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.

Definition at line 51 of file SLMat4.h.

Constructor & Destructor Documentation

◆ SLMat4() [1/11]

template<class T >

SLMat4< T >::SLMat4

Sets identity matrix.

Definition at line 262 of file SLMat4.h.

263 { identity();

264 }

SLMat4::identity

void identity()

Sets the identity matrix.

Definition: SLMat4.h:1333

◆ SLMat4() [2/11]

template<class T >

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

Sets mat by other SLMat4.

Definition at line 267 of file SLMat4.h.

268 { setMatrix(A);

269 }

SLMat4::setMatrix

void setMatrix(const SLMat4 &A)

Set matrix by other 4x4 matrix.

Definition: SLMat4.h:335

◆ SLMat4() [3/11]

template<class T >

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

Sets mat by other SLMat3.

Definition at line 272 of file SLMat4.h.

273 { setMatrix(A);

274 }

◆ SLMat4() [4/11]

template<class T >

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

Sets mat by array.

Definition at line 289 of file SLMat4.h.

 {
     setMatrix(M);
 }

◆ 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
	)

Definition at line 277 of file SLMat4.h.

 {
     setMatrix(M0, M4, M8, M12,
               M1, M5, M9, M13,
               M2, M6, M10,M14,
               M3, M7, M11,M15);
 }

◆ SLMat4() [6/11]

template<class T >

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

Sets translate matrix.

Definition at line 295 of file SLMat4.h.

 {
     translation(tx, ty, tz, false);
 }

◆ SLMat4() [7/11]

template<class T >

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

explicit

Sets rotation matrix.

Definition at line 307 of file SLMat4.h.

 {   
     rotation(degAng, ax, ay, az, false);
 }

◆ SLMat4() [8/11]

template<class T >

SLMat4< T >::SLMat4 ( T scale_xyz )

explicit

Sets scaling matrix.

Definition at line 313 of file SLMat4.h.

 {
     scaling(scale_xyz);
 }

◆ SLMat4() [9/11]

template<class T >

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

explicit

Sets translate matrix.

Definition at line 301 of file SLMat4.h.

 {
     translation(translationVec.x, translationVec.y, translationVec.z, false);
 }

◆ SLMat4() [10/11]

template<class T >

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

Sets rotation matrix.

Definition at line 319 of file SLMat4.h.

 {
     rotation(fromUnitVec, toUnitVec);
 }

◆ 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.

Definition at line 325 of file SLMat4.h.

 {
     setMatrix(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.

Definition at line 566 of file SLMat4.h.

 {
     for (SLint i = 0; i < 16; ++i)
         _m[i] = _m[i] + A._m[i];
 }

◆ axisX()

template<class T >

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

inline

Definition at line 185 of file SLMat4.h.

185 {return SLVec3<T>(_m[ 0], _m[ 1], _m[ 2]);}

SLVec3

3D vector template class for standard 3D vector algebra.

Definition: SLVec3.h:40

◆ axisY()

template<class T >

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

inline

Definition at line 186 of file SLMat4.h.

186 {return SLVec3<T>(_m[ 4], _m[ 5], _m[ 6]);}

◆ axisZ()

template<class T >

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

inline

Definition at line 187 of file SLMat4.h.

187 {return SLVec3<T>(_m[ 8], _m[ 9], _m[10]);}

◆ 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.

Definition at line 1468 of file SLMat4.h.

 {  
     fromEulerAnglesXYZ(rotEulerRAD.x, rotEulerRAD.y, rotEulerRAD.z);
     scale(scaleFactors);
     translate(trans);
 }

◆ 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

Definition at line 1506 of file SLMat4.h.

 {  
     SLVec4f rotQuat;
     decompose(trans, rotQuat, scale);
  
     // Convert quaternion to 3x3 matrix
     SLfloat qx = rotQuat.x;
     SLfloat qy = rotQuat.y;
     SLfloat qz = rotQuat.z;
     SLfloat qw = rotQuat.w;
  
     SLfloat  x2 = qx * 2.0f;  
     SLfloat  y2 = qy * 2.0f;  
     SLfloat  z2 = qz * 2.0f;
  
     SLfloat wx2 = qw * x2;  SLfloat wy2 = qw * y2;  SLfloat wz2 = qw * z2;
     SLfloat xx2 = qx * x2;  SLfloat xy2 = qx * y2;  SLfloat xz2 = qx * z2;
     SLfloat yy2 = qy * y2;  SLfloat yz2 = qy * z2;  SLfloat zz2 = qz * z2;
  
     rotMat.setMatrix(1.0f-(yy2 + zz2),       xy2 - wz2 ,       xz2 + wy2,
                             xy2 + wz2 , 1.0f-(xx2 + zz2),       yz2 - wx2,
                             xz2 - wy2 ,       yz2 + wx2 , 1.0f-(xx2 + yy2));
 }

◆ 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

Definition at line 1536 of file SLMat4.h.

 {  
     SLMat3f rotMat;
     decompose(trans, rotMat, scale);
  
     SLfloat rotAngleXRAD, rotAngleYRAD, rotAngleZRAD;
     rotMat.toEulerAnglesXYZ(rotAngleXRAD, rotAngleYRAD, rotAngleZRAD);
  
     rotEulerRAD.set(rotAngleXRAD, rotAngleYRAD, rotAngleZRAD);
 }

◆ 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

Definition at line 1483 of file SLMat4.h.

 {  
     // Input matrix A
     HMatrix A;
     A[0][0]=_m[0]; A[0][1]=_m[4]; A[0][2]=_m[ 8]; A[0][3]=_m[12]; 
     A[1][0]=_m[1]; A[1][1]=_m[5]; A[1][2]=_m[ 9]; A[1][3]=_m[13]; 
     A[2][0]=_m[2]; A[2][1]=_m[6]; A[2][2]=_m[10]; A[2][3]=_m[14]; 
     A[3][0]=_m[3]; A[3][1]=_m[7]; A[3][2]=_m[11]; A[3][3]=_m[15]; 
  
     AffineParts parts;
     decomp_affine(A, &parts);
  
     trans.set(parts.t.x, parts.t.y, parts.t.z);
     scale.set(parts.k.x, parts.k.y, parts.k.z);
     rotQuat.set(parts.q.x, parts.q.y, parts.q.z, parts.q.w);
 }

◆ 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

Definition at line 1214 of file SLMat4.h.

