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matrix4f.h
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26 // matrix4.template.h file to make changes.
27 
28 #ifndef PXR_BASE_GF_MATRIX4F_H
29 #define PXR_BASE_GF_MATRIX4F_H
30 
31 /// \file gf/matrix4f.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/vec4f.h"
39 #include "pxr/base/gf/traits.h"
41 #include "pxr/base/gf/limits.h"
42 #include "pxr/base/gf/math.h"
43 #include "pxr/base/gf/vec3f.h"
44 #include "pxr/base/tf/hash.h"
45 
46 #include <iosfwd>
47 #include <vector>
48 
50 
51 template <>
52 struct GfIsGfMatrix<class GfMatrix4f> { static const bool value = true; };
53 
54 class GfMatrix4d;
55 class GfMatrix4f;
56 class GfQuatf;
57 class GfRotation;
58 class GfMatrix3f;
59 
60 /// \class GfMatrix4f
61 /// \ingroup group_gf_LinearAlgebra
62 ///
63 /// Stores a 4x4 matrix of \c float elements. A basic type.
64 ///
65 /// Matrices are defined to be in row-major order, so <c>matrix[i][j]</c>
66 /// indexes the element in the \e i th row and the \e j th column.
67 ///
68 /// <h3>3D Transformations</h3>
69 ///
70 /// The following methods interpret a GfMatrix4f as a 3D
71 /// transformation: SetRotate(), SetScale(), SetTranslate(), SetLookAt(),
72 /// Factor(), ExtractTranslation(), ExtractRotation(), Transform(), TransformDir().
73 /// By convention, vectors are treated primarily as row vectors,
74 /// implying the following:
75 /// \li Transformation matrices are organized to deal with row
76 /// vectors, not column vectors. For example, the last row of a matrix
77 /// contains the translation amounts.
78 /// \li Each of the Set() methods below completely rewrites the
79 /// matrix; for example, SetTranslate() yields a matrix
80 /// which does nothing but translate.
81 /// \li When multiplying two transformation matrices, the matrix
82 /// on the left applies a more local transformation to a row
83 /// vector. For example, if R represents a rotation
84 /// matrix and T represents a translation matrix, the
85 /// product R*T will rotate a row vector, then translate
86 /// it.
88 {
89 public:
90  typedef float ScalarType;
91 
92  static const size_t numRows = 4;
93  static const size_t numColumns = 4;
94 
95  /// Default constructor. Leaves the matrix component values undefined.
96  GfMatrix4f() = default;
97 
98  /// Constructor. Initializes the matrix from 16 independent
99  /// \c float values, specified in row-major order. For example,
100  /// parameter \e m10 specifies the value in row 1 and column 0.
101  GfMatrix4f(float m00, float m01, float m02, float m03,
102  float m10, float m11, float m12, float m13,
103  float m20, float m21, float m22, float m23,
104  float m30, float m31, float m32, float m33) {
105  Set(m00, m01, m02, m03,
106  m10, m11, m12, m13,
107  m20, m21, m22, m23,
108  m30, m31, m32, m33);
109  }
110 
111  /// Constructor. Initializes the matrix from a 4x4 array
112  /// of \c float values, specified in row-major order.
113  GfMatrix4f(const float m[4][4]) {
114  Set(m);
115  }
116 
117  /// Constructor. Explicitly initializes the matrix to \e s times the
118  /// identity matrix.
119  explicit GfMatrix4f(float s) {
120  SetDiagonal(s);
121  }
122 
123  /// Constructor. Explicitly initializes the matrix to diagonal form,
124  /// with the \e i th element on the diagonal set to <c>v[i]</c>.
125  explicit GfMatrix4f(const GfVec4f& v) {
126  SetDiagonal(v);
127  }
128 
129  /// Constructor. Initialize the matrix from a vector of vectors of
130  /// double. The vector is expected to be 4x4. If it is
131  /// too big, only the first 4 rows and/or columns will be used.
132  /// If it is too small, uninitialized elements will be filled in with
133  /// the corresponding elements from an identity matrix.
134  ///
135  GF_API
136  explicit GfMatrix4f(const std::vector< std::vector<double> >& v);
137 
138  /// Constructor. Initialize the matrix from a vector of vectors of
139  /// float. The vector is expected to be 4x4. If it is
140  /// too big, only the first 4 rows and/or columns will be used.
141  /// If it is too small, uninitialized elements will be filled in with
142  /// the corresponding elements from an identity matrix.
143  ///
144  GF_API
145  explicit GfMatrix4f(const std::vector< std::vector<float> >& v);
146 
147  /// Constructor. Initialize the matrix from 4 row vectors of
148  /// double. Each vector is expected to length 4. If it is too
149  /// big, only the first 4 items will be used. If it is too small,
150  /// uninitialized elements will be filled in with the
151  /// corresponding elements from an identity matrix.
