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matrix3d.h
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26 // matrix3.template.h file to make changes.
27 
28 #ifndef GF_MATRIX3D_H
29 #define GF_MATRIX3D_H
30 
31 /// \file gf/matrix3d.h
32 /// \ingroup group_gf_LinearAlgebra
33 
34 #include "pxr/pxr.h"
35 #include "pxr/base/gf/api.h"
36 #include "pxr/base/gf/declare.h"
37 #include "pxr/base/gf/matrixData.h"
38 #include "pxr/base/gf/vec3d.h"
39 #include "pxr/base/gf/traits.h"
40 
41 #include <hboost/functional/hash.hpp>
42 
43 #include <iosfwd>
44 #include <vector>
45 
47 
48 template <>
49 struct GfIsGfMatrix<class GfMatrix3d> { static const bool value = true; };
50 
51 class GfMatrix3d;
52 class GfMatrix3f;
53 class GfRotation;
54 class GfQuaternion;
55 class GfQuatd;
56 
57 /// \class GfMatrix3d
58 /// \ingroup group_gf_LinearAlgebra
59 ///
60 /// Stores a 3x3 matrix of \c double elements. A basic type.
61 ///
62 /// Matrices are defined to be in row-major order, so <c>matrix[i][j]</c>
63 /// indexes the element in the \e i th row and the \e j th column.
64 ///
65 /// <h3>3D Transformations</h3>
66 ///
67 /// Three methods, SetRotate(), SetScale(), and ExtractRotation(), interpret
68 /// a GfMatrix3d as a 3D transformation. By convention, vectors are treated
69 /// primarily as row vectors, implying the following:
70 ///
71 /// \li Transformation matrices are organized to deal with row
72 /// vectors, not column vectors.
73 /// \li Each of the Set() methods in this class completely rewrites the
74 /// matrix; for example, SetRotate() yields a matrix
75 /// which does nothing but rotate.
76 /// \li When multiplying two transformation matrices, the matrix
77 /// on the left applies a more local transformation to a row
78 /// vector. For example, if R represents a rotation
79 /// matrix and S represents a scale matrix, the
80 /// product R*S will rotate a row vector, then scale
81 /// it.
83 {
84 public:
85  typedef double ScalarType;
86 
87  static const size_t numRows = 3;
88  static const size_t numColumns = 3;
89 
90  /// Default constructor. Leaves the matrix component values undefined.
91  GfMatrix3d() = default;
92 
93  /// Constructor. Initializes the matrix from 9 independent
94  /// \c double values, specified in row-major order. For example,
95  /// parameter \e m10 specifies the value in row 1 and column 0.
96  GfMatrix3d(double m00, double m01, double m02,
97  double m10, double m11, double m12,
98  double m20, double m21, double m22) {
99  Set(m00, m01, m02,
100  m10, m11, m12,
101  m20, m21, m22);
102  }
103 
104  /// Constructor. Initializes the matrix from a 3x3 array
105  /// of \c double values, specified in row-major order.
106  GfMatrix3d(const double m[3][3]) {
107  Set(m);
108  }
109 
110  /// Constructor. Explicitly initializes the matrix to \e s times the
111  /// identity matrix.
112  explicit GfMatrix3d(double s) {
113  SetDiagonal(s);
114  }
115 
116  /// This explicit constructor initializes the matrix to \p s times
117  /// the identity matrix.
118  explicit GfMatrix3d(int s) {
119  SetDiagonal(s);
120  }
121 
122  /// Constructor. Explicitly initializes the matrix to diagonal form,
123  /// with the \e i th element on the diagonal set to <c>v[i]</c>.
124  explicit GfMatrix3d(const GfVec3d& v) {
125  SetDiagonal(v);
126  }
127 
128  /// Constructor. Initialize the matrix from a vector of vectors of
129  /// double. The vector is expected to be 3x3. If it is
130  /// too big, only the first 3 rows and/or columns will be used.
131  /// If it is too small, uninitialized elements will be filled in with
132  /// the corresponding elements from an identity matrix.
