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matrix4f.h
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26 // matrix4.template.h file to make changes.
27 
28 #ifndef GF_MATRIX4F_H
29 #define 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 
45 #include <hboost/functional/hash.hpp>
46 
47 #include <iosfwd>
48 #include <vector>
49 
51 
52 template <>
53 struct GfIsGfMatrix<class GfMatrix4f> { static const bool value = true; };
54 
55 class GfMatrix4d;
56 class GfMatrix4f;
57 class GfQuatf;
58 class GfRotation;
59 class GfMatrix3f;
60 
61 /// \class GfMatrix4f
62 /// \ingroup group_gf_LinearAlgebra
63 ///
64 /// Stores a 4x4 matrix of \c float elements. A basic type.
65 ///
66 /// Matrices are defined to be in row-major order, so <c>matrix[i][j]</c>
67 /// indexes the element in the \e i th row and the \e j th column.
68 ///
69 /// <h3>3D Transformations</h3>
70 ///
71 /// The following methods interpret a GfMatrix4f as a 3D
72 /// transformation: SetRotate(), SetScale(), SetTranslate(), SetLookAt(),
73 /// Factor(), ExtractTranslation(), ExtractRotation(), Transform(), TransformDir().
74 /// By convention, vectors are treated primarily as row vectors,
75 /// implying the following:
76 /// \li Transformation matrices are organized to deal with row
77 /// vectors, not column vectors. For example, the last row of a matrix
78 /// contains the translation amounts.
79 /// \li Each of the Set() methods below completely rewrites the
80 /// matrix; for example, SetTranslate() yields a matrix
81 /// which does nothing but translate.
82 /// \li When multiplying two transformation matrices, the matrix
83 /// on the left applies a more local transformation to a row
84 /// vector. For example, if R represents a rotation
85 /// matrix and T represents a translation matrix, the
86 /// product R*T will rotate a row vector, then translate
87 /// it.
89 {
90 public:
91  typedef float ScalarType;
92 
93  static const size_t numRows = 4;
94  static const size_t numColumns = 4;
95 
96  /// Default constructor. Leaves the matrix component values undefined.
97  GfMatrix4f() = default;
98 
99  /// Constructor. Initializes the matrix from 16 independent
100  /// \c float values, specified in row-major order. For example,
101  /// parameter \e m10 specifies the value in row 1 and column 0.
102  GfMatrix4f(float m00, float m01, float m02, float m03,
103  float m10, float m11, float m12, float m13,
104  float m20, float m21, float m22, float m23,
105  float m30, float m31, float m32, float m33) {
106  Set(m00, m01, m02, m03,
107  m10, m11, m12, m13,
108  m20, m21, m22, m23,
109  m30, m31, m32, m33);
110  }
111 
112  /// Constructor. Initializes the matrix from a 4x4 array
113  /// of \c float values, specified in row-major order.
114  GfMatrix4f(const float m[4][4]) {
115  Set(m);
116  }
117 
118  /// Constructor. Explicitly initializes the matrix to \e s times the
119  /// identity matrix.
120  explicit GfMatrix4f(float s) {
121  SetDiagonal(s);
122  }
123 
124  /// Constructor. Explicitly initializes the matrix to diagonal form,
125  /// with the \e i th element on the diagonal set to <c>v[i]</c>.
126  explicit GfMatrix4f(const GfVec4f& v) {
127  SetDiagonal(v);
128  }
129 
130  /// Constructor. Initialize the matrix from a vector of vectors of
131  /// double. The vector is expected to be 4x4. If it is
132  /// too big, only the first 4 rows and/or columns will be used.
133  /// If it is too small, uninitialized elements will be filled in with
134  /// the corresponding elements from an identity matrix.
135  ///
136  GF_API
137  explicit GfMatrix4f(const std::vector< std::vector<double> >& v);
138 
139  /// Constructor. Initialize the matrix from a vector of vectors of
140  /// float. The vector is expected to be 4x4. If it is
141  /// too big, only the first 4 rows and/or columns will be used.
142  /// If it is too small, uninitialized elements will be filled in with
143  /// the corresponding elements from an identity matrix.