152  ///
153  GF_API
154  explicit GfMatrix4f(const std::vector<double>& r0,
155  const std::vector<double>& r1,
156  const std::vector<double>& r2,
157  const std::vector<double>& r3);
158 
159  /// Constructor. Initialize the matrix from 4 row vectors of
160  /// float. Each vector is expected to length 4. If it is too
161  /// big, only the first 4 items will be used. If it is too small,
162  /// uninitialized elements will be filled in with the
163  /// corresponding elements from an identity matrix.
164  ///
165  GF_API
166  explicit GfMatrix4f(const std::vector<float>& r0,
167  const std::vector<float>& r1,
168  const std::vector<float>& r2,
169  const std::vector<float>& r3);
170 
171  /// Constructor. Initializes a transformation matrix to perform the
172  /// indicated rotation and translation.
173  GF_API
175  const GfVec3f& translate);
176 
177  /// Constructor. Initializes a transformation matrix to perform the
178  /// indicated rotation and translation.
179  GF_API
180  GfMatrix4f(const GfMatrix3f& rotmx,
181  const GfVec3f& translate);
182  /// This explicit constructor converts a "double" matrix to a "float" matrix.
183  GF_API
184  explicit GfMatrix4f(const class GfMatrix4d& m);
185 
186  /// Sets a row of the matrix from a Vec4.
187  void SetRow(int i, const GfVec4f & v) {
188  _mtx[i][0] = v[0];
189  _mtx[i][1] = v[1];
190  _mtx[i][2] = v[2];
191  _mtx[i][3] = v[3];
192  }
193 
194  /// Sets a column of the matrix from a Vec4.
195  void SetColumn(int i, const GfVec4f & v) {
196  _mtx[0][i] = v[0];
197  _mtx[1][i] = v[1];
198  _mtx[2][i] = v[2];
199  _mtx[3][i] = v[3];
200  }
201 
202  /// Gets a row of the matrix as a Vec4.
203  GfVec4f GetRow(int i) const {
204  return GfVec4f(_mtx[i][0], _mtx[i][1], _mtx[i][2], _mtx[i][3]);
205  }
206 
207  /// Gets a column of the matrix as a Vec4.
208  GfVec4f GetColumn(int i) const {
209  return GfVec4f(_mtx[0][i], _mtx[1][i], _mtx[2][i], _mtx[3][i]);
210  }
211 
212  /// Sets the matrix from 16 independent \c float values,
213  /// specified in row-major order. For example, parameter \e m10 specifies
214  /// the value in row 1 and column 0.
215  GfMatrix4f& Set(float m00, float m01, float m02, float m03,
216  float m10, float m11, float m12, float m13,
217  float m20, float m21, float m22, float m23,
218  float m30, float m31, float m32, float m33) {
219  _mtx[0][0] = m00; _mtx[0][1] = m01; _mtx[0][2] = m02; _mtx[0][3] = m03;
220  _mtx[1][0] = m10; _mtx[1][1] = m11; _mtx[1][2] = m12; _mtx[1][3] = m13;
221  _mtx[2][0] = m20; _mtx[2][1] = m21; _mtx[2][2] = m22; _mtx[2][3] = m23;
222  _mtx[3][0] = m30; _mtx[3][1] = m31; _mtx[3][2] = m32; _mtx[3][3] = m33;
223  return *this;
224  }
225 
226  /// Sets the matrix from a 4x4 array of \c float
227  /// values, specified in row-major order.
228  GfMatrix4f& Set(const float m[4][4]) {
229  _mtx[0][0] = m[0][0];
230  _mtx[0][1] = m[0][1];
231  _mtx[0][2] = m[0][2];
232  _mtx[0][3] = m[0][3];
233  _mtx[1][0] = m[1][0];
234  _mtx[1][1] = m[1][1];
235  _mtx[1][2] = m[1][2];
236  _mtx[1][3] = m[1][3];
237  _mtx[2][0] = m[2][0];
238  _mtx[2][1] = m[2][1];
239  _mtx[2][2] = m[2][2];
240  _mtx[2][3] = m[2][3];
241  _mtx[3][0] = m[3][0];
242  _mtx[3][1] = m[3][1];
243  _mtx[3][2] = m[3][2];
244  _mtx[3][3] = m[3][3];
245  return *this;
246  }
247 
248  /// Sets the matrix to the identity matrix.
250  return SetDiagonal(1);
251  }
252 
253  /// Sets the matrix to zero.
255  return SetDiagonal(0);
256  }
257 
258  /// Sets the matrix to \e s times the identity matrix.
259  GF_API
260  GfMatrix4f& SetDiagonal(float s);
261 
262  /// Sets the matrix to have diagonal (<c>v[0], v[1], v[2], v[3]</c>).
263  GF_API
264  GfMatrix4f& SetDiagonal(const GfVec4f&);
265 
266  /// Fills a 4x4 array of \c float values with the values in
267  /// the matrix, specified in row-major order.
268  GF_API
269  float* Get(float m[4][4]) const;
270 
271  /// Returns raw access to components of matrix as an array of
272  /// \c float values. Components are in row-major order.
273  float* data() {
274  return _mtx.GetData();
275  }
276 
277  /// Returns const raw access to components of matrix as an array of
278  /// \c float values. Components are in row-major order.