133  ///
134  GF_API
135  explicit GfMatrix3d(const std::vector< std::vector<double> >& v);
136 
137  /// Constructor. Initialize the matrix from a vector of vectors of
138  /// float. The vector is expected to be 3x3. If it is
139  /// too big, only the first 3 rows and/or columns will be used.
140  /// If it is too small, uninitialized elements will be filled in with
141  /// the corresponding elements from an identity matrix.
142  ///
143  GF_API
144  explicit GfMatrix3d(const std::vector< std::vector<float> >& v);
145 
146  /// Constructor. Initialize matrix from rotation.
147  GF_API
148  GfMatrix3d(const GfRotation& rot);
149 
150  /// Constructor. Initialize matrix from a quaternion.
151  GF_API
152  explicit GfMatrix3d(const GfQuatd& rot);
153 
154  /// This explicit constructor converts a "float" matrix to a "double" matrix.
155  GF_API
156  explicit GfMatrix3d(const class GfMatrix3f& m);
157 
158  /// Sets a row of the matrix from a Vec3.
159  void SetRow(int i, const GfVec3d & v) {
160  _mtx[i][0] = v[0];
161  _mtx[i][1] = v[1];
162  _mtx[i][2] = v[2];
163  }
164 
165  /// Sets a column of the matrix from a Vec3.
166  void SetColumn(int i, const GfVec3d & v) {
167  _mtx[0][i] = v[0];
168  _mtx[1][i] = v[1];
169  _mtx[2][i] = v[2];
170  }
171 
172  /// Gets a row of the matrix as a Vec3.
173  GfVec3d GetRow(int i) const {
174  return GfVec3d(_mtx[i][0], _mtx[i][1], _mtx[i][2]);
175  }
176 
177  /// Gets a column of the matrix as a Vec3.
178  GfVec3d GetColumn(int i) const {
179  return GfVec3d(_mtx[0][i], _mtx[1][i], _mtx[2][i]);
180  }
181 
182  /// Sets the matrix from 9 independent \c double values,
183  /// specified in row-major order. For example, parameter \e m10 specifies
184  /// the value in row 1 and column 0.
185  GfMatrix3d& Set(double m00, double m01, double m02,
186  double m10, double m11, double m12,
187  double m20, double m21, double m22) {
188  _mtx[0][0] = m00; _mtx[0][1] = m01; _mtx[0][2] = m02;
189  _mtx[1][0] = m10; _mtx[1][1] = m11; _mtx[1][2] = m12;
190  _mtx[2][0] = m20; _mtx[2][1] = m21; _mtx[2][2] = m22;
191  return *this;
192  }
193 
194  /// Sets the matrix from a 3x3 array of \c double
195  /// values, specified in row-major order.
196  GfMatrix3d& Set(const double m[3][3]) {
197  _mtx[0][0] = m[0][0];
198  _mtx[0][1] = m[0][1];
199  _mtx[0][2] = m[0][2];
200  _mtx[1][0] = m[1][0];
201  _mtx[1][1] = m[1][1];
202  _mtx[1][2] = m[1][2];
203  _mtx[2][0] = m[2][0];
204  _mtx[2][1] = m[2][1];
205  _mtx[2][2] = m[2][2];
206  return *this;
207  }
208 
209  /// Sets the matrix to the identity matrix.
211  return SetDiagonal(1);
212  }
213 
214  /// Sets the matrix to zero.
216  return SetDiagonal(0);
217  }
218 
219  /// Sets the matrix to \e s times the identity matrix.
220  GF_API
221  GfMatrix3d& SetDiagonal(double s);
222 
223  /// Sets the matrix to have diagonal (<c>v[0], v[1], v[2]</c>).
224  GF_API
225  GfMatrix3d& SetDiagonal(const GfVec3d&);
226 
227  /// Fills a 3x3 array of \c double values with the values in
228  /// the matrix, specified in row-major order.
229  GF_API
230  double* Get(double m[3][3]) const;
231 
232  /// Returns raw access to components of matrix as an array of
233  /// \c double values. Components are in row-major order.
