SLMat3< T > Class Template Reference

3x3 matrix template class More...

#include <SLMat3.h>

Public Member Functions
	SLMat3 ()
	Sets identity matrix. More...
	SLMat3 (const SLMat3 &A)
	Sets mat by other SLMat3. More...
	SLMat3 (const T M0, const T M3, const T M6, const T M1, const T M4, const T M7, const T M2, const T M5, const T M8)
	Sets matrix by components. More...
	SLMat3 (const T angleDEG, const T axis_x, const T axis_y, const T axis_z)
	Sets rotate matrix from axis & angle. More...
	SLMat3 (const T angleDEG, const SLVec3< T > axis)
	Sets rotate matrix. More...
	SLMat3 (const T scale_xyz)
	Sets uniform scaling matrix. More...
	SLMat3 (const T angleXRAD, const T angleYRAD, const T angleZRAD)
	Sets rotation matrix from Euler angles in radians. More...
void	setMatrix (const SLMat3 &A)
void	setMatrix (const SLMat3 *A)
void	setMatrix (const T *M)
void	setMatrix (T M0, T M3, T M6, T M1, T M4, T M7, T M2, T M5, T M8)
void	m (int i, T val)
const T *	m () const
T	m (int i) const
SLMat3< T > &	operator= (const SLMat3 &A)
SLMat3< T > &	operator*= (const SLMat3 &A)
SLMat3< T > &	operator= (const T *a)
SLMat3< T >	operator+ (const SLMat3 &A) const
SLMat3< T >	operator- (const SLMat3 &A) const
SLMat3< T >	operator* (const SLMat3 &A) const
SLVec3< T >	operator* (const SLVec3< T > &v) const
SLMat3< T >	operator* (T a) const
	scalar multiplication More...
SLMat3< T > &	operator*= (T a)
	scalar multiplication More...
SLMat3< T >	operator/ (T a) const
	scalar division More...
SLMat3< T > &	operator/= (T a)
	scalar division More...
	operator const T * () const
	operator T* ()
T &	operator() (SLint row, SLint col)
const T &	operator() (SLint row, SLint col) const
void	rotation (const T angleDEG, const SLVec3< T > &axis)
	Sets the rotation components More...
void	rotation (const T angleDEG, const T axisx, const T axisy, const T axisz)
void	rotation (const T zAngleRAD, const T yAngleRAD, const T xAngleRAD)
void	scale (const T sx, const T sy, const T sz)
	Sets the scaling components. More...
void	scale (const SLVec3< T > &s)
void	scale (const T s)
void	identity ()
void	transpose ()
	Transposes the matrix. More...
SLMat3< T >	transposed () const
	Returns the transposed of the matrix and leaves the itself unchanged. More...
void	invert ()
	Inverts the matrix. More...
SLMat3< T >	inverted ()
	Returns the inverse of the matrix and leaves itself unchanged. More...
T	trace () const
T	det () const
	det returns the determinant More...
void	toAngleAxis (T &angleDEG, SLVec3< T > &axis) const
	Conversion to axis and angle in radians. More...
void	toEulerAnglesXYZ (T &xRotRAD, T &yRotRAD, T &zRotRAD)
void	toEulerAnglesZYX (T &zRotRAD, T &yRotRAD, T &xRotRAD)
void	fromEulerAnglesXYZ (const T angleXRAD, const T angleYRAD, const T angleZRAD)
void	fromEulerAnglesZYX (const T angleZ1RAD, const T angleY2RAD, const T angleX3RAD)
void	fromEulerAnglesZXZ (const T angleZ1RAD, const T angleX2RAD, const T angleZ2RAD)
void	print (const SLchar *str) const

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

Public Attributes
T	_m [9]

Detailed Description

template<class T>
class SLMat3< T >

3x3 matrix template class

Implements a 3 by 3 matrix template. 9 floats were used instead of the normal [3][3] array. The order is columnwise as in OpenGL

| 0 3 6 | | 1 4 7 | | 2 5 8 |

type definitions for 3x3 matrice:
Use SLMat3f for a specific float type 3x3 matrix
Use SLMat3d for a specific double type 3x3 matrix

Definition at line 38 of file SLMat3.h.