279  const float* data() const {
280  return _mtx.GetData();
281  }
282 
283  /// Returns vector components as an array of \c float values.
284  float* GetArray() {
285  return _mtx.GetData();
286  }
287 
288  /// Returns vector components as a const array of \c float values.
289  const float* GetArray() const {
290  return _mtx.GetData();
291  }
292 
293  /// Accesses an indexed row \e i of the matrix as an array of 4 \c
294  /// float values so that standard indexing (such as <c>m[0][1]</c>)
295  /// works correctly.
296  float* operator [](int i) { return _mtx[i]; }
297 
298  /// Accesses an indexed row \e i of the matrix as an array of 4 \c
299  /// float values so that standard indexing (such as <c>m[0][1]</c>)
300  /// works correctly.
301  const float* operator [](int i) const { return _mtx[i]; }
302 
303  /// Hash.
304  friend inline size_t hash_value(GfMatrix4f const &m) {
305  return TfHash::Combine(
306  m._mtx[0][0],
307  m._mtx[0][1],
308  m._mtx[0][2],
309  m._mtx[0][3],
310  m._mtx[1][0],
311  m._mtx[1][1],
312  m._mtx[1][2],
313  m._mtx[1][3],
314  m._mtx[2][0],
315  m._mtx[2][1],
316  m._mtx[2][2],
317  m._mtx[2][3],
318  m._mtx[3][0],
319  m._mtx[3][1],
320  m._mtx[3][2],
321  m._mtx[3][3]
322  );
323  }
324 
325  /// Tests for element-wise matrix equality. All elements must match
326  /// exactly for matrices to be considered equal.
327  GF_API
328  bool operator ==(const GfMatrix4d& m) const;
329 
330  /// Tests for element-wise matrix equality. All elements must match
331  /// exactly for matrices to be considered equal.
332  GF_API
333  bool operator ==(const GfMatrix4f& m) const;
334 
335  /// Tests for element-wise matrix inequality. All elements must match
336  /// exactly for matrices to be considered equal.
337  bool operator !=(const GfMatrix4d& m) const {
338  return !(*this == m);
339  }
340 
341  /// Tests for element-wise matrix inequality. All elements must match
342  /// exactly for matrices to be considered equal.
343  bool operator !=(const GfMatrix4f& m) const {
344  return !(*this == m);
345  }
346 
347  /// Returns the transpose of the matrix.
348  GF_API
349  GfMatrix4f GetTranspose() const;
350 
351  /// Returns the inverse of the matrix, or FLT_MAX * SetIdentity() if the
352  /// matrix is singular. (FLT_MAX is the largest value a \c float can have,
353  /// as defined by the system.) The matrix is considered singular if the
354  /// determinant is less than or equal to the optional parameter \e eps. If
355  /// \e det is non-null, <c>*det</c> is set to the determinant.
356  GF_API
357  GfMatrix4f GetInverse(double* det = NULL, double eps = 0) const;
358 
359  /// Returns the determinant of the matrix.
360  GF_API
361  double GetDeterminant() const;
362 
363  /// Sets a row of the matrix from a Vec3.
364  /// The fourth element of the row is ignored.
365  void SetRow3(int i, const GfVec3f & v) {
366  _mtx[i][0] = v[0];
367  _mtx[i][1] = v[1];
368  _mtx[i][2] = v[2];
369  }
370 
371  /// Gets a row of the matrix as a Vec3.
372  GfVec3f GetRow3(int i) const {
373  return GfVec3f(_mtx[i][0], _mtx[i][1], _mtx[i][2]);
374  }
375 
376  /// Returns the determinant of the upper 3x3 matrix. This method is useful
377  /// when the matrix describes a linear transformation such as a rotation or
378  /// scale because the other values in the 4x4 matrix are not important.
379  double GetDeterminant3() const {
380  return _GetDeterminant3(0, 1, 2, 0, 1, 2);
381  }
382 
383  /// Returns true, if the row vectors of the upper 3x3 matrix form an
384  /// orthogonal basis. Note they do not have to be unit length for this
385  /// test to return true.
386  bool HasOrthogonalRows3() const {
387  // XXX Should add GfAreOrthogonal(v0, v1, v2) (which also
388  // GfRotation::Decompose() could use).
389  GfVec3f axis0(GetRow3(0)), axis1(GetRow3(1)), axis2(GetRow3(2));
390  return (GfAbs(GfDot(axis0, axis1)) < GF_MIN_ORTHO_TOLERANCE &&
391  GfAbs(GfDot(axis0, axis2)) < GF_MIN_ORTHO_TOLERANCE &&
392  GfAbs(GfDot(axis1, axis2)) < GF_MIN_ORTHO_TOLERANCE);
393  }
394 
395  /// Makes the matrix orthonormal in place. This is an iterative method
396  /// that is much more stable than the previous cross/cross method. If the
397  /// iterative method does not converge, a warning is issued.
398  ///
399  /// Returns true if the iteration converged, false otherwise. Leaves any
400  /// translation part of the matrix unchanged. If \a issueWarning is true,
401  /// this method will issue a warning if the iteration does not converge,
402  /// otherwise it will be silent.