144  ///
145  GF_API
146  explicit GfMatrix4f(const std::vector< std::vector<float> >& v);
147 
148  /// Constructor. Initialize the matrix from 4 row vectors of
149  /// double. Each vector is expected to length 4. If it is too
150  /// big, only the first 4 items will be used. If it is too small,
151  /// uninitialized elements will be filled in with the
152  /// corresponding elements from an identity matrix.
153  ///
154  GF_API
155  explicit GfMatrix4f(const std::vector<double>& r0,
156  const std::vector<double>& r1,
157  const std::vector<double>& r2,
158  const std::vector<double>& r3);
159 
160  /// Constructor. Initialize the matrix from 4 row vectors of
161  /// float. Each vector is expected to length 4. If it is too
162  /// big, only the first 4 items will be used. If it is too small,
163  /// uninitialized elements will be filled in with the
164  /// corresponding elements from an identity matrix.
165  ///
166  GF_API
167  explicit GfMatrix4f(const std::vector<float>& r0,
168  const std::vector<float>& r1,
169  const std::vector<float>& r2,
170  const std::vector<float>& r3);
171 
172  /// Constructor. Initializes a transformation matrix to perform the
173  /// indicated rotation and translation.
174  GF_API
176  const GfVec3f& translate);
177 
178  /// Constructor. Initializes a transformation matrix to perform the
179  /// indicated rotation and translation.
180  GF_API
181  GfMatrix4f(const GfMatrix3f& rotmx,
182  const GfVec3f& translate);
183  /// This explicit constructor converts a "double" matrix to a "float" matrix.
184  GF_API
185  explicit GfMatrix4f(const class GfMatrix4d& m);
186 
187  /// Sets a row of the matrix from a Vec4.
188  void SetRow(int i, const GfVec4f & v) {
189  _mtx[i][0] = v[0];
190  _mtx[i][1] = v[1];
191  _mtx[i][2] = v[2];
192  _mtx[i][3] = v[3];
193  }
194 
195  /// Sets a column of the matrix from a Vec4.
196  void SetColumn(int i, const GfVec4f & v) {
197  _mtx[0][i] = v[0];
198  _mtx[1][i] = v[1];
199  _mtx[2][i] = v[2];
200  _mtx[3][i] = v[3];
201  }
202 
203  /// Gets a row of the matrix as a Vec4.
204  GfVec4f GetRow(int i) const {
205  return GfVec4f(_mtx[i][0], _mtx[i][1], _mtx[i][2], _mtx[i][3]);
206  }
207 
208  /// Gets a column of the matrix as a Vec4.
209  GfVec4f GetColumn(int i) const {
210  return GfVec4f(_mtx[0][i], _mtx[1][i], _mtx[2][i], _mtx[3][i]);
211  }
212 
213  /// Sets the matrix from 16 independent \c float values,
214  /// specified in row-major order. For example, parameter \e m10 specifies
215  /// the value in row 1 and column 0.
216  GfMatrix4f& Set(float m00, float m01, float m02, float m03,
217  float m10, float m11, float m12, float m13,
218  float m20, float m21, float m22, float m23,
219  float m30, float m31, float m32, float m33) {
220  _mtx[0][0] = m00; _mtx[0][1] = m01; _mtx[0][2] = m02; _mtx[0][3] = m03;
221  _mtx[1][0] = m10; _mtx[1][1] = m11; _mtx[1][2] = m12; _mtx[1][3] = m13;
222  _mtx[2][0] = m20; _mtx[2][1] = m21; _mtx[2][2] = m22; _mtx[2][3] = m23;
223  _mtx[3][0] = m30; _mtx[3][1] = m31; _mtx[3][2] = m32; _mtx[3][3] = m33;
224  return *this;
225  }
226 
227  /// Sets the matrix from a 4x4 array of \c float
228  /// values, specified in row-major order.