Constructor & Destructor Documentation

SLMat3() [1/7]

template<class T >

SLMat3< T >::SLMat3

Sets identity matrix.

Definition at line 133 of file SLMat3.h.

{
    identity(); 
}

SLMat3() [2/7]

template<class T >

SLMat3< T >::SLMat3

(

const SLMat3< T > &

A

)

Sets mat by other SLMat3.

Definition at line 139 of file SLMat3.h.

{
    setMatrix(A);
}

SLMat3() [3/7]

template<class T >

SLMat3< T >::SLMat3	(	const T	M0,
		const T	M3,
		const T	M6,
		const T	M1,
		const T	M4,
		const T	M7,
		const T	M2,
		const T	M5,
		const T	M8
	)

Sets matrix by components.

Definition at line 145 of file SLMat3.h.

{  
    _m[0]=M0; _m[3]=M3; _m[6]=M6; 
    _m[1]=M1; _m[4]=M4; _m[7]=M7; 
    _m[2]=M2; _m[5]=M5; _m[8]=M8;
}

SLMat3() [4/7]

template<class T >

SLMat3< T >::SLMat3	(	const T	angleDEG,
		const T	axis_x,
		const T	axis_y,
		const T	axis_z
	)

Sets rotate matrix from axis & angle.

Definition at line 155 of file SLMat3.h.

{
    rotation(angleDEG, axisx, axisy, axisz);
}

SLMat3() [5/7]

template<class T >

SLMat3< T >::SLMat3	(	const T	angleDEG,
		const SLVec3< T >	axis
	)

Sets rotate matrix.

Definition at line 161 of file SLMat3.h.

{
    rotation(angleDEG, axis);
}

SLMat3() [6/7]

template<class T >

SLMat3< T >::SLMat3

(

const T

scale_xyz

)

Sets uniform scaling matrix.

Definition at line 167 of file SLMat3.h.

{
    scale(scale_xyz);
}

SLMat3() [7/7]

template<class T >

SLMat3< T >::SLMat3	(	const T	angleXRAD,
		const T	angleYRAD,
		const T	angleZRAD
	)

Sets rotation matrix from Euler angles in radians.

Definition at line 173 of file SLMat3.h.

{
    fromEulerAnglesXYZ(angleXRAD,
                       angleYRAD,
                       angleZRAD);
}

Member Function Documentation

det()

template<class T >

T SLMat3< T >::det

inline

det returns the determinant

Definition at line 493 of file SLMat3.h.

{
    return _m[0]*(_m[4]*_m[8] - _m[7]*_m[5]) -
           _m[3]*(_m[1]*_m[8] - _m[7]*_m[2]) +
           _m[6]*(_m[1]*_m[5] - _m[4]*_m[2]);
}

fromEulerAnglesXYZ()

template<class T >

void SLMat3< T >::fromEulerAnglesXYZ	(	const T	angleX1RAD,
		const T	angleY2RAD,
		const T	angleZ3RAD
	)

Sets the linear 3x3 sub-matrix as a rotation matrix from the 3 euler angles in radians around the z-axis, y-axis & x-axis := Rx * Ry * Rz See: http://en.wikipedia.org/wiki/Euler_angles

Definition at line 683 of file SLMat3.h.

{
    T s1 = sin(angleX1RAD), c1 = cos(angleX1RAD);
    T s2 = sin(angleY2RAD), c2 = cos(angleY2RAD);
    T s3 = sin(angleZ3RAD), c3 = cos(angleZ3RAD);
 
    _m[0]=(T) (c2*c3);              _m[3]=(T)-(c2*s3);              _m[6] =(T) s2;
    _m[1]=(T) (s1*s2*c3) + (c1*s3); _m[4]=(T)-(s1*s2*s3) + (c1*c3); _m[7] =(T)-(c2*s1);
    _m[2]=(T)-(c1*s2*c3) + (s1*s3); _m[5]=(T) (c1*s2*s3) + (s1*c3); _m[8] =(T) (c1*c2);
}

fromEulerAnglesZXZ()

template<class T >

void SLMat3< T >::fromEulerAnglesZXZ	(	const T	angleZ1RAD,
		const T	angleX2RAD,
		const T	angleZ3RAD
	)

Sets the linear 3x3 sub-matrix as a rotation matrix from the 3 euler angles in radians around the z-axis, x-axis & z-axis:= Z1*X2*Z3 See: http://en.wikipedia.org/wiki/Euler_angles

Definition at line 721 of file SLMat3.h.