403  GF_API
404  bool Orthonormalize(bool issueWarning=true);
405 
406  /// Returns an orthonormalized copy of the matrix.
407  GF_API
408  GfMatrix4f GetOrthonormalized(bool issueWarning=true) const;
409 
410  /// Returns the sign of the determinant of the upper 3x3 matrix, i.e. 1
411  /// for a right-handed matrix, -1 for a left-handed matrix, and 0 for a
412  /// singular matrix.
413  GF_API
414  double GetHandedness() const;
415 
416  /// Returns true if the vectors in the upper 3x3 matrix form a
417  /// right-handed coordinate system.
418  bool IsRightHanded() const {
419  return GetHandedness() == 1.0;
420  }
421 
422  /// Returns true if the vectors in the upper 3x3 matrix form a left-handed
423  /// coordinate system.
424  bool IsLeftHanded() const {
425  return GetHandedness() == -1.0;
426  }
427 
428  /// Post-multiplies matrix \e m into this matrix.
429  GF_API
430  GfMatrix4f& operator *=(const GfMatrix4f& m);
431 
432  /// Multiplies the matrix by a float.
433  GF_API
434  GfMatrix4f& operator *=(double);
435 
436  /// Returns the product of a matrix and a float.
437  friend GfMatrix4f operator *(const GfMatrix4f& m1, double d)
438  {
439  GfMatrix4f m = m1;
440  return m *= d;
441  }
442 
443  ///
444  // Returns the product of a matrix and a float.
445  friend GfMatrix4f operator *(double d, const GfMatrix4f& m)
446  {
447  return m * d;
448  }
449 
450  /// Adds matrix \e m to this matrix.
451  GF_API
452  GfMatrix4f& operator +=(const GfMatrix4f& m);
453 
454  /// Subtracts matrix \e m from this matrix.
455  GF_API
456  GfMatrix4f& operator -=(const GfMatrix4f& m);
457 
458  /// Returns the unary negation of matrix \e m.
459  GF_API
460  friend GfMatrix4f operator -(const GfMatrix4f& m);
461 
462  /// Adds matrix \e m2 to \e m1
463  friend GfMatrix4f operator +(const GfMatrix4f& m1, const GfMatrix4f& m2)
464  {
465  GfMatrix4f tmp(m1);
466  tmp += m2;
467  return tmp;
468  }
469 
470  /// Subtracts matrix \e m2 from \e m1.
471  friend GfMatrix4f operator -(const GfMatrix4f& m1, const GfMatrix4f& m2)
472  {
473  GfMatrix4f tmp(m1);
474  tmp -= m2;
475  return tmp;
476  }
477 
478  /// Multiplies matrix \e m1 by \e m2.
479  friend GfMatrix4f operator *(const GfMatrix4f& m1, const GfMatrix4f& m2)
480  {
481  GfMatrix4f tmp(m1);
482  tmp *= m2;
483  return tmp;
484  }
485 
486  /// Divides matrix \e m1 by \e m2 (that is, <c>m1 * inv(m2)</c>).
487  friend GfMatrix4f operator /(const GfMatrix4f& m1, const GfMatrix4f& m2)
488  {
489  return(m1 * m2.GetInverse());
490  }
491 
492  /// Returns the product of a matrix \e m and a column vector \e vec.
493  friend inline GfVec4f operator *(const GfMatrix4f& m, const GfVec4f& vec) {
494  return GfVec4f(vec[0] * m._mtx[0][0] + vec[1] * m._mtx[0][1] + vec[2] * m._mtx[0][2] + vec[3] * m._mtx[0][3],
495  vec[0] * m._mtx[1][0] + vec[1] * m._mtx[1][1] + vec[2] * m._mtx[1][2] + vec[3] * m._mtx[1][3],
496  vec[0] * m._mtx[2][0] + vec[1] * m._mtx[2][1] + vec[2] * m._mtx[2][2] + vec[3] * m._mtx[2][3],
497  vec[0] * m._mtx[3][0] + vec[1] * m._mtx[3][1] + vec[2] * m._mtx[3][2] + vec[3] * m._mtx[3][3]);
498  }
499 
500  /// Returns the product of row vector \e vec and a matrix \e m.
501  friend inline GfVec4f operator *(const GfVec4f &vec, const GfMatrix4f& m) {
502  return GfVec4f(vec[0] * m._mtx[0][0] + vec[1] * m._mtx[1][0] + vec[2] * m._mtx[2][0] + vec[3] * m._mtx[3][0],
503  vec[0] * m._mtx[0][1] + vec[1] * m._mtx[1][1] + vec[2] * m._mtx[2][1] + vec[3] * m._mtx[3][1],
504  vec[0] * m._mtx[0][2] + vec[1] * m._mtx[1][2] + vec[2] * m._mtx[2][2] + vec[3] * m._mtx[3][2],
505  vec[0] * m._mtx[0][3] + vec[1] * m._mtx[1][3] + vec[2] * m._mtx[2][3] + vec[3] * m._mtx[3][3]);
506  }
507 
508  /// Sets matrix to specify a uniform scaling by \e scaleFactor.