234  double* data() {
235  return _mtx.GetData();
236  }
237 
238  /// Returns const raw access to components of matrix as an array of
239  /// \c double values. Components are in row-major order.
240  const double* data() const {
241  return _mtx.GetData();
242  }
243 
244  /// Returns vector components as an array of \c double values.
245  double* GetArray() {
246  return _mtx.GetData();
247  }
248 
249  /// Returns vector components as a const array of \c double values.
250  const double* GetArray() const {
251  return _mtx.GetData();
252  }
253 
254  /// Accesses an indexed row \e i of the matrix as an array of 3 \c
255  /// double values so that standard indexing (such as <c>m[0][1]</c>)
256  /// works correctly.
257  double* operator [](int i) { return _mtx[i]; }
258 
259  /// Accesses an indexed row \e i of the matrix as an array of 3 \c
260  /// double values so that standard indexing (such as <c>m[0][1]</c>)
261  /// works correctly.
262  const double* operator [](int i) const { return _mtx[i]; }
263 
264  /// Hash.
265  friend inline size_t hash_value(GfMatrix3d const &m) {
266  int nElems = 3 * 3;
267  size_t h = 0;
268  const double *p = m.GetArray();
269  while (nElems--)
270  hboost::hash_combine(h, *p++);
271  return h;
272  }
273 
274  /// Tests for element-wise matrix equality. All elements must match
275  /// exactly for matrices to be considered equal.
276  GF_API
277  bool operator ==(const GfMatrix3d& m) const;
278 
279  /// Tests for element-wise matrix equality. All elements must match
280  /// exactly for matrices to be considered equal.
281  GF_API
282  bool operator ==(const GfMatrix3f& m) const;
283 
284  /// Tests for element-wise matrix inequality. All elements must match
285  /// exactly for matrices to be considered equal.
286  bool operator !=(const GfMatrix3d& m) const {
287  return !(*this == m);
288  }
289 
290  /// Tests for element-wise matrix inequality. All elements must match
291  /// exactly for matrices to be considered equal.
292  bool operator !=(const GfMatrix3f& m) const {
293  return !(*this == m);
294  }
295 
296  /// Returns the transpose of the matrix.
297  GF_API
298  GfMatrix3d GetTranspose() const;
299 
300  /// Returns the inverse of the matrix, or FLT_MAX * SetIdentity() if the
301  /// matrix is singular. (FLT_MAX is the largest value a \c float can have,
302  /// as defined by the system.) The matrix is considered singular if the
303  /// determinant is less than or equal to the optional parameter \e eps. If
304  /// \e det is non-null, <c>*det</c> is set to the determinant.
305  GF_API
306  GfMatrix3d GetInverse(double* det = NULL, double eps = 0) const;
307 
308  /// Returns the determinant of the matrix.
309  GF_API
310  double GetDeterminant() const;
311 
312  /// Makes the matrix orthonormal in place. This is an iterative method that
313  /// is much more stable than the previous cross/cross method. If the
314  /// iterative method does not converge, a warning is issued.
315  ///
316  /// Returns true if the iteration converged, false otherwise. Leaves any
317  /// translation part of the matrix unchanged. If \a issueWarning is true,
318  /// this method will issue a warning if the iteration does not converge,
319  /// otherwise it will be silent.
320  GF_API
321  bool Orthonormalize(bool issueWarning=true);
322 
323  /// Returns an orthonormalized copy of the matrix.
324  GF_API
325  GfMatrix3d GetOrthonormalized(bool issueWarning=true) const;
326 
327  /// Returns the sign of the determinant of the matrix, i.e. 1 for a
328  /// right-handed matrix, -1 for a left-handed matrix, and 0 for a
329  /// singular matrix.
330  GF_API
331  double GetHandedness() const;
332 
333  /// Returns true if the vectors in the matrix form a right-handed
334  /// coordinate system.
335  bool IsRightHanded() const {
336  return GetHandedness() == 1.0;
337  }
338 
339  /// Returns true if the vectors in matrix form a left-handed
340  /// coordinate system.