{
    T s1 = sin(angleZ1RAD), c1 = cos(angleZ1RAD);
    T s2 = sin(angleX2RAD), c2 = cos(angleX2RAD);
    T s3 = sin(angleZ3RAD), c3 = cos(angleZ3RAD);
 
    _m[0]=(T)( c1*c3 - s1*c2*s3); _m[3]=(T)( s1*c3 + c1*c2*s3);  _m[6] =(T)( s2*s3);
    _m[1]=(T)(-c1*s3 - s1*c2*c3); _m[4]=(T)( c1*c2*c3 - s1*s3);  _m[7] =(T)( s2*c3);
    _m[2]=(T)( s1*s2);            _m[5]=(T)(-c1*s2);             _m[8] =(T)( c2);
}

fromEulerAnglesZYX()

template<class T >

void SLMat3< T >::fromEulerAnglesZYX	(	const T	angleZ1RAD,
		const T	angleY2RAD,
		const T	angleX3RAD
	)

Sets the linear 3x3 sub-matrix as a rotation matrix from the 3 euler angles in radians around the x-axis, y-axis & z-axis := Rz * Ry * Rx See: http://en.wikipedia.org/wiki/Euler_angles

Definition at line 702 of file SLMat3.h.

{
    T s1 = sin(angleZ1RAD), c1 = cos(angleZ1RAD);
    T s2 = sin(angleY2RAD), c2 = cos(angleY2RAD);
    T s3 = sin(angleX3RAD), c3 = cos(angleX3RAD);
 
    _m[0]=(T) (c1*c2); _m[3]=(T) (c1*s2*s3) - (c3*s1); _m[6] =(T) (s1*s3) + (c1*c3*s2);
    _m[1]=(T) (c2*s1); _m[4]=(T) (c1*c3) + (s1*s2*s3); _m[7] =(T) (c3*s1*s2) - (c1*s3);
    _m[2]=(T)-s2;      _m[5]=(T) (c2*s3);              _m[8] =(T) (c2*c3);
}

identity()

template<class T >

void SLMat3< T >::identity

Definition at line 329 of file SLMat3.h.

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

invert()

template<class T >

void SLMat3< T >::invert

Inverts the matrix.

Definition at line 356 of file SLMat3.h.

{
    setMatrix(inverted());
}

inverted()

template<class T >

SLMat3< T > SLMat3< T >::inverted

Returns the inverse of the matrix and leaves itself unchanged.

Definition at line 363 of file SLMat3.h.

{
    // Compute determinant as early as possible using these cofactors.      
    T d = det();
 
    if (fabs(d) < FLT_EPSILON) 
    {
        SLMATH_LOG("3x3-Matrix is singular. Inversion impossible.");
        exit(0);
    }
 
    SLMat3<T> i;
    i._m[0] = _m[4]*_m[8] - _m[7]*_m[5];
    i._m[1] = _m[7]*_m[2] - _m[1]*_m[8];
    i._m[2] = _m[1]*_m[5] - _m[4]*_m[2];
    i._m[3] = _m[6]*_m[5] - _m[3]*_m[8];
    i._m[4] = _m[0]*_m[8] - _m[6]*_m[2];
    i._m[5] = _m[3]*_m[2] - _m[0]*_m[5];
    i._m[6] = _m[3]*_m[7] - _m[6]*_m[4];
    i._m[7] = _m[6]*_m[1] - _m[0]*_m[7];
    i._m[8] = _m[0]*_m[4] - _m[3]*_m[1];
 
    i /= d;
    return i;
}

m() [1/3]

template<class T >

const T* SLMat3< T >::m ( ) const

inline

Definition at line 70 of file SLMat3.h.

