Euler matrix. More...

#include <JEulerMatrix3D.hh>

Inheritance diagram for JGEOMETRY3D::JEulerMatrix3D:

Public Member Functions
	JEulerMatrix3D ()
	Default constructor (= identity matrix).

	JEulerMatrix3D (const JEulerAngle3D &euler)
	Constructor.

const JRotation3D &	getRotation () const
	Get rotation.

	operator JQuaternion3D () const
	Type conversion operator.

JRotation3D &	transpose ()
	Transpose.

JRotation3D &	mul (const JRotation3D &A, const JRotation3D &B)
	Matrix multiplication.

JMatrix3D &	mul (const double factor)
	Scale matrix.

JMatrix3D &	mul (const JMatrix3D &A, const JMatrix3D &B)
	Matrix multiplication.

JMatrix3D &	mul (const JSecond_t &object)
	Multiply with object.

JFirst_t &	mul (const JSecond_t &object)
	Multiply with object.

void	rotate (double &__x, double &__y, double &__z) const
	Rotate.

void	rotate_back (double &__x, double &__y, double &__z) const
	Rotate back.

JMatrix3D &	setIdentity ()
	Set to identity matrix.

void	set (const JMatrix3D &A)
	Set matrix.

JMatrix3D &	reset ()
	Set matrix to the null matrix.

JMatrix3D &	negate ()
	Negate matrix.

JMatrix3D &	add (const JMatrix3D &A)
	Matrix addition.

JMatrix3D &	sub (const JMatrix3D &A)
	Matrix subtraction.

JMatrix3D &	div (const double factor)
	Scale matrix.

bool	equals (const JMatrix3D &A, const double eps=std::numeric_limits< double >::min()) const
	Equality.

bool	isIdentity (const double eps=std::numeric_limits< double >::min()) const
	Test identity.

double	getDeterminant () const
	Get determinant of matrix.

void	transform (double &__x, double &__y, double &__z) const
	Transform.

Static Public Member Functions
static const JMatrix3D &	getInstance ()
	Get reference to unique instance of this class object.

static const JMatrix3D &	getIdentity ()
	Get reference to unique instance of this class object.

Public Attributes
double	a00

double	a01

double	a02

double	a10

double	a11

double	a12

double	a20

double	a21

double	a22

Detailed Description

Euler matrix.

The Euler matrix is a genuine 3D rotation matrix, i.e. the inverse of an Euler matrix is equal to its tranpose.

The Euler angles are defined as follows:

alpha 2D rotation around Z -axis;
beta 2D rotation around X' -axis;
gamma 2D rotation around Z''-axis;

Definition at line 32 of file JEulerMatrix3D.hh.

Constructor & Destructor Documentation

◆ JEulerMatrix3D() [1/2]

JGEOMETRY3D::JEulerMatrix3D::JEulerMatrix3D ( )

inline

Default constructor (= identity matrix).

Definition at line 39 of file JEulerMatrix3D.hh.

                     :
      JRotation3D()
    {}

◆ JEulerMatrix3D() [2/2]

JGEOMETRY3D::JEulerMatrix3D::JEulerMatrix3D ( const JEulerAngle3D & euler )

inline

Constructor.

Parameters

euler Euler angles

Definition at line 49 of file JEulerMatrix3D.hh.

                                               :
      JRotation3D()
    {
      const double ca = cos(euler.getAlpha());
      const double sa = sin(euler.getAlpha());
      const double cb = cos(euler.getBeta());
      const double sb = sin(euler.getBeta());
      const double cg = cos(euler.getGamma());
      const double sg = sin(euler.getGamma());
 
      a00 =  cg*ca - sg*cb*sa;  a01 = -cg*sa - sg*cb*ca;  a02 =  sg*sb;
      a10 =  sg*ca + cg*cb*sa;  a11 = -sg*sa + cg*cb*ca;  a12 = -cg*sb;
      a20 =  sb*sa;             a21 =  sb*ca;             a22 =  cb;
    }

Member Function Documentation

◆ getRotation()

const JRotation3D & JGEOMETRY3D::JRotation3D::getRotation ( ) const

inlineinherited

Get rotation.

Returns: rotation

Definition at line 272 of file JRotation3D.hh.

    {
      return static_cast<const JRotation3D&>(*this);
    }

◆ operator JQuaternion3D()

JGEOMETRY3D::JRotation3D::operator JQuaternion3D ( ) const

inlineinherited

Type conversion operator.

