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JGEOMETRY3D::JEulerMatrix3D Class Reference

Euler matrix. More...

#include <JEulerMatrix3D.hh>

Inheritance diagram for JGEOMETRY3D::JEulerMatrix3D:
JGEOMETRY3D::JRotation3D JMATH::JMatrix3D JMATH::JMath< JFirst_t, JSecond_t > JMATH::JMath< JMatrix3D > JLANG::JEquals< JFirst_t, JSecond_t >

Public Member Functions

 JEulerMatrix3D ()
 Default constructor (= identity matrix). More...
 
 JEulerMatrix3D (const JEulerAngle3D &euler)
 Constructor. More...
 
const JRotation3D & getRotation () const
 Get rotation. More...
 
 operator JQuaternion3D () const
 Type conversion operator. More...
 
JRotation3D & transpose ()
 Transpose. More...
 
JRotation3D & mul (const JRotation3D &A, const JRotation3D &B)
 Matrix multiplication. More...
 
JMatrix3D & mul (const double factor)
 Scale matrix. More...
 
JMatrix3D & mul (const JMatrix3D &A, const JMatrix3D &B)
 Matrix multiplication. More...
 
JMatrix3D & mul (const JNullType &object)
 Multiply with object. More...
 
JFirst_t & mul (const JSecond_t &object)
 Multiply with object. More...
 
void rotate (double &__x, double &__y, double &__z) const
 Rotate. More...
 
void rotate_back (double &__x, double &__y, double &__z) const
 Rotate back. More...
 
JMatrix3D & setIdentity ()
 Set to identity matrix. More...
 
void set (const JMatrix3D &A)
 Set matrix. More...
 
JMatrix3D & reset ()
 Set matrix to the null matrix. More...
 
JMatrix3D & negate ()
 Negate matrix. More...
 
JMatrix3D & add (const JMatrix3D &A)
 Matrix addition. More...
 
JMatrix3D & sub (const JMatrix3D &A)
 Matrix subtraction. More...
 
JMatrix3D & div (const double factor)
 Scale matrix. More...
 
bool equals (const JMatrix3D &A, const double eps=std::numeric_limits< double >::min()) const
 Equality. More...
 
bool isIdentity (const double eps=std::numeric_limits< double >::min()) const
 Test identity. More...
 
double getDeterminant () const
 Get determinant of matrix. More...
 
void transform (double &__x, double &__y, double &__z) const
 Transform. More...
 

Static Public Member Functions

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

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:

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

Definition at line 32 of file JEulerMatrix3D.hh.

Constructor & Destructor Documentation

JGEOMETRY3D::JEulerMatrix3D::JEulerMatrix3D ( )
inline

Default constructor (= identity matrix).

Definition at line 39 of file JEulerMatrix3D.hh.

39  :
40  JRotation3D()
41  {}
JGEOMETRY3D::JRotation3D::JRotation3D
JRotation3D()
Default constructor (= identity matrix).
Definition: JRotation3D.hh:122
JGEOMETRY3D::JEulerMatrix3D::JEulerMatrix3D ( const JEulerAngle3D &  euler)
inline

Constructor.

Parameters
eulerEuler angles

Definition at line 49 of file JEulerMatrix3D.hh.

49  :
50  JRotation3D()
51  {
52  const double ca = cos(euler.getAlpha());
53  const double sa = sin(euler.getAlpha());
54  const double cb = cos(euler.getBeta());
55  const double sb = sin(euler.getBeta());
56  const double cg = cos(euler.getGamma());
57  const double sg = sin(euler.getGamma());
58 
59  a00 = cg*ca - sg*cb*sa; a01 = -cg*sa - sg*cb*ca; a02 = sg*sb;
60  a10 = sg*ca + cg*cb*sa; a11 = -sg*sa + cg*cb*ca; a12 = -cg*sb;
61  a20 = sb*sa; a21 = sb*ca; a22 = cb;
62  }
JGEOMETRY3D::JEulerAngle3D::getGamma
double getGamma() const
Get gamma angle.
Definition: JEulerAngle3D.hh:218
JGEOMETRY3D::JRotation3D::JRotation3D
JRotation3D()
Default constructor (= identity matrix).
Definition: JRotation3D.hh:122
JGEOMETRY3D::JEulerAngle3D::getAlpha
double getAlpha() const
Get alpha angle.
Definition: JEulerAngle3D.hh:196
JGEOMETRY3D::JEulerAngle3D::getBeta
double getBeta() const
Get beta angle.
Definition: JEulerAngle3D.hh:207

Member Function Documentation

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

Get rotation.