 {
     double s1 = sin(angle1RAD), c1 = cos(angle1RAD);
     double s2 = sin(angle2RAD), c2 = cos(angle2RAD);
     double s3 = sin(angle3RAD), c3 = cos(angle3RAD);
  
     _m[0]=(T) (c2*c3);              _m[4]=(T)-(c2*s3);              _m[8] =(T) s2;
     _m[1]=(T) (s1*s2*c3) + (c1*s3); _m[5]=(T)-(s1*s2*s3) + (c1*c3); _m[9] =(T)-(s1*c2);
     _m[2]=(T)-(c1*s2*c3) + (s1*s3); _m[6]=(T) (c1*s2*s3) + (s1*c3); _m[10]=(T) (c1*c2);
  
     _m[3]=_m[7]=_m[11]=0; _m[15]=1;
  
     if (!keepTrans)
     {  _m[12] = _m[13] = _m[14] = 0;
     }
 }

◆ 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

Definition at line 1187 of file SLMat4.h.

 {
     double s1 = sin(angle1RAD), c1 = cos(angle1RAD);
     double s2 = sin(angle2RAD), c2 = cos(angle2RAD);
     double s3 = sin(angle3RAD), c3 = cos(angle3RAD);
  
     _m[0]=(T)( c1*c3 - s1*c2*s3); _m[4]=(T)( s1*c3 + c1*c2*s3);  _m[8] =(T)( s2*s3);
     _m[1]=(T)(-c1*s3 - s1*c2*c3); _m[5]=(T)( c1*c2*c3 - s1*s3);  _m[9] =(T)( s2*c3);
     _m[2]=(T)( s1*s2);            _m[6]=(T)(-c1*s2);             _m[10]=(T)( c2);
  
     _m[3]=_m[7]=_m[11]=0; _m[15]=1;
  
     if (!keepTrans)
     {  _m[12] = _m[13] = _m[14] = 0;
     }
 }

◆ 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.

Definition at line 855 of file SLMat4.h.

 {
     _m[0]=2*n/(r-l); _m[4]=0;         _m[8] = (r+l)/(r-l); _m[12]=0;
     _m[1]=0;         _m[5]=2*n/(t-b); _m[9] = (t+b)/(t-b); _m[13]=0;
     _m[2]=0;         _m[6]=0;         _m[10]=-(f+n)/(f-n); _m[14]=-2*f*n/(f-n);
     _m[3]=0;         _m[7]=0;         _m[11]=-1;           _m[15]=0;
 }

◆ identity()

template<class T >

void SLMat4< T >::identity

Sets the identity matrix.

Definition at line 1333 of file SLMat4.h.

 {
     _m[0]=_m[5]=_m[10]=_m[15]=1;
     _m[1]=_m[2]=_m[3]=_m[4]=_m[6]=_m[7]=_m[8]=_m[9]=_m[11]=_m[12]=_m[13]=_m[14]=0;
 }

◆ 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.

Definition at line 1441 of file SLMat4.h.

 {
     SLMat3<T> i(_m[0], _m[4], _m[8],
                 _m[1], _m[5], _m[9],
                 _m[2], _m[6], _m[10]);
     i.invert();
     i.transpose();
     return i;
 }

◆ invert()

template<class T >

void SLMat4< T >::invert

Inverts the matrix.

Definition at line 1364 of file SLMat4.h.

 {
     setMatrix(inverted());
 }

◆ inverted()

template<class T >

SLMat4< T > SLMat4< T >::inverted

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

Definition at line 1371 of file SLMat4.h.

 {
     SLMat4<T> i;
    
     // Code from Mesa-2.2\src\glu\project.c
     T det, d12, d13, d23, d24, d34, d41;
  
     // Inverse = adjoint / det. (See linear algebra texts.)
     // pre-compute 2x2 dets for last two rows when computing
     // cof_actors of first two rows.
     d12 = ( _m[2]*_m[ 7] - _m[ 3]*_m[ 6]);
     d13 = ( _m[2]*_m[11] - _m[ 3]*_m[10]);
     d23 = ( _m[6]*_m[11] - _m[ 7]*_m[10]);
     d24 = ( _m[6]*_m[15] - _m[ 7]*_m[14]);
     d34 = (_m[10]*_m[15] - _m[11]*_m[14]);
     d41 = (_m[14]*_m[ 3] - _m[15]*_m[ 2]);
  
     i._m[0] =  (_m[5]*d34 - _m[9]*d24 + _m[13]*d23);
     i._m[1] = -(_m[1]*d34 + _m[9]*d41 + _m[13]*d13);
     i._m[2] =  (_m[1]*d24 + _m[5]*d41 + _m[13]*d12);
     i._m[3] = -(_m[1]*d23 - _m[5]*d13 + _m[ 9]*d12);
  
     // Compute determinant as early as possible using these cof_actors.
     det = _m[0]*i._m[0] + _m[4]*i._m[1] + _m[8]*i._m[2] + _m[12]*i._m[3];
  
     // Run singularity test.
     if (fabs(det) < FLT_EPSILON) 
     {
         SL_LOG("4x4-Matrix is singular. Inversion impossible.");
         exit(-1);
     }
     else
     {
         T invDet = 1 / det;
         // Compute rest of inverse.
         i._m[0] *= invDet;
         i._m[1] *= invDet;
         i._m[2] *= invDet;
         i._m[3] *= invDet;
  
         i._m[4] = -(_m[4]*d34 - _m[8]*d24 + _m[12]*d23)*invDet;
         i._m[5] =  (_m[0]*d34 + _m[8]*d41 + _m[12]*d13)*invDet;
         i._m[6] = -(_m[0]*d24 + _m[4]*d41 + _m[12]*d12)*invDet;
         i._m[7] =  (_m[0]*d23 - _m[4]*d13 +  _m[8]*d12)*invDet;
  