341  bool IsLeftHanded() const {
342  return GetHandedness() == -1.0;
343  }
344 
345  /// Post-multiplies matrix \e m into this matrix.
346  GF_API
348 
349  /// Multiplies the matrix by a double.
350  GF_API
351  GfMatrix3d& operator *=(double);
352 
353  /// Returns the product of a matrix and a double.
354  friend GfMatrix3d operator *(const GfMatrix3d& m1, double d)
355  {
356  GfMatrix3d m = m1;
357  return m *= d;
358  }
359 
360  ///
361  // Returns the product of a matrix and a double.
362  friend GfMatrix3d operator *(double d, const GfMatrix3d& m)
363  {
364  return m * d;
365  }
366 
367  /// Adds matrix \e m to this matrix.
368  GF_API
370 
371  /// Subtracts matrix \e m from this matrix.
372  GF_API
374 
375  /// Returns the unary negation of matrix \e m.
376  GF_API
377  friend GfMatrix3d operator -(const GfMatrix3d& m);
378 
379  /// Adds matrix \e m2 to \e m1
380  friend GfMatrix3d operator +(const GfMatrix3d& m1, const GfMatrix3d& m2)
381  {
382  GfMatrix3d tmp(m1);
383  tmp += m2;
384  return tmp;
385  }
386 
387  /// Subtracts matrix \e m2 from \e m1.
388  friend GfMatrix3d operator -(const GfMatrix3d& m1, const GfMatrix3d& m2)
389  {
390  GfMatrix3d tmp(m1);
391  tmp -= m2;
392  return tmp;
393  }
394 
395  /// Multiplies matrix \e m1 by \e m2.
396  friend GfMatrix3d operator *(const GfMatrix3d& m1, const GfMatrix3d& m2)
397  {
398  GfMatrix3d tmp(m1);
399  tmp *= m2;
400  return tmp;
401  }
402 
403  /// Divides matrix \e m1 by \e m2 (that is, <c>m1 * inv(m2)</c>).
404  friend GfMatrix3d operator /(const GfMatrix3d& m1, const GfMatrix3d& m2)
405  {
406  return(m1 * m2.GetInverse());
407  }
408 
409  /// Returns the product of a matrix \e m and a column vector \e vec.
410  friend inline GfVec3d operator *(const GfMatrix3d& m, const GfVec3d& vec) {
411  return GfVec3d(vec[0] * m._mtx[0][0] + vec[1] * m._mtx[0][1] + vec[2] * m._mtx[0][2],
412  vec[0] * m._mtx[1][0] + vec[1] * m._mtx[1][1] + vec[2] * m._mtx[1][2],
413  vec[0] * m._mtx[2][0] + vec[1] * m._mtx[2][1] + vec[2] * m._mtx[2][2]);
414  }
415 
416  /// Returns the product of row vector \e vec and a matrix \e m.
417  friend inline GfVec3d operator *(const GfVec3d &vec, const GfMatrix3d& m) {
418  return GfVec3d(vec[0] * m._mtx[0][0] + vec[1] * m._mtx[1][0] + vec[2] * m._mtx[2][0],
419  vec[0] * m._mtx[0][1] + vec[1] * m._mtx[1][1] + vec[2] * m._mtx[2][1],
420  vec[0] * m._mtx[0][2] + vec[1] * m._mtx[1][2] + vec[2] * m._mtx[2][2]);
421  }
422 
423  /// Returns the product of a matrix \e m and a column vector \e vec.
424  /// Note that the return type is a \c GfVec3f.
425  GF_API
426  friend GfVec3f operator *(const GfMatrix3d& m, const GfVec3f& vec);
427 
428  /// Returns the product of row vector \e vec and a matrix \e m.
429  /// Note that the return type is a \c GfVec3f.
430  GF_API
431  friend GfVec3f operator *(const GfVec3f &vec, const GfMatrix3d& m);
432 
433  /// Sets matrix to specify a uniform scaling by \e scaleFactor.
434  GF_API
435  GfMatrix3d& SetScale(double scaleFactor);
436 
437  /// \name 3D Transformation Utilities
438  /// @{
439 
440  /// Sets the matrix to specify a rotation equivalent to \e rot.