Returns
rotation

Definition at line 272 of file JRotation3D.hh.

273  {
274  return static_cast<const JRotation3D&>(*this);
275  }
JGEOMETRY3D::JRotation3D
Rotation matrix.
Definition: JRotation3D.hh:111
JGEOMETRY3D::JRotation3D::operator JQuaternion3D ( ) const
inlineinherited

Type conversion operator.

Returns
quaternion

Definition at line 283 of file JRotation3D.hh.

284  {
285  const double q2 = 0.25 * (1.0 + a00 + a11 + a22);
286 
287  if (q2 > 0.0) {
288 
289  const double a = sqrt(q2);
290  const double w = 0.25 / a;
291  const double b = (a21 - a12) * w;
292  const double c = (a02 - a20) * w;
293  const double d = (a10 - a01) * w;
294 
295  return JQuaternion3D(a,b,c,d).normalise();
296  }
297 
298  return JQuaternion3D(1.0, 0.0, 0.0, 0.0);
299  }
JTOOLS::w
data_type w[N+1][M+1]
Definition: JPolint.hh:757
JGEOMETRY3D::JQuaternion3D
Data structure for unit quaternion in three dimensions.
Definition: JQuaternion3D.hh:303
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Definition: JMuonPath.sh:47
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Definition: JTuneHV.sh:116
JGEOMETRY3D::JQuaternion3D::normalise
JQuaternion3D & normalise()
Normalise quaternion.
Definition: JQuaternion3D.hh:959
c
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JRotation3D& JGEOMETRY3D::JRotation3D::transpose ( )
inlineinherited

Transpose.

Definition at line 305 of file JRotation3D.hh.

306  {
307  static_cast<JMatrix3D&>(*this).transpose();
308 
309  return *this;
310  }
JMATH::JMatrix3D::JMatrix3D
JMatrix3D()
Default constructor.
Definition: JMath/JMatrix3D.hh:44
JRotation3D& JGEOMETRY3D::JRotation3D::mul ( const JRotation3D &  A,
const JRotation3D &  B 
)
inlineinherited

Matrix multiplication.

Parameters
Amatrix
Bmatrix
Returns
this matrix

Definition at line 320 of file JRotation3D.hh.

322  {
323  static_cast<JMatrix3D&>(*this).mul(A, B);
324 
325  return *this;
326  }
JMATH::JMatrix3D::JMatrix3D
JMatrix3D()
Default constructor.
Definition: JMath/JMatrix3D.hh:44
JMatrix3D& JMATH::JMatrix3D::mul ( const double  factor)
inlineinherited

Scale matrix.

Parameters
factorfactor
Returns
this matrix * factor

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

209  {
210  a00 *= factor; a01 *= factor; a02 *= factor;
211  a10 *= factor; a11 *= factor; a12 *= factor;
212  a20 *= factor; a21 *= factor; a22 *= factor;
213 
214  return *this;
215  }
JMatrix3D& JMATH::JMatrix3D::mul ( const JMatrix3D &  A,
const JMatrix3D &  B 
)
inlineinherited

Matrix multiplication.

Parameters
Amatrix
Bmatrix
Returns
this matrix

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

243  {
244  a00 = A.a00 * B.a00 + A.a01 * B.a10 + A.a02 * B.a20;
245  a01 = A.a00 * B.a01 + A.a01 * B.a11 + A.a02 * B.a21;
246  a02 = A.a00 * B.a02 + A.a01 * B.a12 + A.a02 * B.a22;
247 
248  a10 = A.a10 * B.a00 + A.a11 * B.a10 + A.a12 * B.a20;
249  a11 = A.a10 * B.a01 + A.a11 * B.a11 + A.a12 * B.a21;
250  a12 = A.a10 * B.a02 + A.a11 * B.a12 + A.a12 * B.a22;
251 
252  a20 = A.a20 * B.a00 + A.a21 * B.a10 + A.a22 * B.a20;
253  a21 = A.a20 * B.a01 + A.a21 * B.a11 + A.a22 * B.a21;
254  a22 = A.a20 * B.a02 + A.a21 * B.a12 + A.a22 * B.a22;
255 
256  return *this;
257  }
JMatrix3D & JMATH::JMath< JMatrix3D , JNullType >::mul ( const JNullType &  object)
inlineinherited

Multiply with object.