{return _m;}

m() [2/3]

template<class T >

T SLMat3< T >::m ( int  i ) const

inline

Definition at line 71 of file SLMat3.h.

{assert(i>=0 && i<9); return _m[i];}

m() [3/3]

template<class T >

void SLMat3< T >::m ( int  i, T  val  )

inline

Definition at line 67 of file SLMat3.h.

{assert(i>=0 && i<9); _m[i] = val;}

operator const T *()

template<class T >

SLMat3< T >::operator const T * ( ) const

inline

Definition at line 86 of file SLMat3.h.

{return _m;}

operator T*()

template<class T >

SLMat3< T >::operator T* ( )

inline

Definition at line 87 of file SLMat3.h.

{return _m;}

operator()() [1/2]

template<class T >

T& SLMat3< T >::operator() ( SLint  row, SLint  col  )

inline

Definition at line 88 of file SLMat3.h.

{return _m[3*col+row];}

operator()() [2/2]

template<class T >

const T& SLMat3< T >::operator() ( SLint  row, SLint  col  ) const

inline

Definition at line 89 of file SLMat3.h.

{return _m[3*col+row];}

operator*() [1/3]

template<class T >

SLMat3< T > SLMat3< T >::operator*

(

const SLMat3< T > &

A

)

const

Definition at line 221 of file SLMat3.h.

{
    SLMat3<T> NewM(_m[0]*A._m[0] + _m[3]*A._m[1] + _m[6]*A._m[2],      // ROW 1
                   _m[0]*A._m[3] + _m[3]*A._m[4] + _m[6]*A._m[5],
                   _m[0]*A._m[6] + _m[3]*A._m[7] + _m[6]*A._m[8],
                   _m[1]*A._m[0] + _m[4]*A._m[1] + _m[7]*A._m[2],      // ROW 2
                   _m[1]*A._m[3] + _m[4]*A._m[4] + _m[7]*A._m[5],
                   _m[1]*A._m[6] + _m[4]*A._m[7] + _m[7]*A._m[8],
                   _m[2]*A._m[0] + _m[5]*A._m[1] + _m[8]*A._m[2],      // ROW 3
                   _m[2]*A._m[3] + _m[5]*A._m[4] + _m[8]*A._m[5],
                   _m[2]*A._m[6] + _m[5]*A._m[7] + _m[8]*A._m[8]);              
  return(NewM);
}

operator*() [2/3]

template<class T >

SLVec3< T > SLMat3< T >::operator*

(

const SLVec3< T > &

v

)

const

Definition at line 252 of file SLMat3.h.

{
    SLVec3<T> NewV;
    NewV.x = _m[0]*v.x + _m[3]*v.y + _m[6]*v.z;
    NewV.y = _m[1]*v.x + _m[4]*v.y + _m[7]*v.z;
    NewV.z = _m[2]*v.x + _m[5]*v.y + _m[8]*v.z;
    return(NewV);
}

operator*() [3/3]

template<class T >

SLMat3< T > SLMat3< T >::operator*

(

T

a

)

const

scalar multiplication

Definition at line 262 of file SLMat3.h.

{
    SLMat3<T> NewM(_m[0] * a, _m[3] * a, _m[6] * a, 
                   _m[1] * a, _m[4] * a, _m[7] * a,
                   _m[2] * a, _m[5] * a, _m[8] * a);
    return NewM;
}

operator*=() [1/2]

template<class T >

SLMat3< T > & SLMat3< T >::operator*=

(

const SLMat3< T > &

A

)

Definition at line 237 of file SLMat3.h.