Returns: quaternion

Definition at line 283 of file JRotation3D.hh.

    {
      const double q2 = 0.25 * (1.0 + a00 + a11 + a22);
 
      if (q2 > 0.0) {
 
        const double a =  sqrt(q2);
        const double w =  0.25 / a;
        const double b = (a21 - a12) * w;
        const double c = (a02 - a20) * w;
        const double d = (a10 - a01) * w;
        
        return JQuaternion3D(a,b,c,d).normalise();
      }
 
      return JQuaternion3D(1.0, 0.0, 0.0, 0.0);
    }

◆ transpose()

JRotation3D & JGEOMETRY3D::JRotation3D::transpose ( )

inlineinherited

Transpose.

Definition at line 305 of file JRotation3D.hh.

    {
      static_cast<JMatrix3D&>(*this).transpose();
 
      return *this;
    }

◆ mul() [1/5]

JRotation3D & JGEOMETRY3D::JRotation3D::mul	(	const JRotation3D &	A,
		const JRotation3D &	B )

inlineinherited

Matrix multiplication.

Parameters

A	matrix
B	matrix

Returns: this matrix

Definition at line 320 of file JRotation3D.hh.

    {
      static_cast<JMatrix3D&>(*this).mul(A, B);
 
      return *this;
    }      

◆ mul() [2/5]

JMatrix3D & JMATH::JMatrix3D::mul ( const double factor )

inlineinherited

Scale matrix.

Parameters

factor factor

Returns: this matrix * factor

Definition at line 208 of file JMath/JMatrix3D.hh.

    {
      a00 *= factor; a01 *= factor; a02 *= factor;
      a10 *= factor; a11 *= factor; a12 *= factor;
      a20 *= factor; a21 *= factor; a22 *= factor;
 
      return *this;
    }

◆ mul() [3/5]

JMatrix3D & JMATH::JMatrix3D::mul	(	const JMatrix3D &	A,
		const JMatrix3D &	B )

inlineinherited

Matrix multiplication.

Parameters

A	matrix
B	matrix

Returns: this matrix

Definition at line 241 of file JMath/JMatrix3D.hh.

    {
      a00 = A.a00 * B.a00  +  A.a01 * B.a10  +  A.a02 * B.a20;
      a01 = A.a00 * B.a01  +  A.a01 * B.a11  +  A.a02 * B.a21;
      a02 = A.a00 * B.a02  +  A.a01 * B.a12  +  A.a02 * B.a22;
      
      a10 = A.a10 * B.a00  +  A.a11 * B.a10  +  A.a12 * B.a20;
      a11 = A.a10 * B.a01  +  A.a11 * B.a11  +  A.a12 * B.a21;
      a12 = A.a10 * B.a02  +  A.a11 * B.a12  +  A.a12 * B.a22;
      
      a20 = A.a20 * B.a00  +  A.a21 * B.a10  +  A.a22 * B.a20;
      a21 = A.a20 * B.a01  +  A.a21 * B.a11  +  A.a22 * B.a21;
      a22 = A.a20 * B.a02  +  A.a21 * B.a12  +  A.a22 * B.a22;
      
      return *this;
    }

◆ mul() [4/5]

JMatrix3D & JMATH::JMath< JMatrix3D, JSecond_t >::mul ( const JSecond_t & object )

inlineinherited

Multiply with object.

Parameters

object object

Returns: result object

Definition at line 354 of file JMath.hh.

    {
      return static_cast<JFirst_t&>(*this) = JFirst_t().mul(static_cast<const JFirst_t&>(*this), object);
    }

◆ mul() [5/5]

template<class JFirst_t , class JSecond_t >

JFirst_t & JMATH::JMath< JFirst_t, JSecond_t >::mul ( const JSecond_t & object )

inlineinherited

Multiply with object.

Parameters

object object

Returns: result object

Definition at line 354 of file JMath.hh.

    {
      return static_cast<JFirst_t&>(*this) = JFirst_t().mul(static_cast<const JFirst_t&>(*this), object);
    }

◆ rotate()

void JGEOMETRY3D::JRotation3D::rotate	(	double &	__x,
		double &	__y,
		double &	__z ) const

inlineinherited

Rotate.

Parameters

__x	x value
__y	y value
__z	z value

Definition at line 336 of file JRotation3D.hh.