         // Pre-compute 2x2 dets for first two rows when computing
         // cofactors of last two rows.
         d12 = _m[ 0]*_m[ 5] - _m[ 1]*_m[ 4];
         d13 = _m[ 0]*_m[ 9] - _m[ 1]*_m[ 8];
         d23 = _m[ 4]*_m[ 9] - _m[ 5]*_m[ 8];
         d24 = _m[ 4]*_m[13] - _m[ 5]*_m[12];
         d34 = _m[ 8]*_m[13] - _m[ 9]*_m[12];
         d41 = _m[12]*_m[ 1] - _m[13]*_m[ 0];
  
         i._m[ 8] =  (_m[7]*d34 - _m[11]*d24 + _m[15]*d23)*invDet;
         i._m[ 9] = -(_m[3]*d34 + _m[11]*d41 + _m[15]*d13)*invDet;
         i._m[10] =  (_m[3]*d24 + _m[ 7]*d41 + _m[15]*d12)*invDet;
         i._m[11] = -(_m[3]*d23 - _m[ 7]*d13 + _m[11]*d12)*invDet;
         i._m[12] = -(_m[6]*d34 - _m[10]*d24 + _m[14]*d23)*invDet;
         i._m[13] =  (_m[2]*d34 + _m[10]*d41 + _m[14]*d13)*invDet;
         i._m[14] = -(_m[2]*d24 + _m[ 6]*d41 + _m[14]*d12)*invDet;
         i._m[15] =  (_m[2]*d23 - _m[ 6]*d13 + _m[10]*d12)*invDet;
     }
     return i;
 }

◆ 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.

Definition at line 521 of file SLMat4.h.

 {
     for (SLuint i = 0; i < 16; ++i)
     {
         if (std::abs(_m[i] - A._m[i]) > epsilon)
             return false;
     }
     return true;
 }

◆ 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.

Definition at line 795 of file SLMat4.h.

 {
     SLVec3<T> VX, VY, VZ;
     SLMat3<T> xz(0.0, 0.0, 1.0,         // matrix that transforms VZ into a
                  0.0, 0.0, 0.0,         // vector that is perpendicular to YZ and 
                 -1.0, 0.0, 0.0);        // lies in the x-z plane
  
     VZ = pos-At;   VZ.normalize();
  
     if (Up==SLVec3<T>::ZERO)  
     {   VX = xz*VZ;  VX.normalize();
         VY = VZ^VX;  VY.normalize();
     } else
     {   VX = Up^VZ;  VX.normalize();
         VY = VZ^VX;  VY.normalize();
     }
  
     setMatrix(VX.x, VY.x, VZ.x, pos.x,
               VX.y, VY.y, VZ.y, pos.y,
               VX.z, VY.z, VZ.z, pos.z,
                0.0,  0.0,  0.0, 1.0);
 }

◆ 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

Definition at line 778 of file SLMat4.h.

 {
     lightAt(SLVec3<T>(PosX,PosY,PosZ),
             SLVec3<T>( AtX, AtY, AtZ),
             SLVec3<T>( UpX, UpY, UpZ));
 }

◆ 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.

Definition at line 727 of file SLMat4.h.

 {
     SLVec3<T> VX, VY, VZ, VT;
     SLMat3<T> xz(0.0, 0.0, 1.0,         // matrix that transforms YZ into a 
                  0.0, 0.0, 0.0,         // vector that is perpendicular to YZ and 
                 -1.0, 0.0, 0.0);        // lies in the x-z plane
  
     VZ = Eye-At; 
     VZ.normalize(); 
  
     if (Up==SLVec3<T>::ZERO || Up==VZ)  
     {   VX.set(xz*VZ);    
         VX.normalize();
     } else
     {   VX.cross(Up, VZ); 
         VX.normalize();
     }
     VY.cross(VZ, VX); VY.normalize();
     VT = -Eye;
  
     setMatrix(VX.x, VX.y, VX.z, VX*VT,
               VY.x, VY.y, VY.z, VY*VT,
               VZ.x, VZ.y, VZ.z, VZ*VT,
               0.0,  0.0,  0.0,  1.0);
 }

◆ 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.

Definition at line 760 of file SLMat4.h.

 {
     SLMat4<T> invRot(_m);               // get the current view matrix
     invRot.translation(0,0,0);          // remove the translation
     invRot.transpose();                 // transpose it to get inverse rot.
     eye->set(invRot.multVec(-translation())); // setMatrix eye
     ri->set( _m[0], _m[4], _m[8]);            // normalized look right vector
     up->set( _m[1], _m[5], _m[9]);            // normalized look up vector
     at->set(-_m[2],-_m[6],-_m[10]);           // normalized look at vector
 }

◆ 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.

Definition at line 708 of file SLMat4.h.

 {
     lookAt(SLVec3<T>(EyeX,EyeY,EyeZ),
            SLVec3<T>( AtX, AtY, AtZ),
            SLVec3<T>( UpX, UpY, UpZ));
 }

◆ m() [1/3]

template<class T >

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

inline

Definition at line 96 of file SLMat4.h.

96 {return _m;}

◆ m() [2/3]

template<class T >

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

inline

Definition at line 97 of file SLMat4.h.

97 {assert(i>=0 && i<16); return _m[i];}

◆ m() [3/3]

template<class T >

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

inline

Definition at line 93 of file SLMat4.h.

93 {assert(i>=0 && i<16); _m[i] = val;}

◆ mat3()

template<class T >

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

inline

Definition at line 98 of file SLMat4.h.

                                                 {SLMat3<T> m3;
                                                  m3.setMatrix(_m[0], _m[4], _m[ 8], 
                                                               _m[1], _m[5], _m[ 9], 
                                                               _m[2], _m[6], _m[10]);
                                                  return m3;}

◆ 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*.

Definition at line 536 of file SLMat4.h.