509  GF_API
510  GfMatrix4f& SetScale(float scaleFactor);
511 
512  /// Returns the matrix with any scaling or shearing removed,
513  /// leaving only the rotation and translation.
514  /// If the matrix cannot be decomposed, returns the original matrix.
515  GF_API
517 
518  /// \name 3D Transformation Utilities
519  /// @{
520 
521  /// Sets the matrix to specify a rotation equivalent to \e rot,
522  /// and clears the translation.
523  GF_API
524  GfMatrix4f& SetRotate(const GfQuatf &rot);
525 
526  /// Sets the matrix to specify a rotation equivalent to \e rot,
527  /// without clearing the translation.
528  GF_API
530 
531  /// Sets the matrix to specify a rotation equivalent to \e rot,
532  /// and clears the translation.
533  GF_API
535 
536  /// Sets the matrix to specify a rotation equivalent to \e rot,
537  /// without clearing the translation.
538  GF_API
540 
541  /// Sets the matrix to specify a rotation equivalent to \e mx,
542  /// and clears the translation.
543  GF_API
544  GfMatrix4f& SetRotate(const GfMatrix3f &mx);
545 
546  /// Sets the matrix to specify a rotation equivalent to \e mx,
547  /// without clearing the translation.
548  GF_API
549  GfMatrix4f& SetRotateOnly(const GfMatrix3f &mx);
550 
551  /// Sets the matrix to specify a nonuniform scaling in x, y, and z by
552  /// the factors in vector \e scaleFactors.
553  GF_API
554  GfMatrix4f& SetScale(const GfVec3f &scaleFactors);
555 
556  /// Sets matrix to specify a translation by the vector \e trans,
557  /// and clears the rotation.
558  GF_API
560 
561  /// Sets matrix to specify a translation by the vector \e trans,
562  /// without clearing the rotation.
563  GF_API
565 
566  /// Sets matrix to specify a rotation by \e rotate and a
567  /// translation by \e translate.
568  GF_API
570  const GfVec3f& translate);
571 
572  /// Sets matrix to specify a rotation by \e rotmx and a
573  /// translation by \e translate.
574  GF_API
575  GfMatrix4f& SetTransform(const GfMatrix3f& rotmx,
576  const GfVec3f& translate);
577 
578  /// Sets the matrix to specify a viewing matrix from parameters
579  /// similar to those used by <c>gluLookAt(3G)</c>. \e eyePoint
580  /// represents the eye point in world space. \e centerPoint
581  /// represents the world-space center of attention. \e upDirection
582  /// is a vector indicating which way is up.
583  GF_API
584  GfMatrix4f& SetLookAt(const GfVec3f &eyePoint,
585  const GfVec3f &centerPoint,
586  const GfVec3f &upDirection);
587 
588  /// Sets the matrix to specify a viewing matrix from a world-space
589  /// \e eyePoint and a world-space rotation that rigidly rotates the
590  /// orientation from its canonical frame, which is defined to be
591  /// looking along the <c>-z</c> axis with the <c>+y</c> axis as the up
592  /// direction.
593  GF_API
594  GfMatrix4f& SetLookAt(const GfVec3f &eyePoint,
595  const GfRotation &orientation);
596 
597  /// Factors the matrix into 5 components:
598  /// \li <c>\e M = r * s * -r * u * t</c>
599  /// where
600  /// \li \e t is a translation.
601  /// \li \e u and \e r are rotations, and \e -r is the transpose
602  /// (inverse) of \e r. The \e u matrix may contain shear
603  /// information.
604  /// \li \e s is a scale.
605  /// Any projection information could be returned in matrix \e p,
606  /// but currently p is never modified.
607  ///
608  /// Returns \c false if the matrix is singular (as determined by \e eps).
609  /// In that case, any zero scales in \e s are clamped to \e eps
610  /// to allow computation of \e u.
611  GF_API
612  bool Factor(GfMatrix4f* r, GfVec3f* s, GfMatrix4f* u,
613  GfVec3f* t, GfMatrix4f* p,
614  float eps = 1e-5) const;
615 
616  /// Returns the translation part of the matrix, defined as the first three
617  /// elements of the last row.
619  return GfVec3f(_mtx[3][0], _mtx[3][1], _mtx[3][2]);
620  }
621 
622  /// Returns the rotation corresponding to this matrix. This works well
623  /// only if the matrix represents a rotation.
624  ///
625  /// For good results, consider calling Orthonormalize() before calling
626  /// this method.
627  GF_API
628  GfRotation ExtractRotation() const;
629 
630  /// Return the rotation corresponding to this matrix as a quaternion.
631  /// This works well only if the matrix represents a rotation.
632  ///
633  /// For good results, consider calling Orthonormalize() before calling
634  /// this method.
635  GF_API
637 
638  /// Decompose the rotation corresponding to this matrix about 3 orthogonal
639  /// axes. If the axes are not orthogonal, warnings will be spewed.
640  ///
641  /// This is a convenience method that is equivalent to calling
642  /// ExtractRotation().Decompose().