    {
      const double x = a00 * __x  +  a01 * __y  +  a02 * __z;
      const double y = a10 * __x  +  a11 * __y  +  a12 * __z;
      const double z = a20 * __x  +  a21 * __y  +  a22 * __z;
 
      __x = x;
      __y = y;
      __z = z;
    }

◆ rotate_back()

void JGEOMETRY3D::JRotation3D::rotate_back	(	double &	__x,
		double &	__y,
		double &	__z ) const

inlineinherited

Rotate back.

Parameters

__x	x value
__y	y value
__z	z value

Definition at line 355 of file JRotation3D.hh.

    {
      const double x = a00 * __x  +  a10 * __y  +  a20 * __z;
      const double y = a01 * __x  +  a11 * __y  +  a21 * __z;
      const double z = a02 * __x  +  a12 * __y  +  a22 * __z;
 
      __x = x;
      __y = y;
      __z = z;
    }

◆ getInstance()

static const JMatrix3D & JMATH::JMatrix3D::getInstance ( )

inlinestaticinherited

Get reference to unique instance of this class object.

Returns: zero matrix

Definition at line 78 of file JMath/JMatrix3D.hh.

    {
      static JMatrix3D matrix;
 
      return matrix;
    }

◆ setIdentity()

JMatrix3D & JMATH::JMatrix3D::setIdentity ( )

inlineinherited

Set to identity matrix.

Returns: this matrix

Definition at line 91 of file JMath/JMatrix3D.hh.

    {
      a00 = 1.0;  a01 = 0.0;  a02 = 0.0;
      a10 = 0.0;  a11 = 1.0;  a12 = 0.0;
      a20 = 0.0;  a21 = 0.0;  a22 = 1.0;
 
      return *this;
    }

◆ getIdentity()

static const JMatrix3D & JMATH::JMatrix3D::getIdentity ( )

inlinestaticinherited

Get reference to unique instance of this class object.

Returns: identity matrix

Definition at line 106 of file JMath/JMatrix3D.hh.

    {
      static JMatrix3D matrix(JMatrix3D().setIdentity());
 
      return matrix;
    }

◆ set()

void JMATH::JMatrix3D::set ( const JMatrix3D & A )

inlineinherited

Set matrix.

Parameters

A matrix

Definition at line 119 of file JMath/JMatrix3D.hh.

    {
      static_cast<JMatrix3D&>(*this) = A;
    }

◆ reset()

JMatrix3D & JMATH::JMatrix3D::reset ( )

inlineinherited

Set matrix to the null matrix.

Returns: this matrix

Definition at line 130 of file JMath/JMatrix3D.hh.

    {
      *this = JMatrix3D();
 
      return *this;
    }

◆ negate()

JMatrix3D & JMATH::JMatrix3D::negate ( )

inlineinherited

Negate matrix.

Returns: -this matrix

Definition at line 160 of file JMath/JMatrix3D.hh.

    {
      a00 = -a00;  a01 = -a01;  a02 = -a02;
      a10 = -a10;  a11 = -a11;  a12 = -a12;
      a20 = -a20;  a21 = -a21;  a22 = -a22;
 
      return *this;
    }

◆ add()

JMatrix3D & JMATH::JMatrix3D::add ( const JMatrix3D & A )

inlineinherited

Matrix addition.

Parameters

A matrix

Returns: this matrix + A

Definition at line 176 of file JMath/JMatrix3D.hh.

    {
      a00 += A.a00;  a01 += A.a01;  a02 += A.a02;
      a10 += A.a10;  a11 += A.a11;  a12 += A.a12;
      a20 += A.a20;  a21 += A.a21;  a22 += A.a22;
  
      return *this;
    }

◆ sub()

JMatrix3D & JMATH::JMatrix3D::sub ( const JMatrix3D & A )

inlineinherited

Matrix subtraction.

Parameters

A matrix

Returns: this matrix - A

Definition at line 192 of file JMath/JMatrix3D.hh.

    {
      a00 -= A.a00;  a01 -= A.a01;  a02 -= A.a02;
      a10 -= A.a10;  a11 -= A.a11;  a12 -= A.a12;
      a20 -= A.a20;  a21 -= A.a21;  a22 -= A.a22;
  
      return *this;
    }

◆ div()

JMatrix3D & JMATH::JMatrix3D::div ( const double factor )

inlineinherited

Scale matrix.

Parameters

factor factor

Returns: this matrix / factor

Definition at line 224 of file JMath/JMatrix3D.hh.