441  GF_API
442  GfMatrix3d& SetRotate(const GfQuatd &rot);
443 
444  /// Sets the matrix to specify a rotation equivalent to \e rot.
445  GF_API
447 
448  /// Sets the matrix to specify a nonuniform scaling in x, y, and z by
449  /// the factors in vector \e scaleFactors.
450  GF_API
451  GfMatrix3d& SetScale(const GfVec3d &scaleFactors);
452 
453  /// Returns the rotation corresponding to this matrix. This works
454  /// well only if the matrix represents a rotation.
455  ///
456  /// For good results, consider calling Orthonormalize() before calling
457  /// this method.
458  GF_API
459  GfRotation ExtractRotation() const;
460 
461  /// Decompose the rotation corresponding to this matrix about 3
462  /// orthogonal axes. If the axes are not orthogonal, warnings
463  /// will be spewed.
464  ///
465  /// This is a convenience method that is equivalent to calling
466  /// ExtractRotation().Decompose().
467  GF_API
468  GfVec3d DecomposeRotation(const GfVec3d &axis0,
469  const GfVec3d &axis1,
470  const GfVec3d &axis2 ) const;
471 
472  /// Returns the quaternion corresponding to this matrix. This works
473  /// well only if the matrix represents a rotation.
474  ///
475  /// For good results, consider calling Orthonormalize() before calling
476  /// this method.
477  GF_API
479 
480  /// @}
481 
482 private:
483  /// Set the matrix to the rotation given by a quaternion,
484  /// defined by the real component \p r and imaginary components \p i.
485  void _SetRotateFromQuat(double r, const GfVec3d& i);
486 
487 
488 private:
489  /// Matrix storage, in row-major order.
491 
492  // Friend declarations
493  friend class GfMatrix3f;
494 };
495 
496 
497 /// Tests for equality within a given tolerance, returning \c true if the
498 /// difference between each component of the matrix is less than or equal
499 /// to \p tolerance, or false otherwise.
500 GF_API
501 bool GfIsClose(GfMatrix3d const &m1, GfMatrix3d const &m2, double tolerance);
502 
503 /// Output a GfMatrix3d
504 /// \ingroup group_gf_DebuggingOutput
505 GF_API std::ostream& operator<<(std::ostream &, GfMatrix3d const &);
506 
508 
509 #endif // GF_MATRIX3D_H
GLdouble s
Definition: glew.h:1390
GF_API bool Orthonormalize(bool issueWarning=true)
bool IsLeftHanded() const
Definition: matrix3d.h:341
GfMatrix3d(const GfVec3d &v)
Definition: matrix3d.h:124
GF_API GfMatrix3d & operator-=(const GfMatrix3d &m)
Subtracts matrix m from this matrix.
GF_API GfMatrix3d & operator+=(const GfMatrix3d &m)
Adds matrix m to this matrix.
GF_API GfMatrix3d GetOrthonormalized(bool issueWarning=true) const
Returns an orthonormalized copy of the matrix.
*get result *(waiting if necessary)*A common idiom is to fire a bunch of sub tasks at the and then *wait for them to all complete We provide a helper class
Definition: thread.h:643
bool operator!=(const GfMatrix3d &m) const
Definition: matrix3d.h:286
GF_API double GetHandedness() const
GfMatrix3d(double s)
Definition: matrix3d.h:112
double * GetArray()
Returns vector components as an array of double values.
Definition: matrix3d.h:245
GfMatrix3d(int s)
Definition: matrix3d.h:118
GA_API const UT_StringHolder rot
Definition: vec3f.h:63
GfMatrix3d()=default
Default constructor. Leaves the matrix component values undefined.
const GLdouble * m
Definition: glew.h:9124
const GLdouble * v
Definition: glew.h:1391
GF_API GfMatrix3d & SetDiagonal(double s)
Sets the matrix to s times the identity matrix.
GF_API GfMatrix3d & SetRotate(const GfQuatd &rot)
Sets the matrix to specify a rotation equivalent to rot.