{  
    setMatrix(_m[0]*A._m[0] + _m[3]*A._m[1] + _m[6]*A._m[2],      // ROW 1
              _m[0]*A._m[3] + _m[3]*A._m[4] + _m[6]*A._m[5],
              _m[0]*A._m[6] + _m[3]*A._m[7] + _m[6]*A._m[8],
              _m[1]*A._m[0] + _m[4]*A._m[1] + _m[7]*A._m[2],      // ROW 2
              _m[1]*A._m[3] + _m[4]*A._m[4] + _m[7]*A._m[5],
              _m[1]*A._m[6] + _m[4]*A._m[7] + _m[7]*A._m[8],
              _m[2]*A._m[0] + _m[5]*A._m[1] + _m[8]*A._m[2],      // ROW 3
              _m[2]*A._m[3] + _m[5]*A._m[4] + _m[8]*A._m[5],
              _m[2]*A._m[6] + _m[5]*A._m[7] + _m[8]*A._m[8]);  
    return *this;
}

operator*=() [2/2]

template<class T >

SLMat3< T > & SLMat3< T >::operator*=

(

T

a

)

scalar multiplication

Definition at line 272 of file SLMat3.h.

{
    for (int i=0; i<9; ++i) _m[i] *= a;
    return *this;
}

operator+()

template<class T >

SLMat3< T > SLMat3< T >::operator+

(

const SLMat3< T > &

A

)

const

Definition at line 201 of file SLMat3.h.

{
    SLMat3<T> sum(_m[0]+A._m[0], _m[3]+A._m[3], _m[6]+A._m[6],
                  _m[1]+A._m[1], _m[4]+A._m[4], _m[7]+A._m[7],
                  _m[2]+A._m[2], _m[5]+A._m[5], _m[8]+A._m[8]);
    return(sum);
}

operator-()

template<class T >

SLMat3< T > SLMat3< T >::operator-

(

const SLMat3< T > &

A

)

const

Definition at line 211 of file SLMat3.h.

{
    SLMat3<T> sub(_m[0]-A._m[0], _m[3]-A._m[3], _m[6]-A._m[6],
                  _m[1]-A._m[1], _m[4]-A._m[4], _m[7]-A._m[7],
                  _m[2]-A._m[2], _m[5]-A._m[5], _m[8]-A._m[8]);
    return(sub);
}

operator/()

template<class T >

SLMat3< T > SLMat3< T >::operator/

(

T

a

)

const

scalar division

Definition at line 280 of file SLMat3.h.

{
    SLMat3<T> NewM(_m[0] / a, _m[3] / a, _m[6] / a, 
                   _m[1] / a, _m[4] / a, _m[7] / a,
                   _m[2] / a, _m[5] / a, _m[8] / a);
    return NewM;
}

operator/=()

template<class T >

SLMat3< T > & SLMat3< T >::operator/=

(

T

a

)

scalar division

Definition at line 290 of file SLMat3.h.

{
    for (int i=0; i<9; ++i) _m[i] /= a;
    return *this;
}

operator=() [1/2]

template<class T >

SLMat3< T > & SLMat3< T >::operator=

(

const SLMat3< T > &

A

)

Definition at line 185 of file SLMat3.h.

{
    _m[0]=A._m[0]; _m[3]=A._m[3]; _m[6]=A._m[6]; 
    _m[1]=A._m[1]; _m[4]=A._m[4]; _m[7]=A._m[7]; 
    _m[2]=A._m[2]; _m[5]=A._m[5]; _m[8]=A._m[8];
    return(*this);
}

operator=() [2/2]

template<class T >

SLMat3< T > & SLMat3< T >::operator=

(

const T *

a

)

Definition at line 194 of file SLMat3.h.

{
    for (int i=0; i<9; ++i) _m[i] = a[i];
}

print()

template<class T >

void SLMat3< T >::print

(

const SLchar *

str

)

const

Definition at line 738 of file SLMat3.h.

{
    if (str) SLMATH_LOG("%s",str);
    SLMATH_LOG("% 3.3f % 3.3f % 3.3f", _m[0],_m[3],_m[6]);
    SLMATH_LOG("% 3.3f % 3.3f % 3.3f", _m[1],_m[4],_m[7]);
    SLMATH_LOG("% 3.3f % 3.3f % 3.3f", _m[2],_m[5],_m[8]);
}

rotation() [1/3]

template<class T >

void SLMat3< T >::rotation	(	const T	angleDEG,
		const SLVec3< T > &	axis
	)

Sets the rotation components

Definition at line 392 of file SLMat3.h.