    {
      a00 /= factor; a01 /= factor; a02 /= factor;
      a10 /= factor; a11 /= factor; a12 /= factor;
      a20 /= factor; a21 /= factor; a22 /= factor;
 
      return *this;
    }

◆ equals()

bool JMATH::JMatrix3D::equals	(	const JMatrix3D &	A,
		const double	eps = std::numeric_limits<double>::min() ) const

inlineinherited

Equality.

Parameters

A	matrix
eps	numerical precision

Returns: true if matrices identical; else false

Definition at line 267 of file JMath/JMatrix3D.hh.

    {
      return (fabs(a00 - A.a00) <= eps  &&
              fabs(a01 - A.a01) <= eps  &&
              fabs(a02 - A.a02) <= eps  &&
              fabs(a10 - A.a10) <= eps  &&
              fabs(a11 - A.a11) <= eps  &&
              fabs(a12 - A.a12) <= eps  &&
              fabs(a20 - A.a20) <= eps  &&
              fabs(a21 - A.a21) <= eps  &&
              fabs(a22 - A.a22) <= eps);
    }

◆ isIdentity()

bool JMATH::JMatrix3D::isIdentity ( const double eps = std::numeric_limits<double>::min() ) const

inlineinherited

Test identity.

Parameters

eps	numerical precision

Returns: true if identity matrix; else false

Definition at line 288 of file JMath/JMatrix3D.hh.

    {
      return equals(getIdentity(), eps);
    }

◆ getDeterminant()

double JMATH::JMatrix3D::getDeterminant ( ) const

inlineinherited

Get determinant of matrix.

Returns: determinant of matrix

Definition at line 299 of file JMath/JMatrix3D.hh.

    {
      double det = 0.0;
 
      det += a00 * (a11 * a22 - a21 * a12);
      det -= a01 * (a10 * a22 - a20 * a12);
      det += a02 * (a10 * a21 - a20 * a11);
 
      return det;
    }

◆ transform()

void JMATH::JMatrix3D::transform	(	double &	__x,
		double &	__y,
		double &	__z ) const

inlineinherited

Transform.

Parameters

__x	x value
__y	y value
__z	z value

Definition at line 318 of file JMath/JMatrix3D.hh.

    {
      const double x = a00 * __x  +  a01 * __y  +  a02 * __z;
      const double y = a10 * __x  +  a11 * __y  +  a12 * __z;
      const double z = a20 * __x  +  a21 * __y  +  a22 * __z;
 
      __x = x;
      __y = y;
      __z = z;
    }

Member Data Documentation

◆ a00

double JMATH::JMatrix3D::a00

inherited

Definition at line 385 of file JMath/JMatrix3D.hh.

◆ a01

double JMATH::JMatrix3D::a01

inherited

Definition at line 385 of file JMath/JMatrix3D.hh.

◆ a02

double JMATH::JMatrix3D::a02

inherited

Definition at line 385 of file JMath/JMatrix3D.hh.

◆ a10

double JMATH::JMatrix3D::a10

inherited

Definition at line 386 of file JMath/JMatrix3D.hh.

◆ a11

double JMATH::JMatrix3D::a11

inherited

Definition at line 386 of file JMath/JMatrix3D.hh.

◆ a12

double JMATH::JMatrix3D::a12

inherited

Definition at line 386 of file JMath/JMatrix3D.hh.

◆ a20

double JMATH::JMatrix3D::a20

inherited

Definition at line 387 of file JMath/JMatrix3D.hh.

◆ a21

double JMATH::JMatrix3D::a21

inherited

Definition at line 387 of file JMath/JMatrix3D.hh.

◆ a22

double JMATH::JMatrix3D::a22

inherited

Definition at line 387 of file JMath/JMatrix3D.hh.

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

JEulerMatrix3D.hh

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ JEulerMatrix3D() [1/2]

◆ JEulerMatrix3D() [2/2]

Member Function Documentation

◆ getRotation()

◆ operator JQuaternion3D()

◆ transpose()

◆ mul() [1/5]

◆ mul() [2/5]

◆ mul() [3/5]

◆ mul() [4/5]

◆ mul() [5/5]

◆ rotate()

◆ rotate_back()

◆ getInstance()

◆ setIdentity()

◆ getIdentity()

◆ set()

◆ reset()

◆ negate()

◆ add()

◆ sub()

◆ div()

◆ equals()

◆ isIdentity()

◆ getDeterminant()

◆ transform()

Member Data Documentation

◆ a00

◆ a01

◆ a02

◆ a10

◆ a11

◆ a12

◆ a20

◆ a21

◆ a22