229  GfMatrix4f& Set(const float m[4][4]) {
230  _mtx[0][0] = m[0][0];
231  _mtx[0][1] = m[0][1];
232  _mtx[0][2] = m[0][2];
233  _mtx[0][3] = m[0][3];
234  _mtx[1][0] = m[1][0];
235  _mtx[1][1] = m[1][1];
236  _mtx[1][2] = m[1][2];
237  _mtx[1][3] = m[1][3];
238  _mtx[2][0] = m[2][0];
239  _mtx[2][1] = m[2][1];
240  _mtx[2][2] = m[2][2];
241  _mtx[2][3] = m[2][3];
242  _mtx[3][0] = m[3][0];
243  _mtx[3][1] = m[3][1];
244  _mtx[3][2] = m[3][2];
245  _mtx[3][3] = m[3][3];
246  return *this;
247  }
248 
249  /// Sets the matrix to the identity matrix.
251  return SetDiagonal(1);
252  }
253 
254  /// Sets the matrix to zero.
256  return SetDiagonal(0);
257  }
258 
259  /// Sets the matrix to \e s times the identity matrix.
260  GF_API
261  GfMatrix4f& SetDiagonal(float s);
262 
263  /// Sets the matrix to have diagonal (<c>v[0], v[1], v[2], v[3]</c>).
264  GF_API
265  GfMatrix4f& SetDiagonal(const GfVec4f&);
266 
267  /// Fills a 4x4 array of \c float values with the values in
268  /// the matrix, specified in row-major order.
269  GF_API
270  float* Get(float m[4][4]) const;
271 
272  /// Returns raw access to components of matrix as an array of
273  /// \c float values. Components are in row-major order.
274  float* data() {
275  return _mtx.GetData();
276  }
277 
278  /// Returns const raw access to components of matrix as an array of
279  /// \c float values. Components are in row-major order.
280  const float* data() const {
281  return _mtx.GetData();
282  }
283 
284  /// Returns vector components as an array of \c float values.
285  float* GetArray() {
286  return _mtx.GetData();
287  }
288 
289  /// Returns vector components as a const array of \c float values.
290  const float* GetArray() const {
291  return _mtx.GetData();
292  }
293 
294  /// Accesses an indexed row \e i of the matrix as an array of 4 \c
295  /// float values so that standard indexing (such as <c>m[0][1]</c>)
296  /// works correctly.
297  float* operator [](int i) { return _mtx[i]; }
298 
299  /// Accesses an indexed row \e i of the matrix as an array of 4 \c
300  /// float values so that standard indexing (such as <c>m[0][1]</c>)
301  /// works correctly.
302  const float* operator [](int i) const { return _mtx[i]; }
303 
304  /// Hash.
305  friend inline size_t hash_value(GfMatrix4f const &m) {
306  int nElems = 4 * 4;
307  size_t h = 0;
308  const float *p = m.GetArray();
309  while (nElems--)
310  hboost::hash_combine(h, *p++);
311  return h;
312  }
313 
314  /// Tests for element-wise matrix equality. All elements must match
315  /// exactly for matrices to be considered equal.
316  GF_API
317  bool operator ==(const GfMatrix4d& m) const;
318 
319  /// Tests for element-wise matrix equality. All elements must match
320  /// exactly for matrices to be considered equal.
321  GF_API
322  bool operator ==(const GfMatrix4f& m) const;
323 
324  /// Tests for element-wise matrix inequality. All elements must match
325  /// exactly for matrices to be considered equal.
326  bool operator !=(const GfMatrix4d& m) const {
327  return !(*this == m);
328  }
329 
330  /// Tests for element-wise matrix inequality. All elements must match
331  /// exactly for matrices to be considered equal.
332  bool operator !=(const GfMatrix4f& m) const {
333  return !(*this == m);
334  }
335 
336  /// Returns the transpose of the matrix.
337  GF_API
338  GfMatrix4f GetTranspose() const;
339 
340  /// Returns the inverse of the matrix, or FLT_MAX * SetIdentity() if the
341  /// matrix is singular. (FLT_MAX is the largest value a \c float can have,
342  /// as defined by the system.) The matrix is considered singular if the
343  /// determinant is less than or equal to the optional parameter \e eps. If
344  /// \e det is non-null, <c>*det</c> is set to the determinant.