 {                                                       
     setMatrix(_m[0]*A._m[ 0] + _m[4]*A._m[ 1] + _m[8] *A._m[ 2] + _m[12]*A._m[ 3], //row 1
               _m[0]*A._m[ 4] + _m[4]*A._m[ 5] + _m[8] *A._m[ 6] + _m[12]*A._m[ 7],
               _m[0]*A._m[ 8] + _m[4]*A._m[ 9] + _m[8] *A._m[10] + _m[12]*A._m[11],
               _m[0]*A._m[12] + _m[4]*A._m[13] + _m[8] *A._m[14] + _m[12]*A._m[15],
               _m[1]*A._m[ 0] + _m[5]*A._m[ 1] + _m[9] *A._m[ 2] + _m[13]*A._m[ 3], //row 2
               _m[1]*A._m[ 4] + _m[5]*A._m[ 5] + _m[9] *A._m[ 6] + _m[13]*A._m[ 7],
               _m[1]*A._m[ 8] + _m[5]*A._m[ 9] + _m[9] *A._m[10] + _m[13]*A._m[11],
               _m[1]*A._m[12] + _m[5]*A._m[13] + _m[9] *A._m[14] + _m[13]*A._m[15],
               _m[2]*A._m[ 0] + _m[6]*A._m[ 1] + _m[10]*A._m[ 2] + _m[14]*A._m[ 3], //row 3
               _m[2]*A._m[ 4] + _m[6]*A._m[ 5] + _m[10]*A._m[ 6] + _m[14]*A._m[ 7],
               _m[2]*A._m[ 8] + _m[6]*A._m[ 9] + _m[10]*A._m[10] + _m[14]*A._m[11],
               _m[2]*A._m[12] + _m[6]*A._m[13] + _m[10]*A._m[14] + _m[14]*A._m[15],
               _m[3]*A._m[ 0] + _m[7]*A._m[ 1] + _m[11]*A._m[ 2] + _m[15]*A._m[ 3], //row 4
               _m[3]*A._m[ 4] + _m[7]*A._m[ 5] + _m[11]*A._m[ 6] + _m[15]*A._m[ 7],
               _m[3]*A._m[ 8] + _m[7]*A._m[ 9] + _m[11]*A._m[10] + _m[15]*A._m[11],
               _m[3]*A._m[12] + _m[7]*A._m[13] + _m[11]*A._m[14] + _m[15]*A._m[15]);
              
               //     | 0  4  8 12 |   | 0  4  8 12 |
               //     | 1  5  9 13 |   | 1  5  9 13 |
               // M = | 2  6 10 14 | x | 2  6 10 14 |
               //     | 3  7 11 15 |   | 3  7 11 15 |
 }

◆ multVec() [1/2]

template<class T >

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

Matrix - 3D vector multiplication with perspective division

Definition at line 576 of file SLMat4.h.

 {
     T W = 1 / (_m[3]*v.x + _m[7]*v.y + _m[11]*v.z + _m[15]);
     return SLVec3<T>((_m[0]*v.x + _m[4]*v.y + _m[ 8]*v.z + _m[12]) * W,
                      (_m[1]*v.x + _m[5]*v.y + _m[ 9]*v.z + _m[13]) * W,
                      (_m[2]*v.x + _m[6]*v.y + _m[10]*v.z + _m[14]) * W);
 }

◆ multVec() [2/2]

template<class T >

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

Matrix - 4D vector multiplication

Definition at line 588 of file SLMat4.h.

 {
     return SLVec4<T>(_m[0]*v.x + _m[4]*v.y + _m[ 8]*v.z + _m[12]*v.w,
                      _m[1]*v.x + _m[5]*v.y + _m[ 9]*v.z + _m[13]*v.w,
                      _m[2]*v.x + _m[6]*v.y + _m[10]*v.z + _m[14]*v.w,
                      _m[3]*v.x + _m[7]*v.y + _m[11]*v.z + _m[15]*v.w);
 }

◆ operator()() [1/2]

template<class T >

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

inline

Definition at line 114 of file SLMat4.h.

114 {return _m[4*col+row];}

◆ operator()() [2/2]

template<class T >

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

inline

Definition at line 115 of file SLMat4.h.

115 {return _m[4*col+row];}

◆ operator*() [1/4]

template<class T >

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

matrix-matrix multiplication

Matrix - matrix multiplication

Definition at line 419 of file SLMat4.h.

 {
     SLMat4<T> newM((const T*)this);
     newM.multiply(A);
     return newM;
 }

◆ 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

Definition at line 452 of file SLMat4.h.

 {
     T W = 1 / (_m[3]*v.x + _m[7]*v.y + _m[11]*v.z + _m[15]);
     return SLVec3<T>((_m[0]*v.x + _m[4]*v.y + _m[ 8]*v.z + _m[12]) * W,
                      (_m[1]*v.x + _m[5]*v.y + _m[ 9]*v.z + _m[13]) * W,
                      (_m[2]*v.x + _m[6]*v.y + _m[10]*v.z + _m[14]) * W);
 }

◆ operator*() [3/4]

template<class T >

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

SLVec4 mult.

Matrix - 4D vector multiplication

Definition at line 464 of file SLMat4.h.

 {
     return SLVec4<T>(_m[0]*v.x + _m[4]*v.y + _m[ 8]*v.z + _m[12]*v.w,
                      _m[1]*v.x + _m[5]*v.y + _m[ 9]*v.z + _m[13]*v.w,
                      _m[2]*v.x + _m[6]*v.y + _m[10]*v.z + _m[14]*v.w,
                      _m[3]*v.x + _m[7]*v.y + _m[11]*v.z + _m[15]*v.w);
 }

◆ operator*() [4/4]

template<class T >

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

scalar mult

Scalar multiplication.

Definition at line 476 of file SLMat4.h.

