > &	At = `SLVec3<T>::ZERO`,
		const SLVec3< T > &	Up = `SLVec3<T>::ZERO`
	)

Defines the a model matrix for light positioning.

Defines the a model matrix for positioning a light source.

Utility method for defining the transformation matrix for a spot light. There is no equivalent function for this purpose in OpenGL. /param pos Vector to the position of the light source. /param At Vector to a target point where a spot light shines to.

◆ lightAt() [2/2]

template<class T >

void SLMat4< T >::lightAt	(	T	PosX,
		T	PosY,
		T	PosZ,
		T	AtX = `0`,
		T	AtY = `0`,
		T	AtZ = `0`,
		T	UpX = `0`,
		T	UpY = `0`,
		T	UpZ = `0`
	)

Defines the a model matrix for light positioning.

Defines the a model matrix for positioning a light at pos and shining at At

◆ lookAt() [1/3]

template<class T >

void SLMat4< T >::lookAt	(	const SLVec3< T > &	Eye,
		const SLVec3< T > &	At = `SLVec3<T>::ZERO`,
		const SLVec3< T > &	Up = `SLVec3<T>::ZERO`
	)

Defines the a view matrix as the corresponding gluLookAt function.

Defines the view matrix with an eye position, a look at point and an up vector.

This method is equivalent to the OpenGL function gluLookAt.

Parameters

Eye	Vector to the position of the eye (view point).
At	Vector to the target point.
Up	Vector that points from the viewpoint upwards. If Up is a zero vector a default up vector is calculated with a default look-right vector (VZ) that lies in the x-z plane.

◆ lookAt() [2/3]

template<class T >

void SLMat4< T >::lookAt	(	SLVec3< T > *	eye,
		SLVec3< T > *	at,
		SLVec3< T > *	up,
		SLVec3< T > *	ri
	)		const

Reads out of the matrix the look at parameters.

This method retrieves the eye position the look at, up & right vector out of the view matrix. Attention: The look-at is normalized vector, not a point.

◆ lookAt() [3/3]

template<class T >

void SLMat4< T >::lookAt	(	T	EyeX,
		T	EyeY,
		T	EyeZ,
		T	AtX = `0`,
		T	AtY = `0`,
		T	AtZ = `0`,
		T	UpX = `0`,
		T	UpY = `0`,
		T	UpZ = `0`
	)

Defines the a view matrix as the corresponding gluLookAt function.

Defines the view matrix with an eye position, a look at point and an up vector.

This method is equivalent to the OpenGL function gluLookAt.

◆ m() [1/3]

template<class T >

const T * SLMat4< T >::m ( ) const

inline

◆ m() [2/3]

template<class T >

T SLMat4< T >::m ( int i ) const

inline

◆ m() [3/3]

template<class T >

void SLMat4< T >::m	(	int	i,
		T	val
	)

inline

◆ mat3()

template<class T >

SLMat3< T > SLMat4< T >::mat3 ( ) const

inline

◆ multiply()

template<class T >

void SLMat4< T >::multiply ( const SLMat4< T > & A )

Multiplies the matrix with a another matrix. Corresponds to the OpenGL function glMultMatrix*.

◆ multVec() [1/2]

template<class T >

SLVec3< T > SLMat4< T >::multVec ( SLVec3< T > v ) const

Matrix - 3D vector multiplication with perspective division

◆ multVec() [2/2]

template<class T >

SLVec4< T > SLMat4< T >::multVec ( SLVec4< T > v ) const

Matrix - 4D vector multiplication

◆ operator()() [1/2]

template<class T >

T & SLMat4< T >::operator()	(	int	row,
		int	col
	)

inline

◆ operator()() [2/2]

template<class T >

const T & SLMat4< T >::operator()	(	int	row,
		int	col
	)		const

inline

◆ operator*() [1/4]

template<class T >

SLMat4< T > SLMat4< T >::operator* ( const SLMat4< T > & A ) const

matrix-matrix multiplication

Matrix - matrix multiplication

◆ operator*() [2/4]

template<class T >

SLVec3< T > SLMat4< T >::operator* ( const SLVec3< T > & v ) const

SLVec3 mult w. persp div.