345  GF_API
346  GfMatrix4f GetInverse(double* det = NULL, double eps = 0) const;
347 
348  /// Returns the determinant of the matrix.
349  GF_API
350  double GetDeterminant() const;
351 
352  /// Sets a row of the matrix from a Vec3.
353  /// The fourth element of the row is ignored.
354  void SetRow3(int i, const GfVec3f & v) {
355  _mtx[i][0] = v[0];
356  _mtx[i][1] = v[1];
357  _mtx[i][2] = v[2];
358  }
359 
360  /// Gets a row of the matrix as a Vec3.
361  GfVec3f GetRow3(int i) const {
362  return GfVec3f(_mtx[i][0], _mtx[i][1], _mtx[i][2]);
363  }
364 
365  /// Returns the determinant of the upper 3x3 matrix. This method is useful
366  /// when the matrix describes a linear transformation such as a rotation or
367  /// scale because the other values in the 4x4 matrix are not important.
368  double GetDeterminant3() const {
369  return _GetDeterminant3(0, 1, 2, 0, 1, 2);
370  }
371 
372  /// Returns true, if the row vectors of the upper 3x3 matrix form an
373  /// orthogonal basis. Note they do not have to be unit length for this
374  /// test to return true.
375  bool HasOrthogonalRows3() const {
376  // XXX Should add GfAreOrthogonal(v0, v1, v2) (which also
377  // GfRotation::Decompose() could use).
378  GfVec3f axis0(GetRow3(0)), axis1(GetRow3(1)), axis2(GetRow3(2));
379  return (GfAbs(GfDot(axis0, axis1)) < GF_MIN_ORTHO_TOLERANCE &&
380  GfAbs(GfDot(axis0, axis2)) < GF_MIN_ORTHO_TOLERANCE &&
381  GfAbs(GfDot(axis1, axis2)) < GF_MIN_ORTHO_TOLERANCE);
382  }
383 
384  /// Makes the matrix orthonormal in place. This is an iterative method
385  /// that is much more stable than the previous cross/cross method. If the
386  /// iterative method does not converge, a warning is issued.
387  ///
388  /// Returns true if the iteration converged, false otherwise. Leaves any
389  /// translation part of the matrix unchanged. If \a issueWarning is true,
390  /// this method will issue a warning if the iteration does not converge,
391  /// otherwise it will be silent.
392  GF_API
393  bool Orthonormalize(bool issueWarning=true);
394 
395  /// Returns an orthonormalized copy of the matrix.
396  GF_API
397  GfMatrix4f GetOrthonormalized(bool issueWarning=true) const;
398 
399  /// Returns the sign of the determinant of the upper 3x3 matrix, i.e. 1
400  /// for a right-handed matrix, -1 for a left-handed matrix, and 0 for a
401  /// singular matrix.
402  GF_API
403  double GetHandedness() const;
404 
405  /// Returns true if the vectors in the upper 3x3 matrix form a
406  /// right-handed coordinate system.
407  bool IsRightHanded() const {
408  return GetHandedness() == 1.0;
409  }
410 
411  /// Returns true if the vectors in the upper 3x3 matrix form a left-handed
412  /// coordinate system.
413  bool IsLeftHanded() const {
414  return GetHandedness() == -1.0;
415  }
416 
417  /// Post-multiplies matrix \e m into this matrix.
418  GF_API
420 
421  /// Multiplies the matrix by a float.
422  GF_API
423  GfMatrix4f& operator *=(double);
424 
425  /// Returns the product of a matrix and a float.
426  friend GfMatrix4f operator *(const GfMatrix4f& m1, double d)
427  {
428  GfMatrix4f m = m1;
429  return m *= d;
430  }
431 
432  ///
433  // Returns the product of a matrix and a float.
434  friend GfMatrix4f operator *(double d, const GfMatrix4f& m)
435  {
436  return m * d;
437  }
438 
439  /// Adds matrix \e m to this matrix.
440  GF_API
442 
443  /// Subtracts matrix \e m from this matrix.
444  GF_API
446 
447  /// Returns the unary negation of matrix \e m.