643  GF_API
644  GfVec3f DecomposeRotation(const GfVec3f &axis0,
645  const GfVec3f &axis1,
646  const GfVec3f &axis2) const;
647 
648  /// Returns the rotation corresponding to this matrix. This works well
649  /// only if the matrix represents a rotation.
650  ///
651  /// For good results, consider calling Orthonormalize() before calling
652  /// this method.
653  GF_API
655 
656  /// Transforms the row vector \e vec by the matrix, returning the result.
657  /// This treats the vector as a 4-component vector whose fourth component
658  /// is 1.
659  GfVec3d Transform(const GfVec3d &vec) const {
660  return GfProject(GfVec4d(
661  vec[0] * _mtx[0][0] + vec[1] * _mtx[1][0] + vec[2] * _mtx[2][0] + _mtx[3][0],
662  vec[0] * _mtx[0][1] + vec[1] * _mtx[1][1] + vec[2] * _mtx[2][1] + _mtx[3][1],
663  vec[0] * _mtx[0][2] + vec[1] * _mtx[1][2] + vec[2] * _mtx[2][2] + _mtx[3][2],
664  vec[0] * _mtx[0][3] + vec[1] * _mtx[1][3] + vec[2] * _mtx[2][3] + _mtx[3][3]));
665  }
666 
667  /// Transforms the row vector \e vec by the matrix, returning the result.
668  /// This treats the vector as a 4-component vector whose fourth component
669  /// is 1. This is an overloaded method; it differs from the other version
670  /// in that it returns a different value type.
671  GfVec3f Transform(const GfVec3f &vec) const {
672  return (GfProject(GfVec4f(
673  vec[0] * _mtx[0][0] + vec[1] * _mtx[1][0] + vec[2] * _mtx[2][0] + _mtx[3][0],
674  vec[0] * _mtx[0][1] + vec[1] * _mtx[1][1] + vec[2] * _mtx[2][1] + _mtx[3][1],
675  vec[0] * _mtx[0][2] + vec[1] * _mtx[1][2] + vec[2] * _mtx[2][2] + _mtx[3][2],
676  vec[0] * _mtx[0][3] + vec[1] * _mtx[1][3] + vec[2] * _mtx[2][3] + _mtx[3][3])));
677  }
678 
679  /// Transforms row vector \e vec by the matrix, returning the result. This
680  /// treats the vector as a direction vector, so the translation
681  /// information in the matrix is ignored. That is, it treats the vector as
682  /// a 4-component vector whose fourth component is 0.
683  GfVec3d TransformDir(const GfVec3d &vec) const {
684  return GfVec3d(
685  vec[0] * _mtx[0][0] + vec[1] * _mtx[1][0] + vec[2] * _mtx[2][0],
686  vec[0] * _mtx[0][1] + vec[1] * _mtx[1][1] + vec[2] * _mtx[2][1],
687  vec[0] * _mtx[0][2] + vec[1] * _mtx[1][2] + vec[2] * _mtx[2][2]);
688  }
689 
690  /// Transforms row vector \e vec by the matrix, returning the result. This
691  /// treats the vector as a direction vector, so the translation
692  /// information in the matrix is ignored. That is, it treats the vector as
693  /// a 4-component vector whose fourth component is 0. This is an
694  /// overloaded method; it differs from the other version in that it
695  /// returns a different value type.
696  GfVec3f TransformDir(const GfVec3f &vec) const {
697  return GfVec3f(
698  vec[0] * _mtx[0][0] + vec[1] * _mtx[1][0] + vec[2] * _mtx[2][0],
699  vec[0] * _mtx[0][1] + vec[1] * _mtx[1][1] + vec[2] * _mtx[2][1],
700  vec[0] * _mtx[0][2] + vec[1] * _mtx[1][2] + vec[2] * _mtx[2][2]);
701  }
702 
703  /// Transforms the row vector \e vec by the matrix, returning the result.
704  /// This treats the vector as a 4-component vector whose fourth component
705  /// is 1 and ignores the fourth column of the matrix (i.e. assumes it is
706  /// (0, 0, 0, 1)).
707  GfVec3d TransformAffine(const GfVec3d &vec) const {
708  return GfVec3d(
709  vec[0] * _mtx[0][0] + vec[1] * _mtx[1][0] + vec[2] * _mtx[2][0] + _mtx[3][0],
710  vec[0] * _mtx[0][1] + vec[1] * _mtx[1][1] + vec[2] * _mtx[2][1] + _mtx[3][1],
711  vec[0] * _mtx[0][2] + vec[1] * _mtx[1][2] + vec[2] * _mtx[2][2] + _mtx[3][2]);
712  }
713 
714  /// Transforms the row vector \e vec by the matrix, returning the result.
715  /// This treats the vector as a 4-component vector whose fourth component
716  /// is 1 and ignores the fourth column of the matrix (i.e. assumes it is
717  /// (0, 0, 0, 1)).