GfVec3d GetRow(int i) const
Gets a row of the matrix as a Vec3.
Definition: matrix3d.h:173
static const size_t numColumns
Definition: matrix3d.h:88
bool IsRightHanded() const
Definition: matrix3d.h:335
GF_API GfRotation ExtractRotation() const
friend GfMatrix3d operator*(const GfMatrix3d &m1, double d)
Returns the product of a matrix and a double.
Definition: matrix3d.h:354
GfMatrix3d(const double m[3][3])
Definition: matrix3d.h:106
T * GetData()
Return a pointer to the start of all the data.
Definition: matrixData.h:50
GF_API GfVec3d DecomposeRotation(const GfVec3d &axis0, const GfVec3d &axis1, const GfVec3d &axis2) const
const double * data() const
Definition: matrix3d.h:240
GfMatrix3d & SetZero()
Sets the matrix to zero.
Definition: matrix3d.h:215
GF_API GfQuaternion ExtractRotationQuaternion() const
GF_API double GetDeterminant() const
Returns the determinant of the matrix.
GF_API GfMatrix3d & operator*=(const GfMatrix3d &m)
Post-multiplies matrix m into this matrix.
friend GfMatrix3d operator+(const GfMatrix3d &m1, const GfMatrix3d &m2)
Adds matrix m2 to m1.
Definition: matrix3d.h:380
GLfloat GLfloat GLfloat GLfloat h
Definition: glew.h:8011
GF_API friend GfMatrix3d operator-(const GfMatrix3d &m)
Returns the unary negation of matrix m.
GF_API GfMatrix3d GetInverse(double *det=NULL, double eps=0) const
double * operator[](int i)
Definition: matrix3d.h:257
GLfloat GLfloat p
Definition: glew.h:16321
PXR_NAMESPACE_CLOSE_SCOPE PXR_NAMESPACE_OPEN_SCOPE
Definition: path.h:1245
void SetColumn(int i, const GfVec3d &v)
Sets a column of the matrix from a Vec3.
Definition: matrix3d.h:166
double ScalarType
Definition: matrix3d.h:85
GF_API double * Get(double m[3][3]) const
GfVec3d GetColumn(int i) const
Gets a column of the matrix as a Vec3.
Definition: matrix3d.h:178
GLdouble GLdouble GLdouble r
Definition: glew.h:1406
Definition: vec3d.h:63
GfMatrix3d & Set(const double m[3][3])
Definition: matrix3d.h:196
GfMatrix3d(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)
Definition: matrix3d.h:96
#define PXR_NAMESPACE_CLOSE_SCOPE
Definition: pxr.h:83
GfMatrix3d & Set(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)
Definition: matrix3d.h:185
GF_API bool GfIsClose(GfMatrix3d const &m1, GfMatrix3d const &m2, double tolerance)
GF_API bool operator==(const GfMatrix3d &m) const
const double * GetArray() const
Returns vector components as a const array of double values.
Definition: matrix3d.h:250
GF_API GfMatrix3d GetTranspose() const
Returns the transpose of the matrix.
Definition: quatd.h:60
GF_API std::ostream & operator<<(std::ostream &, GfMatrix3d const &)
GF_API GfMatrix3d & SetScale(double scaleFactor)
Sets matrix to specify a uniform scaling by scaleFactor.
static const size_t numRows
Definition: matrix3d.h:87
GLsizei const GLfloat * value
Definition: glew.h:1849
double * data()
Definition: matrix3d.h:234
#define GF_API
Definition: api.h:40
friend GfMatrix3d operator/(const GfMatrix3d &m1, const GfMatrix3d &m2)
Divides matrix m1 by m2 (that is, m1 * inv(m2)).
Definition: matrix3d.h:404
GfMatrix3d & SetIdentity()
Sets the matrix to the identity matrix.
Definition: matrix3d.h:210
friend size_t hash_value(GfMatrix3d const &m)
Hash.
Definition: matrix3d.h:265
void SetRow(int i, const GfVec3d &v)
Sets a row of the matrix from a Vec3.
Definition: matrix3d.h:159