448  GF_API
449  friend GfMatrix4f operator -(const GfMatrix4f& m);
450 
451  /// Adds matrix \e m2 to \e m1
452  friend GfMatrix4f operator +(const GfMatrix4f& m1, const GfMatrix4f& m2)
453  {
454  GfMatrix4f tmp(m1);
455  tmp += m2;
456  return tmp;
457  }
458 
459  /// Subtracts matrix \e m2 from \e m1.
460  friend GfMatrix4f operator -(const GfMatrix4f& m1, const GfMatrix4f& m2)
461  {
462  GfMatrix4f tmp(m1);
463  tmp -= m2;
464  return tmp;
465  }
466 
467  /// Multiplies matrix \e m1 by \e m2.
468  friend GfMatrix4f operator *(const GfMatrix4f& m1, const GfMatrix4f& m2)
469  {
470  GfMatrix4f tmp(m1);
471  tmp *= m2;
472  return tmp;
473  }
474 
475  /// Divides matrix \e m1 by \e m2 (that is, <c>m1 * inv(m2)</c>).
476  friend GfMatrix4f operator /(const GfMatrix4f& m1, const GfMatrix4f& m2)
477  {
478  return(m1 * m2.GetInverse());
479  }
480 
481  /// Returns the product of a matrix \e m and a column vector \e vec.
482  friend inline GfVec4f operator *(const GfMatrix4f& m, const GfVec4f& vec) {
483  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],
484  vec[0] * m._mtx[1][0] + vec[1] * m._mtx[1][1] + vec[2] * m._mtx[1][2] + vec[3] * m._mtx[1][3],
485  vec[0] * m._mtx[2][0] + vec[1] * m._mtx[2][1] + vec[2] * m._mtx[2][2] + vec[3] * m._mtx[2][3],
486  vec[0] * m._mtx[3][0] + vec[1] * m._mtx[3][1] + vec[2] * m._mtx[3][2] + vec[3] * m._mtx[3][3]);
487  }
488 
489  /// Returns the product of row vector \e vec and a matrix \e m.
490  friend inline GfVec4f operator *(const GfVec4f &vec, const GfMatrix4f& m) {
491  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],
492  vec[0] * m._mtx[0][1] + vec[1] * m._mtx[1][1] + vec[2] * m._mtx[2][1] + vec[3] * m._mtx[3][1],
493  vec[0] * m._mtx[0][2] + vec[1] * m._mtx[1][2] + vec[2] * m._mtx[2][2] + vec[3] * m._mtx[3][2],
494  vec[0] * m._mtx[0][3] + vec[1] * m._mtx[1][3] + vec[2] * m._mtx[2][3] + vec[3] * m._mtx[3][3]);
495  }
496 
497  /// Sets matrix to specify a uniform scaling by \e scaleFactor.
498  GF_API
499  GfMatrix4f& SetScale(float scaleFactor);
500 
501  /// Returns the matrix with any scaling or shearing removed,
502  /// leaving only the rotation and translation.
503  /// If the matrix cannot be decomposed, returns the original matrix.
504  GF_API
506 
507  /// \name 3D Transformation Utilities
508  /// @{
509 
510  /// Sets the matrix to specify a rotation equivalent to \e rot,
511  /// and clears the translation.
512  GF_API
513  GfMatrix4f& SetRotate(const GfQuatf &rot);
514 
515  /// Sets the matrix to specify a rotation equivalent to \e rot,
516  /// without clearing the translation.
517  GF_API
519 
520  /// Sets the matrix to specify a rotation equivalent to \e rot,
521  /// and clears the translation.
522  GF_API
524 
525  /// Sets the matrix to specify a rotation equivalent to \e rot,
526  /// without clearing the translation.
527  GF_API
529 
530  /// Sets the matrix to specify a rotation equivalent to \e mx,
531  /// and clears the translation.
532  GF_API
533  GfMatrix4f& SetRotate(const GfMatrix3f &mx);
534 
535  /// Sets the matrix to specify a rotation equivalent to \e mx,
536  /// without clearing the translation.