718  GfVec3f TransformAffine(const GfVec3f &vec) const {
719  return GfVec3f(
720  vec[0] * _mtx[0][0] + vec[1] * _mtx[1][0] + vec[2] * _mtx[2][0] + _mtx[3][0],
721  vec[0] * _mtx[0][1] + vec[1] * _mtx[1][1] + vec[2] * _mtx[2][1] + _mtx[3][1],
722  vec[0] * _mtx[0][2] + vec[1] * _mtx[1][2] + vec[2] * _mtx[2][2] + _mtx[3][2]);
723  }
724  /// @}
725 
726 private:
727  /// Returns the determinant of the 3x3 submatrix specified by the three
728  /// given row and column indices (0-3 for each).
729  GF_API
730  double _GetDeterminant3(size_t row1, size_t row2, size_t row3,
731  size_t col1, size_t col2, size_t col3) const;
732 
733  /// Diagonalizes the upper 3x3 matrix of a matrix known to be symmetric.
734  void _Jacobi3(GfVec3d *eigenvalues, GfVec3d eigenvectors[3]) const;
735 
736  /// Set the 3x3 submatrix to the rotation given by a quaternion,
737  /// defined by the real component \p r and imaginary components \p i.
738  void _SetRotateFromQuat(float r, const GfVec3f& i);
739 
740 
741 private:
742  /// Matrix storage, in row-major order.
744 
745  // Friend declarations
746  friend class GfMatrix4d;
747 };
748 
749 
750 /// Tests for equality within a given tolerance, returning \c true if the
751 /// difference between each component of the matrix is less than or equal
752 /// to \p tolerance, or false otherwise.
753 GF_API
754 bool GfIsClose(GfMatrix4f const &m1, GfMatrix4f const &m2, double tolerance);
755 
756 /// Output a GfMatrix4f
757 /// \ingroup group_gf_DebuggingOutput
758 GF_API std::ostream& operator<<(std::ostream &, GfMatrix4f const &);
759 
761 
762 #endif // PXR_BASE_GF_MATRIX4F_H
bool HasOrthogonalRows3() const
Definition: matrix4f.h:386
GfVec3f GfProject(const GfVec4f &v)
Definition: homogeneous.h:65
GF_API GfVec3f DecomposeRotation(const GfVec3f &axis0, const GfVec3f &axis1, const GfVec3f &axis2) const
GfVec4f GetRow(int i) const
Gets a row of the matrix as a Vec4.
Definition: matrix4f.h:203
GF_API std::ostream & operator<<(std::ostream &, GfMatrix4f const &)
GfVec3f TransformDir(const GfVec3f &vec) const
Definition: matrix4f.h:696
GF_API friend GfMatrix4f operator-(const GfMatrix4f &m)
Returns the unary negation of matrix m.
static const size_t numRows
Definition: matrix4f.h:92
GF_API GfMatrix4f & operator*=(const GfMatrix4f &m)
Post-multiplies matrix m into this matrix.
GF_API GfMatrix4f & SetDiagonal(float s)
Sets the matrix to s times the identity matrix.
friend GfMatrix4f operator+(const GfMatrix4f &m1, const GfMatrix4f &m2)
Adds matrix m2 to m1.
Definition: matrix4f.h:463
*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:623
bool IsLeftHanded() const
Definition: matrix4f.h:424
GF_API GfMatrix4f & operator+=(const GfMatrix4f &m)
Adds matrix m to this matrix.
float * data()
Definition: matrix4f.h:273
const GLdouble * v
Definition: glcorearb.h:837
GF_API GfMatrix4f & SetRotate(const GfQuatf &rot)
GA_API const UT_StringHolder rot
GF_API GfMatrix4f & SetRotateOnly(const GfQuatf &rot)
Definition: vec3f.h:62
GLdouble s
Definition: glad.h:3009
Definition: vec4d.h:62
GfVec3d TransformDir(const GfVec3d &vec) const
Definition: matrix4f.h:683
GfVec4f GetColumn(int i) const
Gets a column of the matrix as a Vec4.
Definition: matrix4f.h:208
GF_API GfQuatf ExtractRotationQuat() const
GF_API GfMatrix3f ExtractRotationMatrix() const
double GfAbs(double f)
Definition: math.h:115
Definition: quatf.h:59
GF_API GfMatrix4f & SetTranslateOnly(const GfVec3f &t)
void SetRow3(int i, const GfVec3f &v)
Definition: matrix4f.h:365
GF_API GfMatrix4f GetInverse(double *det=NULL, double eps=0) const
GF_API GfMatrix4f RemoveScaleShear() const
GF_API bool Orthonormalize(bool issueWarning=true)
void SetColumn(int i, const GfVec4f &v)
Sets a column of the matrix from a Vec4.
Definition: matrix4f.h:195
bool IsRightHanded() const
Definition: matrix4f.h:418
friend GfMatrix4f operator*(const GfMatrix4f &m1, double d)
Returns the product of a matrix and a float.
Definition: matrix4f.h:437
GF_API float * Get(float m[4][4]) const
GfMatrix4f & Set(float m00, float m01, float m02, float m03, float m10, float m11, float m12, float m13, float m20, float m21, float m22, float m23, float m30, float m31, float m32, float m33)
Definition: matrix4f.h:215
GF_API GfMatrix4f & SetScale(float scaleFactor)
Sets matrix to specify a uniform scaling by scaleFactor.