Parameters
objectobject
Returns
result object

Definition at line 357 of file JMath.hh.

358  {
359  return static_cast<JFirst_t&>(*this) = JCalculator<JFirst_t>::calculator.mul(static_cast<const JFirst_t&>(*this), object);
360  }
JMATH::JCalculator
Auxiliary class for arithmetic operations on objects.
Definition: JCalculator.hh:18
template<class JFirst_t, class JSecond_t = JNullType>
JFirst_t& JMATH::JMath< JFirst_t, JSecond_t >::mul ( const JSecond_t &  object)
inlineinherited

Multiply with object.

Parameters
objectobject
Returns
result object

Definition at line 357 of file JMath.hh.

358  {
359  return static_cast<JFirst_t&>(*this) = JCalculator<JFirst_t>::calculator.mul(static_cast<const JFirst_t&>(*this), object);
360  }
JMATH::JCalculator
Auxiliary class for arithmetic operations on objects.
Definition: JCalculator.hh:18
void JGEOMETRY3D::JRotation3D::rotate ( double &  __x,
double &  __y,
double &  __z 
) const
inlineinherited

Rotate.

Parameters
__xx value
__yy value
__zz value

Definition at line 336 of file JRotation3D.hh.

337  {
338  const double x = a00 * __x + a01 * __y + a02 * __z;
339  const double y = a10 * __x + a11 * __y + a12 * __z;
340  const double z = a20 * __x + a21 * __y + a22 * __z;
341 
342  __x = x;
343  __y = y;
344  __z = z;
345  }
void JGEOMETRY3D::JRotation3D::rotate_back ( double &  __x,
double &  __y,
double &  __z 
) const
inlineinherited

Rotate back.

Parameters
__xx value
__yy value
__zz value

Definition at line 355 of file JRotation3D.hh.

356  {
357  const double x = a00 * __x + a10 * __y + a20 * __z;
358  const double y = a01 * __x + a11 * __y + a21 * __z;
359  const double z = a02 * __x + a12 * __y + a22 * __z;
360 
361  __x = x;
362  __y = y;
363  __z = z;
364  }
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.

79  {
80  static JMatrix3D matrix;
81 
82  return matrix;
83  }
JMATH::JMatrix3D
3 x 3 matrix
Definition: JMath/JMatrix3D.hh:32
JMatrix3D& JMATH::JMatrix3D::setIdentity ( )
inlineinherited

Set to identity matrix.

Returns
this matrix

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

92  {
93  a00 = 1.0; a01 = 0.0; a02 = 0.0;
94  a10 = 0.0; a11 = 1.0; a12 = 0.0;
95  a20 = 0.0; a21 = 0.0; a22 = 1.0;
96 
97  return *this;
98  }
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.

107  {
108  static JMatrix3D matrix(JMatrix3D().setIdentity());
109 
110  return matrix;
111  }
JMATH::JMatrix3D::JMatrix3D
JMatrix3D()
Default constructor.
Definition: JMath/JMatrix3D.hh:44
JMATH::JMatrix3D
3 x 3 matrix
Definition: JMath/JMatrix3D.hh:32
JMATH::JMatrix3D::setIdentity
JMatrix3D & setIdentity()
Set to identity matrix.
Definition: JMath/JMatrix3D.hh:91
void JMATH::JMatrix3D::set ( const JMatrix3D &  A)
inlineinherited

Set matrix.

Parameters
Amatrix

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

120  {
121  static_cast<JMatrix3D&>(*this) = A;
122  }
JMATH::JMatrix3D
3 x 3 matrix
Definition: JMath/JMatrix3D.hh:32
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Definition: JShellParser.csh:15
JMatrix3D& JMATH::JMatrix3D::reset ( )
inlineinherited

Set matrix to the null matrix.

Returns
this matrix

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

131  {
132  *this = JMatrix3D();
133 
134  return *this;
135  }
JMATH::JMatrix3D::JMatrix3D
JMatrix3D()
Default constructor.
Definition: JMath/JMatrix3D.hh:44
JMatrix3D& JMATH::JMatrix3D::negate ( )
inlineinherited

Negate matrix.