Matrix - 3D vector multiplication with perspective division

◆ operator*() [3/4]

template<class T >

SLVec4< T > SLMat4< T >::operator* ( const SLVec4< T > & v ) const

SLVec4 mult.

Matrix - 4D vector multiplication

◆ operator*() [4/4]

template<class T >

SLMat4< T > SLMat4< T >::operator* ( T a ) const

scalar mult

Scalar multiplication.

◆ operator*=() [1/2]

template<class T >

SLMat4< T > & SLMat4< T >::operator*= ( const SLMat4< T > & A )

matrix-matrix multiplication

◆ operator*=() [2/2]

template<class T >

SLMat4< T > & SLMat4< T >::operator*= ( T a )

scalar mult

Scalar multiplication.

◆ operator+()

template<class T >

SLMat4< T > SLMat4< T >::operator+ ( const SLMat4< T > & A ) const

matrix-matrix addition

◆ operator/()

template<class T >

SLMat4< T > SLMat4< T >::operator/ ( T a ) const

scalar division

Scalar division.

◆ operator/=()

template<class T >

SLMat4< T > & SLMat4< T >::operator/= ( T a )

scalar division

Scalar division.

◆ operator=()

template<class T >

SLMat4< T > & SLMat4< T >::operator= ( const SLMat4< T > & A )

assignment operator

Matrix assignment with instance

◆ ortho()

template<class T >

void SLMat4< T >::ortho	(	T	l,
		T	r,
		T	b,
		T	t,
		T	n,
		T	f
	)

Defines a orthographic projection matrix with a field of view angle.

Defines a ortographic projection matrix equivalent to OpenGL's glOrtho.

Parameters

l	Distance from the center of projection (COP) to the left border on the near clipping plane.
r	Distance from the COP to the right border on the near clipping plane.
b	Distance from the COP to the bottom border on the near clipping plane.
t	Distance from the COP to the top border on the near clipping plane.
n	Distance from the eye to near clipping plane of the view frustum.
f	Distance from the eye to far clipping plane of the view frustum.

◆ perspective()

template<class T >

void SLMat4< T >::perspective	(	T	fov,
		T	aspect,
		T	n,
		T	f
	)

Defines a perspective projection matrix with a field of view angle.

Defines a view frustum projection matrix for a perspective projection.

This method is equivalent to the OpenGL function gluPerspective except that instead of the window aspect the window width and height have to be passed.

Parameters

fov	Vertical field of view angle (zoom angle)
aspect	aspect ratio of of the viewport = width / height
n	Distance from the eye to near clipping plane of the view frustum.
f	Distance from the eye to far clipping plane of the view frustum.

◆ perspectiveCenteredPP()

template<class T >

void SLMat4< T >::perspectiveCenteredPP	(	T	w,
		T	h,
		T	fx,
		T	fy,
		T	cx,
		T	cy,
		T	n,
		T	f
	)

Defines a projection matrix for a calibrated camera, the principle point has to be centered (from intrinsics matrix)

Defines a projection matrix for a calibrated camera (from intrinsics matrix) Attention: The principle point has to be centered

This should give an exact result. http://kgeorge.github.io/2014/03/08/calculating-opengl-perspective-matrix-from-opencv-intrinsic-matrix (see also https://stackoverflow.com/questions/22064084/how-to-create-perspective-projection-matrix-given-focal-points-and-camera-princ but the other solutions did not work as well)

◆ posAtUp() [1/2]

template<class T >

void SLMat4< T >::posAtUp	(	const SLVec3< T > &	pos,
		const SLVec3< T > &	dirAt = `SLVec3<T>::ZERO`,
		const SLVec3< T > &	dirUp = `SLVec3<T>::ZERO`
	)

Same as lightAt.