537  GF_API
538  GfMatrix4f& SetRotateOnly(const GfMatrix3f &mx);
539 
540  /// Sets the matrix to specify a nonuniform scaling in x, y, and z by
541  /// the factors in vector \e scaleFactors.
542  GF_API
543  GfMatrix4f& SetScale(const GfVec3f &scaleFactors);
544 
545  /// Sets matrix to specify a translation by the vector \e trans,
546  /// and clears the rotation.
547  GF_API
549 
550  /// Sets matrix to specify a translation by the vector \e trans,
551  /// without clearing the rotation.
552  GF_API
554 
555  /// Sets matrix to specify a rotation by \e rotate and a
556  /// translation by \e translate.
557  GF_API
559  const GfVec3f& translate);
560 
561  /// Sets matrix to specify a rotation by \e rotmx and a
562  /// translation by \e translate.
563  GF_API
564  GfMatrix4f& SetTransform(const GfMatrix3f& rotmx,
565  const GfVec3f& translate);
566 
567  /// Sets the matrix to specify a viewing matrix from parameters
568  /// similar to those used by <c>gluLookAt(3G)</c>. \e eyePoint
569  /// represents the eye point in world space. \e centerPoint
570  /// represents the world-space center of attention. \e upDirection
571  /// is a vector indicating which way is up.
572  GF_API
573  GfMatrix4f& SetLookAt(const GfVec3f &eyePoint,
574  const GfVec3f &centerPoint,
575  const GfVec3f &upDirection);
576 
577  /// Sets the matrix to specify a viewing matrix from a world-space
578  /// \e eyePoint and a world-space rotation that rigidly rotates the
579  /// orientation from its canonical frame, which is defined to be
580  /// looking along the <c>-z</c> axis with the <c>+y</c> axis as the up
581  /// direction.
582  GF_API
583  GfMatrix4f& SetLookAt(const GfVec3f &eyePoint,
584  const GfRotation &orientation);
585 
586  /// Factors the matrix into 5 components:
587  /// \li <c>\e M = r * s * -r * u * t</c>
588  /// where
589  /// \li \e t is a translation.
590  /// \li \e u and \e r are rotations, and \e -r is the transpose
591  /// (inverse) of \e r. The \e u matrix may contain shear
592  /// information.
593  /// \li \e s is a scale.
594  /// Any projection information could be returned in matrix \e p,
595  /// but currently p is never modified.
596  ///
597  /// Returns \c false if the matrix is singular (as determined by \e eps).
598  /// In that case, any zero scales in \e s are clamped to \e eps
599  /// to allow computation of \e u.
600  GF_API
601  bool Factor(GfMatrix4f* r, GfVec3f* s, GfMatrix4f* u,
602  GfVec3f* t, GfMatrix4f* p,
603  float eps = 1e-5) const;
604 
605  /// Returns the translation part of the matrix, defined as the first three
606  /// elements of the last row.
608  return GfVec3f(_mtx[3][0], _mtx[3][1], _mtx[3][2]);
609  }
610 
611  /// Returns the rotation corresponding to this matrix. This works well
612  /// only if the matrix represents a rotation.
613  ///
614  /// For good results, consider calling Orthonormalize() before calling
615  /// this method.
616  GF_API
617  GfRotation ExtractRotation() const;
618 
619  /// Decompose the rotation corresponding to this matrix about 3 orthogonal
620  /// axes. If the axes are not orthogonal, warnings will be spewed.
621  ///
622  /// This is a convenience method that is equivalent to calling
623  /// ExtractRotation().Decompose().
624  GF_API
625  GfVec3f DecomposeRotation(const GfVec3f &axis0,
626  const GfVec3f &axis1,
627  const GfVec3f &axis2) const;
628 
629  /// Returns the rotation corresponding to this matrix. This works well
630  /// only if the matrix represents a rotation.
631  ///
632  /// For good results, consider calling Orthonormalize() before calling
633  /// this method.
634  GF_API
636 
637  /// Transforms the row vector \e vec by the matrix, returning the result.
638  /// This treats the vector as a 4-component vector whose fourth component
639  /// is 1.