Returns
-this matrix

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

161  {
162  a00 = -a00; a01 = -a01; a02 = -a02;
163  a10 = -a10; a11 = -a11; a12 = -a12;
164  a20 = -a20; a21 = -a21; a22 = -a22;
165 
166  return *this;
167  }
JMatrix3D& JMATH::JMatrix3D::add ( const JMatrix3D &  A)
inlineinherited

Matrix addition.

Parameters
Amatrix
Returns
this matrix + A

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

177  {
178  a00 += A.a00; a01 += A.a01; a02 += A.a02;
179  a10 += A.a10; a11 += A.a11; a12 += A.a12;
180  a20 += A.a20; a21 += A.a21; a22 += A.a22;
181 
182  return *this;
183  }
JMatrix3D& JMATH::JMatrix3D::sub ( const JMatrix3D &  A)
inlineinherited

Matrix subtraction.

Parameters
Amatrix
Returns
this matrix - A

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

193  {
194  a00 -= A.a00; a01 -= A.a01; a02 -= A.a02;
195  a10 -= A.a10; a11 -= A.a11; a12 -= A.a12;
196  a20 -= A.a20; a21 -= A.a21; a22 -= A.a22;
197 
198  return *this;
199  }
JMatrix3D& JMATH::JMatrix3D::div ( const double  factor)
inlineinherited

Scale matrix.

Parameters
factorfactor
Returns
this matrix / factor

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

225  {
226  a00 /= factor; a01 /= factor; a02 /= factor;
227  a10 /= factor; a11 /= factor; a12 /= factor;
228  a20 /= factor; a21 /= factor; a22 /= factor;
229 
230  return *this;
231  }
bool JMATH::JMatrix3D::equals ( const JMatrix3D &  A,
const double  eps = std::numeric_limits<double>::min() 
) const
inlineinherited

Equality.

Parameters
Amatrix
epsnumerical precision
Returns
true if matrices identical; else false

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

269  {
270  return (fabs(a00 - A.a00) <= eps &&
271  fabs(a01 - A.a01) <= eps &&
272  fabs(a02 - A.a02) <= eps &&
273  fabs(a10 - A.a10) <= eps &&
274  fabs(a11 - A.a11) <= eps &&
275  fabs(a12 - A.a12) <= eps &&
276  fabs(a20 - A.a20) <= eps &&
277  fabs(a21 - A.a21) <= eps &&
278  fabs(a22 - A.a22) <= eps);
279  }
bool JMATH::JMatrix3D::isIdentity ( const double  eps = std::numeric_limits<double>::min()) const
inlineinherited

Test identity.

Parameters
epsnumerical precision
Returns
true if identity matrix; else false

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

289  {
290  return equals(getIdentity(), eps);
291  }
JMATH::JMatrix3D::getIdentity
static const JMatrix3D & getIdentity()
Get reference to unique instance of this class object.
Definition: JMath/JMatrix3D.hh:106
JMATH::JMatrix3D::equals
bool equals(const JMatrix3D &A, const double eps=std::numeric_limits< double >::min()) const
Equality.
Definition: JMath/JMatrix3D.hh:267
double JMATH::JMatrix3D::getDeterminant ( ) const
inlineinherited

Get determinant of matrix.

Returns
determinant of matrix

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

300  {
301  double det = 0.0;
302 
303  det += a00 * (a11 * a22 - a21 * a12);
304  det -= a01 * (a10 * a22 - a20 * a12);
305  det += a02 * (a10 * a21 - a20 * a11);
306 
307  return det;
308  }
void JMATH::JMatrix3D::transform ( double &  __x,
double &  __y,
double &  __z 
) const
inlineinherited

Transform.

Parameters
__xx value
__yy value
__zz value

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

319  {
320  const double x = a00 * __x + a01 * __y + a02 * __z;
321  const double y = a10 * __x + a11 * __y + a12 * __z;
322  const double z = a20 * __x + a21 * __y + a22 * __z;
323 
324  __x = x;
325  __y = y;
326  __z = z;
327  }

Member Data Documentation

double JMATH::JMatrix3D::a00
inherited

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

double JMATH::JMatrix3D::a01
inherited

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

double JMATH::JMatrix3D::a02
inherited

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

double JMATH::JMatrix3D::a10
inherited

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

double JMATH::JMatrix3D::a11
inherited

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

double JMATH::JMatrix3D::a12
inherited

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

double JMATH::JMatrix3D::a20
inherited

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

double JMATH::JMatrix3D::a21
inherited

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

double JMATH::JMatrix3D::a22
inherited

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

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