◆ posAtUp() [2/2]

template<class T >

void SLMat4< T >::posAtUp	(	T	PosX,
		T	PosY,
		T	PosZ,
		T	dirAtX = `0`,
		T	dirAtY = `0`,
		T	dirAtZ = `0`,
		T	dirUpX = `0`,
		T	dirUpY = `0`,
		T	dirUpZ = `0`
	)

Same as lightAt.

◆ print()

template<class T >

void SLMat4< T >::print ( const SLchar * str = nullptr ) const

Prints out the matrix row by row.

◆ rotate() [1/3]

template<class T >

void SLMat4< T >::rotate	(	const SLVec3< T > &	fromUnitVec,
		const SLVec3< T > &	toUnitVec
	)

Multiplies the matrix with a rotation matrix created with a rotation between two vectors.

◆ rotate() [2/3]

template<class T >

void SLMat4< T >::rotate	(	T	degAng,
		const SLVec3< T > &	axis
	)

Multiplies the matrix with a rotation matrix. Corresponds to the OpenGL function glRotate*.

◆ rotate() [3/3]

template<class T >

void SLMat4< T >::rotate	(	T	degAng,
		T	axisx,
		T	axisy,
		T	axisz
	)

Multiplies the matrix with a rotation matrix. Corresponds to the OpenGL function glRotate*.

◆ rotation() [1/3]

template<class T >

void SLMat4< T >::rotation	(	const SLVec3< T > &	from,
		const SLVec3< T > &	to
	)

Defines a rotation matrix that rotates the vector from to the vector to. Code and explanation comes from the paper "Efficiently build a matrix to ratate one vector to another" from Thomas Mueller and John Hughes in the Journal of Graphic Tools, volume 4.

◆ rotation() [2/3]

template<class T >

void SLMat4< T >::rotation	(	T	degAng,
		const SLVec3< T > &	axis,
		SLbool	keepTranslation = `true`
	)

Sets the rotation with or without overwriting the translation.

Sets the linear 3x3 submatrix as a rotation matrix with a rotation of degAng degrees around an axis. By default the translation components are set to 0.

◆ rotation() [3/3]

template<class T >

void SLMat4< T >::rotation	(	T	degAng,
		T	axisx,
		T	axisy,
		T	axisz,
		SLbool	keepTranslation = `true`
	)

Sets the linear 3x3 submatrix as a rotation matrix with a rotation of degAng degrees around an axis. By default the translation components are set to 0.

◆ scale() [1/3]

template<class T >

void SLMat4< T >::scale ( const SLVec3< T > & s )

Multiplies the matrix with a scaling matrix. Corresponds to the OpenGL function glScale*.

◆ scale() [2/3]

template<class T >

void SLMat4< T >::scale	(	T	sx,
		T	sy,
		T	sz
	)

Multiplies the matrix with a scaling matrix. Corresponds to the OpenGL function glScale*.

◆ scale() [3/3]

template<class T >

void SLMat4< T >::scale ( T sxyz )

Multiplies the matrix with a scaling matrix. Corresponds to the OpenGL function glScale*.

◆ scaling() [1/3]

template<class T >

void SLMat4< T >::scaling	(	const SLVec3< T > &	scale,
		SLbool	keepTrans = `true`
	)

Sets the linear 3x3 submatrix as a scaling matrix with the scaling vector s. By default the translation components are set to 0.

◆ scaling() [2/3]

template<class T >

void SLMat4< T >::scaling	(	T	sx,
		T	sy,
		T	sz,
		SLbool	keepTranslation = `true`
	)

Sets the linear 3x3 submatrix as a scaling matrix with the scaling f_actors sx, sy and sz. By default the translation components are set to 0.

◆ scaling() [3/3]

template<class T >

void SLMat4< T >::scaling	(	T	sxyz,
		SLbool	keepTrans = `true`
	)

Sets the scaling with or without overwriting the translation.