 {
     return SLMat4<T>(_m[ 0]*a, _m[ 1]*a, _m[ 2]*a, _m[ 3]*a, 
                      _m[ 4]*a, _m[ 5]*a, _m[ 6]*a, _m[ 7]*a,
                      _m[ 8]*a, _m[ 9]*a, _m[10]*a, _m[11]*a, 
                      _m[12]*a, _m[13]*a, _m[14]*a, _m[15]*a);
 }

◆ operator*=() [1/2]

template<class T >

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

matrix-matrix multiplication

Definition at line 430 of file SLMat4.h.

 {
     multiply(A);
     return *this;
 }

◆ operator*=() [2/2]

template<class T >

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

scalar mult

Scalar multiplication.

Definition at line 488 of file SLMat4.h.

 {
     for (auto & i : _m) i *= a;
     return *this;
 }

◆ operator+()

template<class T >

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

matrix-matrix addition

Definition at line 440 of file SLMat4.h.

 {
     SLMat4<T> newM((const T*)this);
     newM.add(A);
     return newM;
 }

◆ operator/()

template<class T >

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

scalar division

Scalar division.

Definition at line 498 of file SLMat4.h.

 {
     T invA = 1 / a;
     SLMat4<T> newM(_m[ 0]*invA, _m[ 1]*invA, _m[ 2]*invA, _m[ 3]*invA, 
                    _m[ 4]*invA, _m[ 5]*invA, _m[ 6]*invA, _m[ 7]*invA,
                    _m[ 8]*invA, _m[ 9]*invA, _m[10]*invA, _m[11]*invA, 
                    _m[12]*invA, _m[13]*invA, _m[14]*invA, _m[15]*invA);
     return newM;
 }

◆ operator/=()

template<class T >

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

scalar division

Scalar division.

Definition at line 512 of file SLMat4.h.

 {  
     T invA = 1 / a;
     for (auto & i : _m) i *= invA;
     return *this;
 }

◆ operator=()

template<class T >

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

assignment operator

Matrix assignment with instance

Definition at line 406 of file SLMat4.h.

 {
     _m[0]=A._m[0]; _m[4]=A._m[4]; _m[ 8]=A._m[ 8]; _m[12]=A._m[12];
     _m[1]=A._m[1]; _m[5]=A._m[5]; _m[ 9]=A._m[ 9]; _m[13]=A._m[13];
     _m[2]=A._m[2]; _m[6]=A._m[6]; _m[10]=A._m[10]; _m[14]=A._m[14];
     _m[3]=A._m[3]; _m[7]=A._m[7]; _m[11]=A._m[11]; _m[15]=A._m[15];
     return *this;
 }

◆ 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.

Definition at line 911 of file SLMat4.h.

 {
     _m[0]=2/(r-l); _m[4]=0;       _m[8]=0;         _m[12]=-(r+l)/(r-l);
     _m[1]=0;       _m[5]=2/(t-b); _m[9]=0;         _m[13]=-(t+b)/(t-b);
     _m[2]=0;       _m[6]=0;       _m[10]=-2/(f-n); _m[14]=-(f+n)/(f-n);
     _m[3]=0;       _m[7]=0;       _m[11]=0;        _m[15]=1;
 }

◆ 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.

Definition at line 874 of file SLMat4.h.

 {
    T t = (T)tan(fov * DEG2RAD * 0.5)*n;
    T b = -t;
    T r = t*aspect;
    T l = -r;
    frustum(l,r,b,t,n,f);
 }

◆ 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)

Definition at line 891 of file SLMat4.h.

 {
     _m[0]=fx/cx; _m[4]=0;     _m[8] = 0;           _m[12]=0;
     _m[1]=0;     _m[5]=fy/cy; _m[9] = 0;           _m[13]=0;
     _m[2]=0;     _m[6]=0;     _m[10]=-(f+n)/(f-n); _m[14]=(-2*f*n)/(f-n);
     _m[3]=0;     _m[7]=0;     _m[11]=-1;           _m[15]=0;
 }

◆ 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.

Definition at line 834 of file SLMat4.h.

 {
     lightAt(pos, dirAt, dirUp);
 }

◆ 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.

Definition at line 822 of file SLMat4.h.

 {
     lightAt(SLVec3<T>(  PosX,   PosY,   PosZ),
             SLVec3<T>(dirAtX, dirAtY, dirAtZ),
             SLVec3<T>(dirUpX, dirUpY, dirUpZ));
 }

◆ print()

template<class T >

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

Prints out the matrix row by row.

Definition at line 1554 of file SLMat4.h.

 {
     if (str) SL_LOG("%s",str);
     SL_LOG("% 3.2f % 3.2f % 3.2f % 3.2f",  _m[0],_m[4],_m[ 8],_m[12]);
     SL_LOG("% 3.2f % 3.2f % 3.2f % 3.2f",  _m[1],_m[5],_m[ 9],_m[13]);
     SL_LOG("% 3.2f % 3.2f % 3.2f % 3.2f",  _m[2],_m[6],_m[10],_m[14]);
     SL_LOG("% 3.2f % 3.2f % 3.2f % 3.2f",  _m[3],_m[7],_m[11],_m[15]);
 }

◆ 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.

Definition at line 645 of file SLMat4.h.

 {
     SLMat4<T> R(fromUnitVec, toUnitVec);
     multiply(R);
 }

◆ 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*.

Definition at line 634 of file SLMat4.h.

 {
     SLMat4<T> R(degAng, axis.x, axis.y, axis.z);
     multiply(R);
 }

◆ 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*.

Definition at line 656 of file SLMat4.h.

 {
     SLMat4<T> R(degAng, axisx, axisy, axisz);
     multiply(R);
 }

◆ 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.

Definition at line 1035 of file SLMat4.h.

 {
     // Creates a rotation matrix that will rotate the Vector 'from' into
     // the Vector 'to'. The resulting matrix is stored in 'this' Matrix.
     // For this method to work correctly, vector 'from' and vector 'to'
     // must both be unit length vectors.
  