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

rotation() [2/3]

template<class T >

void SLMat3< T >::rotation	(	const T	angleDEG,
		const T	axisx,
		const T	axisy,
		const T	axisz
	)

Definition at line 398 of file SLMat3.h.

{
    T angleRAD = (T)angleDEG * DEG2RAD;
    T ca = (T)cos(angleRAD);
    T sa = (T)sin(angleRAD);
 
    if (axisx==1 && axisy==0 && axisz==0)               // about x-axis
    {   _m[0]=1; _m[3]=0;  _m[6]=0;   
        _m[1]=0; _m[4]=ca; _m[7]=-sa; 
        _m[2]=0; _m[5]=sa; _m[8]=ca; 
    }
    else if (axisx==0 && axisy==1 && axisz==0)               // about y-axis
    {   _m[0]=ca;  _m[3]=0; _m[6]=sa; 
        _m[1]=0;   _m[4]=1; _m[7]=0;  
        _m[2]=-sa; _m[5]=0; _m[8]=ca;
    }
    else if (axisx==0 && axisy==0 && axisz==1)               // about z-axis
    {   _m[0]=ca; _m[3]=-sa; _m[6]=0; 
        _m[1]=sa; _m[4]=ca;  _m[7]=0; 
        _m[2]=0;  _m[5]=0;   _m[8]=1;
    }                                              // arbitrary axis
    else
    {
        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[3]=xy - xy*ca - z*sa;  _m[6]=xz - xz*ca + y*sa;
        _m[1]=xy - xy*ca + z*sa;  _m[4]=yy + ca*(1-yy);     _m[7]=yz - yz*ca - x*sa;
        _m[2]=xz - xz*ca - y*sa;  _m[5]=yz - yz*ca + x*sa;  _m[8]=zz + ca*(1-zz);
    }
}

rotation() [3/3]

template<class T >

void SLMat3< T >::rotation	(	const T	zAngleRAD,
		const T	yAngleRAD,
		const T	xAngleRAD
	)

Sets the matrix as a rotation matrix from the 3 euler angles in radians around the z-axis, y-axis & x-axis. See Van Verth: Essential Math for Games, chapter 5: Orientation Representation

Definition at line 442 of file SLMat3.h.

{
    T Cx = (T)cos(xAngleRAD); T Sx = (T)sin(xAngleRAD);
    T Cy = (T)cos(yAngleRAD); T Sy = (T)sin(yAngleRAD);
    T Cz = (T)cos(zAngleRAD); T Sz = (T)sin(zAngleRAD);
 
    _m[0] =  (Cy * Cz);
    _m[3] = -(Cy * Sz);
    _m[6] =  Sy;
 
    _m[1] =  (Sx * Sy * Cz) + (Cx * Sz);
    _m[4] = -(Sx * Sy * Sz) + (Cx * Cz);
    _m[7] = -(Sx * Cy);
 
    _m[2] = -(Cx * Sy * Cz) + (Sx * Sz);
    _m[5] =  (Cx * Sy * Sz) + (Sx * Cz);
    _m[8] =  (Cx * Cy);
}

scale() [1/3]

template<class T >

void SLMat3< T >::scale

(

const SLVec3< T > &

s

)

Definition at line 470 of file SLMat3.h.

{
    _m[0]=s.x; _m[3]=0;   _m[6]=0;  
    _m[1]=0;   _m[4]=s.y; _m[7]=0;  
    _m[2]=0;   _m[5]=0;   _m[8]=s.z;
}

scale() [2/3]

template<class T >

void SLMat3< T >::scale

(

const T

s

)

Definition at line 478 of file SLMat3.h.

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

scale() [3/3]

template<class T >

void SLMat3< T >::scale	(	const T	sx,
		const T	sy,
		const T	sz
	)

Sets the scaling components.

Definition at line 462 of file SLMat3.h.