Sets the linear 3x3 submatrix as a scaling matrix with the scaling vector s. By default the translation components are set to 0.

◆ setMatrix() [1/7]

template<class T >

void SLMat4< T >::setMatrix	(	const int16_t	i,
		const SLfloat	value
	)

inline

◆ setMatrix() [2/7]

template<class T >

void SLMat4< T >::setMatrix ( const SLMat3f & A )

Set matrix by other 3x3 matrix.

◆ setMatrix() [3/7]

template<class T >

void SLMat4< T >::setMatrix ( const SLMat4< T > & A )

Set matrix by other 4x4 matrix.

◆ setMatrix() [4/7]

template<class T >

void SLMat4< T >::setMatrix ( const SLMat4< T > * A )

Set matrix by other matrix pointer.

◆ setMatrix() [5/7]

template<class T >

void SLMat4< T >::setMatrix	(	const SLVec3< T > &	translation,
		const SLMat3< T > &	rotation,
		const SLVec3< T > &	scale
	)

Set matrix by translation, rotation & scale.

◆ setMatrix() [6/7]

template<class T >

void SLMat4< T >::setMatrix ( const T * M )

Set matrix by float[16] array.

◆ setMatrix() [7/7]

template<class T >

void SLMat4< T >::setMatrix	(	T	M0,
		T	M4,
		T	M8,
		T	M12,
		T	M1,
		T	M5,
		T	M9,
		T	M13,
		T	M2,
		T	M6,
		T	M10,
		T	M14,
		T	M3,
		T	M7,
		T	M11,
		T	M15
	)

Set matrix by components.

◆ setRotation()

template<class T >

void SLMat4< T >::setRotation ( const SLMat3< T > & rotation )

Set 3x3 submatrix describing the rotational part.

Parameters

rotation Set 3x3 submatrix describing the rotational part

◆ setTranslation()

template<class T >

void SLMat4< T >::setTranslation ( const SLVec3< T > & translation )

Set vector as submatrix describing the translational part.

Parameters

translation Set vector as submatrix describing the translational part

◆ swap()

template<class T >

static void SLMat4< T >::swap	(	T &	a,
		T &	b
	)

inlinestatic

◆ toEulerAngles()

template<class T >

SLVec3< T > SLMat4< T >::toEulerAngles ( int order )

◆ toEulerAnglesXYZ()

template<class T >

void SLMat4< T >::toEulerAnglesXYZ	(	T &	xRotRAD,
		T &	yRotRAD,
		T &	zRotRAD
	)

Gets one set of possible x-y-z euler angles that will generate this matrix Assumes that upper 3x3 is a rotation matrix Source: Essential Mathematics for Games and Interactive Applications A Programmer's Guide 2nd edition by James M. Van Verth and Lars M. Bishop

◆ toEulerAnglesZYX()

template<class T >

void SLMat4< T >::toEulerAnglesZYX	(	T &	zRotRAD,
		T &	yRotRAD,
		T &	xRotRAD
	)

Gets one set of possible z-y-x euler angles that will generate this matrix Assumes that upper 3x3 is a rotation matrix Source: Essential Mathematics for Games and Interactive Applications A Programmer's Guide 2nd edition by James M. Van Verth and Lars M. Bishop

◆ toString()

template<class T >

SLstring SLMat4< T >::toString

Prints out the matrix row by row.

◆ trace()

template<class T >

T SLMat4< T >::trace

inline

Returns the trace of the matrix that is the sum of the diagonal components.

◆ translate() [1/3]

template<class T >

void SLMat4< T >::translate ( const SLVec2< T > & t )

Multiplies the matrix with a translation matrix. Corresponds to the OpenGL function glTranslate*.

◆ translate() [2/3]

template<class T >

void SLMat4< T >::translate ( const SLVec3< T > & t )

Multiplies the matrix with a translation matrix. Corresponds to the OpenGL function glTranslate*.