     T cosAngle = from.dot(to);
  
     if (fabs(cosAngle-1.0) <= FLT_EPSILON) // cosAngle = 1.0
     {
         // Special case where 'from' is equal to 'to'. In other words,
         // the angle between Vector 'from' and Vector 'to' is zero
         // degrees. In this case the identity matrix is returned in
         // Matrix 'result'.
  
         identity();
     }
     else if (fabs(cosAngle+1.0) <= FLT_EPSILON) // cosAngle = -1.0
     {
         // Special case where 'from' is directly opposite to 'to'. In
         // other words, the angle between Vector 'from' and Vector 'to'
         // is 180 degrees. In this case, the following matrix is used:
         //
         // Let:
         //   F = from
         //   S = vector perpendicular to F
         //   U = S X F
         //
         // We want to rotate from (F, U, S) to (-F, U, -S)
         //
         // | -FxFx+UxUx-SxSx  -FxFy+UxUy-SxSy  -FxFz+UxUz-SxSz  0 |
         // | -FxFy+UxUy-SxSy  -FyFy+UyUy-SySy  -FyFz+UyUz-SySz  0 |
         // | -FxFz+UxUz-SxSz  -FyFz+UyUz-SySz  -FzFz+UzUz-SzSz  0 |
         // |       0                 0                0         1 |
  
         SLVec3<T> side(0.f, from.z, -from.y);
  
         if (fabs(side.dot(side)) <= FLT_EPSILON)
         {   side.x = -from.z;
             side.y = 0.f;
             side.z = from.x;
         }
  
         side.normalize();
  
         SLVec3<T> up;
         up.cross(side, from);
         up.normalize();
  
         _m[ 0] = -(from.x * from.x) + (up.x * up.x) - (side.x * side.x);
         _m[ 4] = -(from.x * from.y) + (up.x * up.y) - (side.x * side.y);
         _m[ 8] = -(from.x * from.z) + (up.x * up.z) - (side.x * side.z);
         _m[12] = 0.f;
         _m[ 1] = -(from.x * from.y) + (up.x * up.y) - (side.x * side.y);
         _m[ 5] = -(from.y * from.y) + (up.y * up.y) - (side.y * side.y);
         _m[ 9] = -(from.y * from.z) + (up.y * up.z) - (side.y * side.z);
         _m[13] = 0.f;
         _m[ 2] = -(from.x * from.z) + (up.x * up.z) - (side.x * side.z);
         _m[ 6] = -(from.y * from.z) + (up.y * up.z) - (side.y * side.z);
         _m[10] = -(from.z * from.z) + (up.z * up.z) - (side.z * side.z);
         _m[14] = 0.f;
         _m[ 3] = 0.f;
         _m[ 7] = 0.f;
         _m[11] = 0.f;
         _m[15] = 1.f;
     }
     else
     {
         // This is the most common case. Creates the rotation matrix:
         //
         //               | E + HVx^2    HVxVy - Vz   HVxVz + Vy   0 |
         // R(from, to) = | HVxVy + Vz   E + HVy^2    HVyVz - Vx   0 |
         //               | HVxVz - Vy   HVyVz + Vx   E + HVz^2    0 |
         //               |     0            0            0        1 |
         //
         // where,
         //   V = from X to
         //   E = from.dot(to)
         //   H = (1 - E) / V.dot(V)
  
         SLVec3<T> v;
         v.cross(from, to);
         v.normalize();
  
         T h = (1.f - cosAngle) / v.dot(v);
  
         _m[ 0] = cosAngle + h * v.x * v.x;
         _m[ 4] = h * v.x * v.y - v.z;
         _m[ 8] = h * v.x * v.z + v.y;
         _m[12] = 0.f;
         _m[ 1] = h * v.x * v.y + v.z;
         _m[ 5] = cosAngle + h * v.y * v.y;
         _m[ 9] = h * v.y * v.z - v.x;
         _m[13] = 0.f;
         _m[ 2] = h * v.x * v.z - v.y;
         _m[ 6] = h * v.y * v.z + v.x;
         _m[10] = cosAngle + h * v.z * v.z;
         _m[14] = 0.f;
         _m[ 3] = 0.f;
         _m[ 7] = 0.f;
         _m[11] = 0.f;
         _m[15] = 1.f;
     }
 }

◆ 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.

Definition at line 978 of file SLMat4.h.

 {
     rotation(degAng, axis.x, axis.y, axis.z, keepTrans);
 }

◆ 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.

Definition at line 989 of file SLMat4.h.

 {
     T RadAng = (T)degAng * DEG2RAD;
     T ca=(T)cos(RadAng), sa=(T)sin(RadAng);
     if (axisx==1 && axisy==0 && axisz==0)              // about x-axis
     {   _m[0]=1; _m[4]=0;  _m[8]=0;   
         _m[1]=0; _m[5]=ca; _m[9]=-sa; 
         _m[2]=0; _m[6]=sa; _m[10]=ca; 
     } else 
     if (axisx==0 && axisy==1 && axisz==0)              // about y-axis
     {   _m[0]=ca;  _m[4]=0; _m[8]=sa; 
         _m[1]=0;   _m[5]=1; _m[9]=0;  
         _m[2]=-sa; _m[6]=0; _m[10]=ca;
     } else 
     if (axisx==0 && axisy==0 && axisz==1)              // about z-axis
     {   _m[0]=ca; _m[4]=-sa; _m[8]=0; 
         _m[1]=sa; _m[5]=ca;  _m[9]=0; 
         _m[2]=0;  _m[6]=0;   _m[10]=1;
     } else                                             // arbitrary axis
     {   T l = axisx*axisx + axisy*axisy + axisz*axisz;  // length squared
         T x, y, z;
         x=axisx, y=axisy, z=axisz;
         if ((l > T(1.0001) || l < T(0.9999)) && l!=0)
         {   l=T(1.0)/sqrt(l);
             x*=l; y*=l; z*=l;
         }
         T xy=x*y, yz=y*z, xz=x*z, xx=x*x, yy=y*y, zz=z*z;
         _m[0]=xx + ca*(1-xx);     _m[4]=xy - xy*ca - z*sa;  _m[8] =xz - xz*ca + y*sa;
         _m[1]=xy - xy*ca + z*sa;  _m[5]=yy + ca*(1-yy);     _m[9] =yz - yz*ca - x*sa;
         _m[2]=xz - xz*ca - y*sa;  _m[6]=yz - yz*ca + x*sa;  _m[10]=zz + ca*(1-zz);
     }
     _m[3]=_m[7]=_m[11]=0; _m[15]=1;
  
     if (!keepTrans) 
         _m[12] = _m[13] = _m[14] = 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*.