GF_API GfMatrix4f & SetTransform(const GfRotation &rotate, const GfVec3f &translate)
GfVec3d Transform(const GfVec3d &vec) const
Definition: matrix4f.h:659
double GetDeterminant3() const
Definition: matrix4f.h:379
T * GetData()
Return a pointer to the start of all the data.
Definition: matrixData.h:50
GA_API const UT_StringHolder trans
GfVec3f GetRow3(int i) const
Gets a row of the matrix as a Vec3.
Definition: matrix4f.h:372
friend size_t hash_value(GfMatrix4f const &m)
Hash.
Definition: matrix4f.h:304
GF_API double GetHandedness() const
GF_API bool Factor(GfMatrix4f *r, GfVec3f *s, GfMatrix4f *u, GfVec3f *t, GfMatrix4f *p, float eps=1e-5) const
float * operator[](int i)
Definition: matrix4f.h:296
GfMatrix4f & SetZero()
Sets the matrix to zero.
Definition: matrix4f.h:254
GF_API bool operator==(const GfMatrix4d &m) const
float ScalarType
Definition: matrix4f.h:90
double GfDot(const GfDualQuatd &dq1, const GfDualQuatd &dq2)
Return the dot (inner) product of two dual quaternions.
Definition: dualQuatd.h:277
ImageBuf OIIO_API rotate(const ImageBuf &src, float angle, string_view filtername=string_view(), float filterwidth=0.0f, bool recompute_roi=false, ROI roi={}, int nthreads=0)
GLdouble t
Definition: glad.h:2397
GfMatrix4f(const GfVec4f &v)
Definition: matrix4f.h:125
Definition: vec4f.h:62
GfMatrix4f & SetIdentity()
Sets the matrix to the identity matrix.
Definition: matrix4f.h:249
GF_API GfMatrix4f GetTranspose() const
Returns the transpose of the matrix.
GF_API GfMatrix4f & SetTranslate(const GfVec3f &trans)
GF_API GfMatrix4f & SetLookAt(const GfVec3f &eyePoint, const GfVec3f &centerPoint, const GfVec3f &upDirection)
static size_t Combine(Args &&...args)
Produce a hash code by combining the hash codes of several objects.
Definition: hash.h:492
PXR_NAMESPACE_CLOSE_SCOPE PXR_NAMESPACE_OPEN_SCOPE
Definition: path.h:1432
GfMatrix4f & Set(const float m[4][4])
Definition: matrix4f.h:228
GfMatrix4f(const float m[4][4])
Definition: matrix4f.h:113
friend GfMatrix4f operator/(const GfMatrix4f &m1, const GfMatrix4f &m2)
Divides matrix m1 by m2 (that is, m1 * inv(m2)).
Definition: matrix4f.h:487
GF_API double GetDeterminant() const
Returns the determinant of the matrix.
GF_API bool GfIsClose(GfMatrix4f const &m1, GfMatrix4f const &m2, double tolerance)
GfVec3f ExtractTranslation() const
Definition: matrix4f.h:618
Definition: vec3d.h:62
#define PXR_NAMESPACE_CLOSE_SCOPE
Definition: pxr.h:91
GfMatrix4f()=default
Default constructor. Leaves the matrix component values undefined.
GfVec3f TransformAffine(const GfVec3f &vec) const
Definition: matrix4f.h:718
GfMatrix4f(float m00, float m01, float m02, float m03, float m10, float m11, float m12, float m13, float m20, float m21, float m22, float m23, float m30, float m31, float m32, float m33)
Definition: matrix4f.h:101
GF_API GfRotation ExtractRotation() const
Definition: core.h:1131
GfVec3f Transform(const GfVec3f &vec) const
Definition: matrix4f.h:671
GLboolean r
Definition: glcorearb.h:1222
PUGI__FN char_t * translate(char_t *buffer, const char_t *from, const char_t *to, size_t to_length)
Definition: pugixml.cpp:8352
static const size_t numColumns
Definition: matrix4f.h:93
GfMatrix4f(float s)
Definition: matrix4f.h:119
GF_API GfMatrix4f & operator-=(const GfMatrix4f &m)
Subtracts matrix m from this matrix.
GfVec3d TransformAffine(const GfVec3d &vec) const
Definition: matrix4f.h:707
void SetRow(int i, const GfVec4f &v)
Sets a row of the matrix from a Vec4.
Definition: matrix4f.h:187
GF_API GfMatrix4f GetOrthonormalized(bool issueWarning=true) const
Returns an orthonormalized copy of the matrix.
#define GF_MIN_ORTHO_TOLERANCE
Definition: limits.h:39
const float * data() const
Definition: matrix4f.h:279
#define GF_API
Definition: api.h:40
float * GetArray()
Returns vector components as an array of float values.
Definition: matrix4f.h:284
bool operator!=(const GfMatrix4d &m) const
Definition: matrix4f.h:337
const float * GetArray() const
Returns vector components as a const array of float values.
Definition: matrix4f.h:289