{
    _m[0]=sx; _m[3]=0;  _m[6]=0;
    _m[1]=0;  _m[4]=sy; _m[7]=0;
    _m[2]=0;  _m[5]=0;  _m[8]=sz;
}

setMatrix() [1/4]

template<class T >

void SLMat3< T >::setMatrix

(

const SLMat3< T > &

A

)

Definition at line 299 of file SLMat3.h.

{
    for (int i=0; i<9; ++i) _m[i] = A._m[i];
}

setMatrix() [2/4]

template<class T >

void SLMat3< T >::setMatrix

(

const SLMat3< T > *

A

)

Definition at line 305 of file SLMat3.h.

{
    for (int i=0; i<9; ++i) _m[i] = A->_m[i];
}

setMatrix() [3/4]

template<class T >

void SLMat3< T >::setMatrix

(

const T *

M

)

Definition at line 311 of file SLMat3.h.

{
    for (int i=0; i<9; ++i) _m[i] = M[i];
}

setMatrix() [4/4]

template<class T >

void SLMat3< T >::setMatrix	(	T	M0,
		T	M3,
		T	M6,
		T	M1,
		T	M4,
		T	M7,
		T	M2,
		T	M5,
		T	M8
	)

Definition at line 317 of file SLMat3.h.

{
    _m[0]=M0; _m[3]=M3; _m[6]=M6; 
    _m[1]=M1; _m[4]=M4; _m[7]=M7; 
    _m[2]=M2; _m[5]=M5; _m[8]=M8;
}

swap()

template<class T >

static void SLMat3< T >::swap ( T &  a, T &  b  )

inlinestatic

Definition at line 126 of file SLMat3.h.

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

toAngleAxis()

template<typename T >

void SLMat3< T >::toAngleAxis	(	T &	angleDEG,
		SLVec3< T > &	axis
	)		const

Conversion to axis and angle in radians.

The matrix must be a rotation matrix for this functions to be valid. The last function uses Gram-Schmidt orthonormalization applied to the columns of the rotation matrix. The angle must be in radians, not degrees.

Definition at line 507 of file SLMat3.h.

{
    // Let (x,y,z) be the unit-length axis and let A be an angle of rotation.
    // The rotation matrix is R = I + sin(A)*P + (1-cos(A))*P^2 where
    // I is the identity and
    //
    //       +-        -+
    //       |  0 -z +y |
    //   P = | +z  0 -x |
    //       | -y +x  0 |
    //       +-        -+
    //
    // If A > 0, R represents a counterclockwise rotation about the axis in
    // the sense of looking from the tip of the axis vector towards the
    // origin.  Some algebra will show that
    //
    //   cos(A) = (trace(R)-1)/2  and  R - R^t = 2*sin(A)*P
    //
    // In the event that A = pi, R-R^t = 0 which prevents us from extracting
    // the axis through P.  Instead note that R = I+2*P^2 when A = pi, so
    // P^2 = (R-I)/2.  The diagonal entries of P^2 are x^2-1, y^2-1, and
    // z^2-1.  We can solve these for axis (x,y,z).  Because the angle is pi,
    // it does not matter which sign you choose on the square roots.
    
    T tr       = trace();
    T cs       = ((T)0.5) * (tr - (T)1);
    T angleRAD = acos(cs);  // in [0,PI]
 