Definition at line 694 of file SLMat4.h.

 {
     SLMat4<T> S(s.x,  0,  0,  0,
                 0,s.y,  0,  0,
                 0,  0,s.z,  0,
                 0,  0,  0,  1);
     multiply(S);
 }

◆ 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*.

Definition at line 680 of file SLMat4.h.

 {
     SLMat4<T> S(sx, 0, 0, 0,
                 0,sy, 0, 0,
                 0, 0,sz, 0,
                 0, 0, 0, 1);
     multiply(S);
 }

◆ 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*.

Definition at line 667 of file SLMat4.h.

 {   SLMat4<T> S(s, 0, 0, 0,
                 0, s, 0, 0,
                 0, 0, s, 0,
                 0, 0, 0, 1);
     multiply(S);
 }

◆ 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.

Definition at line 1157 of file SLMat4.h.

 {
     scaling(scale.x, scale.y, scale.z);
 }

◆ 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.

Definition at line 1168 of file SLMat4.h.

 {
     _m[0]=sx; _m[4]=0;  _m[8]=0;   
     _m[1]=0;  _m[5]=sy; _m[9]=0; 
     _m[2]=0;  _m[6]=0;  _m[10]=sz;
     _m[3]=0;  _m[7]=0;  _m[11]=0; _m[15]=1;
  
     if (!keepTrans) 
         _m[12] = _m[13] = _m[14] = 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.

Definition at line 1146 of file SLMat4.h.

 {
     scaling(sxyz, sxyz, sxyz);
 }

◆ setMatrix() [1/7]

template<class T >

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

inline

Definition at line 90 of file SLMat4.h.

90 { assert(i >= 0 && i < 16); _m[i] = value; }

◆ setMatrix() [2/7]

template<class T >

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

Set matrix by other 3x3 matrix.

Definition at line 341 of file SLMat4.h.

 {
     _m[0]=A._m[0]; _m[4]=A._m[3]; _m[ 8]=A._m[6];  _m[12]=0;
     _m[1]=A._m[1]; _m[5]=A._m[4]; _m[ 9]=A._m[7];  _m[13]=0;
     _m[2]=A._m[2]; _m[6]=A._m[5]; _m[10]=A._m[8];  _m[14]=0;
     _m[3]=0;       _m[7]=0;       _m[11]=0;        _m[15]=1;
 }

◆ setMatrix() [3/7]

template<class T >

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

Set matrix by other 4x4 matrix.

Definition at line 335 of file SLMat4.h.

 {
     for (int i=0; i<16; ++i) _m[i] = A._m[i];
 }

◆ setMatrix() [4/7]

template<class T >

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

Set matrix by other matrix pointer.

Definition at line 350 of file SLMat4.h.

 {
     for (int i=0; i<16; ++i) _m[i] = A->_m[i];
 }

◆ 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.

Definition at line 374 of file SLMat4.h.

 {
     setMatrix(scale.x * rotation[0], scale.y * rotation[3], scale.z * rotation[6], translation.x,
               scale.x * rotation[1], scale.y * rotation[4], scale.z * rotation[7], translation.y,
               scale.x * rotation[2], scale.y * rotation[5], scale.z * rotation[8], translation.z,
               0                    , 0                    , 0                    , 1);
 }

◆ setMatrix() [6/7]

template<class T >

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

Set matrix by float[16] array.

Definition at line 356 of file SLMat4.h.

 {
     for (int i=0; i<16; ++i) _m[i] = M[i];
 }

◆ 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.

Definition at line 362 of file SLMat4.h.

 {
     _m[0]=M0; _m[4]=M4; _m[ 8]=M8;  _m[12]=M12;
     _m[1]=M1; _m[5]=M5; _m[ 9]=M9;  _m[13]=M13;
     _m[2]=M2; _m[6]=M6; _m[10]=M10; _m[14]=M14;
     _m[3]=M3; _m[7]=M7; _m[11]=M11; _m[15]=M15;
 }

◆ 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

Definition at line 385 of file SLMat4.h.

 {
     _m[0]=rotation[0]; _m[4]=rotation[3]; _m[8]=rotation[6];
     _m[1]=rotation[1]; _m[5]=rotation[4]; _m[9]=rotation[7];
     _m[2]=rotation[2]; _m[6]=rotation[5]; _m[10]=rotation[8];
 }

◆ 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

Definition at line 393 of file SLMat4.h.

 {
     _m[12]=translation.x;
     _m[13]=translation.y;
     _m[14]=translation.z;
 }

◆ swap()

template<class T >

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

inlinestatic

Definition at line 252 of file SLMat4.h.

252 {T t; t=a;a=b;b=t;}

◆ toEulerAngles()

template<class T >

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

Definition at line 1310 of file SLMat4.h.

 {
     HMatrix A;
     A[0][0]=_m[0]; A[0][1]=_m[4]; A[0][2]=_m[ 8]; A[0][3]=_m[12];
     A[1][0]=_m[1]; A[1][1]=_m[5]; A[1][2]=_m[ 9]; A[1][3]=_m[13];
     A[2][0]=_m[2]; A[2][1]=_m[6]; A[2][2]=_m[10]; A[2][3]=_m[14];
     A[3][0]=_m[3]; A[3][1]=_m[7]; A[3][2]=_m[11]; A[3][3]=_m[15];
     
     EulerAngles eulerAngles = Eul_FromHMatrix(A, order);
  
     SLVec3<T> angles;
     angles.x = eulerAngles.x;
     angles.y = eulerAngles.y;
     angles.z = eulerAngles.z;
     return angles;
 }

◆ 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

Definition at line 1278 of file SLMat4.h.