◆ translate() [3/3]

template<class T >

void SLMat4< T >::translate	(	T	tx,
		T	ty,
		T	tz = `0`
	)

Multiplies the matrix with a translation matrix. Corresponds to the OpenGL function glTranslate*.

◆ translation() [1/3]

template<class T >

SLVec3< T > SLMat4< T >::translation ( ) const

inline

◆ translation() [2/3]

template<class T >

void SLMat4< T >::translation	(	const SLVec3< T > &	t,
		SLbool	keepLinear = `true`
	)

Sets the translation components. By default the linear 3x3 submatrix containing rotations and scaling is reset to identity.

◆ translation() [3/3]

template<class T >

void SLMat4< T >::translation	(	T	tx,
		T	ty,
		T	tz,
		SLbool	keepLinear = `true`
	)

Sets the translation with or without overwriting the linear submatrix.

Sets the translation components. By default the linear 3x3 submatrix containing rotations and scaling is reset to identity.

◆ transpose()

template<class T >

void SLMat4< T >::transpose

Sets the transposed matrix by swaping around the main diagonal.

◆ transposed()

template<class T >

SLMat4< T > SLMat4< T >::transposed

Returns the transposed of the matrix and leaves the itself unchanged.

◆ viewport()

template<class T >

void SLMat4< T >::viewport	(	T	x,
		T	y,
		T	ww,
		T	wh,
		T	n = `0.0f`,
		T	f = `1.0f`
	)

Defines the viewport matrix.

Defines a viewport matrix as it will be produced by glViewport.

Parameters

x	left window coord. in px.
y	top window coord. in px.
ww	window width in px.
wh	window height in px.
n	near depth range (default 0)
f	far depth range (default 1)

Member Data Documentation

◆ _m

template<class T >

T SLMat4< T >::_m[16]

private

The 16 elements of the matrix.

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

SLMat4.h

Public Member Functions

Static Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ SLMat4() [1/11]

◆ SLMat4() [2/11]

◆ SLMat4() [3/11]

◆ SLMat4() [4/11]

◆ SLMat4() [5/11]

◆ SLMat4() [6/11]

◆ SLMat4() [7/11]

◆ SLMat4() [8/11]

◆ SLMat4() [9/11]

◆ SLMat4() [10/11]

◆ SLMat4() [11/11]

Member Function Documentation

◆ add()

◆ axisX()

◆ axisY()

◆ axisZ()

◆ compose()

◆ decompose() [1/3]

◆ decompose() [2/3]

◆ decompose() [3/3]

◆ fromEulerAnglesXYZ()

◆ fromEulerAnglesZXZ()

◆ frustum()

◆ identity()

◆ inverseTransposed()

◆ invert()

◆ inverted()

◆ isEqual()

◆ lightAt() [1/2]

◆ lightAt() [2/2]

◆ lookAt() [1/3]

◆ lookAt() [2/3]

◆ lookAt() [3/3]

◆ m() [1/3]

◆ m() [2/3]

◆ m() [3/3]

◆ mat3()

◆ multiply()

◆ multVec() [1/2]

◆ multVec() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/4]

◆ operator*() [2/4]

◆ operator*() [3/4]

◆ operator*() [4/4]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator/()

◆ operator/=()

◆ operator=()

◆ ortho()

◆ perspective()

◆ perspectiveCenteredPP()

◆ posAtUp() [1/2]

◆ posAtUp() [2/2]

◆ print()

◆ rotate() [1/3]

◆ rotate() [2/3]

◆ rotate() [3/3]

◆ rotation() [1/3]

◆ rotation() [2/3]

◆ rotation() [3/3]

◆ scale() [1/3]

◆ scale() [2/3]

◆ scale() [3/3]

◆ scaling() [1/3]

◆ scaling() [2/3]

◆ scaling() [3/3]

◆ setMatrix() [1/7]

◆ setMatrix() [2/7]

◆ setMatrix() [3/7]

◆ setMatrix() [4/7]

◆ setMatrix() [5/7]