    if (angleRAD > (T)0)
    {
        if (angleRAD < PI)
        {
            axis.x = _m[5] - _m[7];
            axis.y = _m[6] - _m[2];
            axis.z = _m[1] - _m[3];
            axis.normalize();
        }
        else
        {
            // angle is PI
            T halfInverse;
            if (_m[0] >= _m[4])
            {
                // r00 >= r11
                if (_m[0] >= _m[8])
                {
                    // r00 is maximum diagonal term
                    axis.x = ((T)0.5)*sqrt((T)1 + _m[0] - _m[4] - _m[8]);
                    halfInverse = ((T)0.5)/axis.x;
                    axis.y = halfInverse*_m[3];
                    axis.z = halfInverse*_m[6];
                }
                else
                {
                    // r22 is maximum diagonal term
                    axis.z = ((T)0.5)*sqrt((T)1 + _m[8] - _m[0] - _m[4]);
                    halfInverse = ((T)0.5)/axis.z;
                    axis.x = halfInverse*_m[6];
                    axis.y = halfInverse*_m[7];
                }
            }
            else
            {
                // r11 > r00
                if (_m[4] >= _m[8])
                {
                    // r11 is maximum diagonal term
                    axis.y = ((T)0.5)*sqrt((T)1 + _m[4] - _m[0] - _m[8]);
                    halfInverse  = ((T)0.5)/axis.y;
                    axis.x = halfInverse*_m[3];
                    axis.z = halfInverse*_m[7];
                }
                else
                {
                    // r22 is maximum diagonal term
                    axis.z = ((T)0.5)*sqrt((T)1 + _m[8] - _m[0] - _m[4]);
                    halfInverse = ((T)0.5)/axis.z;
                    axis.x = halfInverse*_m[6];
                    axis.y = halfInverse*_m[7];
                }
            }
        }
    }
    else
    {
        // The angle is 0 and the matrix is the identity.  Any axis will
        // work, so just use the x-axis.
        axis.x = (T)1;
        axis.y = (T)0;
        axis.z = (T)0;
    }
    angleDEG = angleRAD * RAD2DEG;
}

toEulerAnglesXYZ()

template<class T >

void SLMat3< T >::toEulerAnglesXYZ	(	T &	xRotRAD,
		T &	yRotRAD,
		T &	zRotRAD
	)

Gets one set of possible x-y-z euler angles that will generate this 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 608 of file SLMat3.h.

{
    T Cx, Sx;
    T Cy, Sy;
    T Cz, Sz;
 
    Sy = _m[6];
    Cy = (T)sqrt(1.0 - Sy*Sy);
    
    // normal case
    if (Utils::abs(Cy) > FLT_EPSILON)
    {
        T factor = (T)1.0 / Cy;
        Sx = -_m[7]*factor;
        Cx =  _m[8]*factor;
        Sz = -_m[3]*factor;
        Cz =  _m[0]*factor;
    }
    else // x and z axes aligned
    {
        Sz = 0.0f;
        Cz = 1.0f;
        Sx = _m[5];
        Cx = _m[4];
    }
 
    zRotRAD = atan2f(Sz, Cz);
    yRotRAD = atan2f(Sy, Cy);
    xRotRAD = atan2f(Sx, Cx);
}

toEulerAnglesZYX()

template<class T >

void SLMat3< T >::toEulerAnglesZYX	(	T &	zRotRAD,
		T &	yRotRAD,
		T &	xRotRAD
	)

Gets one set of possible z-y-x euler angles that will generate this 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 645 of file SLMat3.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[5]*factor;
        Cx = _m[8]*factor;
        Sz = _m[1]*factor;
        Cz = _m[0]*factor;
    }
    else // x and z axes aligned
    {
        Sz = 0.0f;
        Cz = 1.0f;
        Sx = _m[3];
        Cx = _m[6];
    }
 
    zRotRAD = atan2f(Sz, Cz);
    yRotRAD = atan2f(Sy, Cy);
    xRotRAD = atan2f(Sx, Cx);
}

trace()

template<class T >

T SLMat3< T >::trace

inline

Definition at line 486 of file SLMat3.h.

{
    return _m[0] + _m[4] + _m[8];
}

transpose()

template<class T >

void SLMat3< T >::transpose

Transposes the matrix.

Definition at line 337 of file SLMat3.h.

{
    swap(_m[1],_m[3]);
    swap(_m[2],_m[6]);
    swap(_m[5],_m[7]);
}

transposed()

template<class T >

SLMat3< T > SLMat3< T >::transposed

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

Definition at line 346 of file SLMat3.h.

{
    SLMat3<T> t(_m[0],_m[1],_m[2],
                _m[3],_m[4],_m[5],
                _m[6],_m[7],_m[8]);
    return t;
}

Member Data Documentation

_m

template<class T >

T SLMat3< T >::_m[9]

Definition at line 41 of file SLMat3.h.

---

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

• SLMat3.h