 {
     T Cx, Sx;
     T Cy, Sy;
     T Cz, Sz;
  
     Sy = _m[8];
     Cy = (T)sqrt(1.0 - Sy*Sy);
     
     // normal case
     if (Utils::abs(Cy) > FLT_EPSILON)
     {
         T factor = (T)(1.0 / Cy);
         Sx = -_m[ 9]*factor;
         Cx =  _m[10]*factor;
         Sz = -_m[ 4]*factor;
         Cz =  _m[ 0]*factor;
     }
     else // x and z axes aligned
     {
         Sz = 0.0;
         Cz = 1.0;
         Sx = _m[6];
         Cx = _m[5];
     }
  
     zRotRAD = atan2f(Sz, Cz);
     yRotRAD = atan2f(Sy, Cy);
     xRotRAD = atan2f(Sx, Cx);
 }

◆ 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

Definition at line 1241 of file SLMat4.h.

 {
     T Cx, Sx;
     T Cy, Sy;
     T Cz, Sz;
  
     Sy = -_m[2];
     Cy = (T)sqrt(1.0 - Sy*Sy);
  
     // normal case
     if (Utils::abs(Cy) > FLT_EPSILON)
     {
         T factor = (T)(1.0 / Cy);
         Sx = _m[ 6]*factor;
         Cx = _m[10]*factor;
         Sz = _m[ 1]*factor;
         Cz = _m[ 0]*factor;
     }
     else // x and z axes aligned
     {
         Sz = 0.0;
         Cz = 1.0;
         Sx = _m[4];
         Cx = _m[8];
     }
  
     zRotRAD = atan2f(Sz, Cz);
     yRotRAD = atan2f(Sy, Cy);
     xRotRAD = atan2f(Sx, Cx);
 }

◆ toString()

template<class T >

SLstring SLMat4< T >::toString

Prints out the matrix row by row.

Definition at line 1567 of file SLMat4.h.

 {
     SLchar cstr[500];
     snprintf(cstr,
         sizeof(cstr),
             "% 3.3f % 3.3f % 3.3f % 3.3f\n% 3.3f % 3.3f % 3.3f % 3.3f\n% 3.3f % 3.3f % 3.3f % 3.3f\n% 3.3f % 3.3f % 3.3f % 3.3f",
             _m[0],_m[4],_m[ 8],_m[12],
             _m[1],_m[5],_m[ 9],_m[13],
             _m[2],_m[6],_m[10],_m[14],
             _m[3],_m[7],_m[11],_m[15]);
     SLstring cppstr = cstr;
     return cppstr;
 }

◆ trace()

template<class T >

T SLMat4< T >::trace

inline

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

Definition at line 1455 of file SLMat4.h.

 {
     return _m[0] + _m[5] + _m[10] + _m[15];
 }

◆ 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*.

Definition at line 612 of file SLMat4.h.

 {
     SLMat4<T> trans(t.x, t.y, 0);
     multiply(trans);
 }

◆ 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*.

Definition at line 623 of file SLMat4.h.

 {
     SLMat4<T> trans(t.x, t.y, t.z);
     multiply(trans);
 }

◆ 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*.

Definition at line 601 of file SLMat4.h.

 {
     SLMat4<T> trans(tx, ty, tz);
     multiply(trans);
 }

◆ translation() [1/3]

template<class T >

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

inline

Definition at line 184 of file SLMat4.h.

184 {return SLVec3<T>(_m[12], _m[13], _m[14]);}

◆ 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.

Definition at line 948 of file SLMat4.h.

 {
     translation(t.x, t.y, t.z, keepLinear);
 }

◆ 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.

Definition at line 958 of file SLMat4.h.

 {
     _m[12]=tx;
     _m[13]=ty;
     _m[14]=tz;
  
     if (!keepLinear)
     {   _m[0]=1; _m[4]=0;  _m[8]=0;
         _m[1]=0; _m[5]=1;  _m[9]=0;  
         _m[2]=0; _m[6]=0;  _m[10]=1; 
         _m[3]=0; _m[7]=0;  _m[11]=0; _m[15]=1;
     }
 }

◆ transpose()

template<class T >

void SLMat4< T >::transpose

Sets the transposed matrix by swaping around the main diagonal.

Definition at line 1341 of file SLMat4.h.

 {
     swap(_m[1], _m[ 4]);
     swap(_m[2], _m[ 8]);
     swap(_m[6], _m[ 9]);
     swap(_m[3], _m[12]);
     swap(_m[7], _m[13]);
     swap(_m[11],_m[14]);
 }

◆ transposed()

template<class T >

SLMat4< T > SLMat4< T >::transposed

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

Definition at line 1353 of file SLMat4.h.

 {
     SLMat4<T> t( _m[0], _m[1], _m[2], _m[3],
                  _m[4], _m[5], _m[6], _m[7],
                  _m[8], _m[9],_m[10],_m[11],
                 _m[12],_m[13],_m[14],_m[15]);
     return t;
 }

◆ 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)

Definition at line 930 of file SLMat4.h.

 {
     T ww2 = ww*0.5f;
     T wh2 = wh*0.5f;
    
     // negate the first wh2 because windows has topdown window coords
     _m[0]=ww2; _m[4]=0;    _m[8] =0;          _m[12]=x+ww2;
     _m[1]=0;   _m[5]=-wh2; _m[9] =0;          _m[13]=y+wh2;
     _m[2]=0;   _m[6]=0;    _m[10]=(f-n)*0.5f; _m[14]=(f+n)*0.5f;
     _m[3]=0;   _m[7]=0;    _m[11]=0;          _m[15]=1;
 }

Member Data Documentation

◆ _m

template<class T >

T SLMat4< T >::_m[16]

private

The 16 elements of the matrix.

Definition at line 255 of file SLMat4.h.

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

SLMat4.h

Public Member Functions

Static Public Member Functions

Private Attributes

Detailed Description

template<class T> class SLMat4< T >

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]

template<class T>
class SLMat4< T >