640  GfVec3d Transform(const GfVec3d &vec) const {
641  return GfProject(GfVec4d(
642  vec[0] * _mtx[0][0] + vec[1] * _mtx[1][0] + vec[2] * _mtx[2][0] + _mtx[3][0],
643  vec[0] * _mtx[0][1] + vec[1] * _mtx[1][1] + vec[2] * _mtx[2][1] + _mtx[3][1],
644  vec[0] * _mtx[0][2] + vec[1] * _mtx[1][2] + vec[2] * _mtx[2][2] + _mtx[3][2],
645  vec[0] * _mtx[0][3] + vec[1] * _mtx[1][3] + vec[2] * _mtx[2][3] + _mtx[3][3]));
646  }
647 
648  /// Transforms the row vector \e vec by the matrix, returning the result.
649  /// This treats the vector as a 4-component vector whose fourth component
650  /// is 1. This is an overloaded method; it differs from the other version
651  /// in that it returns a different value type.
652  GfVec3f Transform(const GfVec3f &vec) const {
653  return (GfProject(GfVec4f(
654  vec[0] * _mtx[0][0] + vec[1] * _mtx[1][0] + vec[2] * _mtx[2][0] + _mtx[3][0],
655  vec[0] * _mtx[0][1] + vec[1] * _mtx[1][1] + vec[2] * _mtx[2][1] + _mtx[3][1],
656  vec[0] * _mtx[0][2] + vec[1] * _mtx[1][2] + vec[2] * _mtx[2][2] + _mtx[3][2],
657  vec[0] * _mtx[0][3] + vec[1] * _mtx[1][3] + vec[2] * _mtx[2][3] + _mtx[3][3])));
658  }
659 
660  /// Transforms row vector \e vec by the matrix, returning the result. This
661  /// treats the vector as a direction vector, so the translation
662  /// information in the matrix is ignored. That is, it treats the vector as
663  /// a 4-component vector whose fourth component is 0.
664  GfVec3d TransformDir(const GfVec3d &vec) const {
665  return GfVec3d(
666  vec[0] * _mtx[0][0] + vec[1] * _mtx[1][0] + vec[2] * _mtx[2][0],
667  vec[0] * _mtx[0][1] + vec[1] * _mtx[1][1] + vec[2] * _mtx[2][1],
668  vec[0] * _mtx[0][2] + vec[1] * _mtx[1][2] + vec[2] * _mtx[2][2]);
669  }
670 
671  /// Transforms row vector \e vec by the matrix, returning the result. This
672  /// treats the vector as a direction vector, so the translation
673  /// information in the matrix is ignored. That is, it treats the vector as
674  /// a 4-component vector whose fourth component is 0. This is an
675  /// overloaded method; it differs from the other version in that it
676  /// returns a different value type.
677  GfVec3f TransformDir(const GfVec3f &vec) const {
678  return GfVec3f(
679  vec[0] * _mtx[0][0] + vec[1] * _mtx[1][0] + vec[2] * _mtx[2][0],
680  vec[0] * _mtx[0][1] + vec[1] * _mtx[1][1] + vec[2] * _mtx[2][1],
681  vec[0] * _mtx[0][2] + vec[1] * _mtx[1][2] + vec[2] * _mtx[2][2]);
682  }
683 
684  /// Transforms the row vector \e vec by the matrix, returning the result.
685  /// This treats the vector as a 4-component vector whose fourth component
686  /// is 1 and ignores the fourth column of the matrix (i.e. assumes it is
687  /// (0, 0, 0, 1)).
688  GfVec3d TransformAffine(const GfVec3d &vec) const {
689  return GfVec3d(
690  vec[0] * _mtx[0][0] + vec[1] * _mtx[1][0] + vec[2] * _mtx[2][0] + _mtx[3][0],
691  vec[0] * _mtx[0][1] + vec[1] * _mtx[1][1] + vec[2] * _mtx[2][1] + _mtx[3][1],
692  vec[0] * _mtx[0][2] + vec[1] * _mtx[1][2] + vec[2] * _mtx[2][2] + _mtx[3][2]);
693  }
694 
695  /// Transforms the row vector \e vec by the matrix, returning the result.
696  /// This treats the vector as a 4-component vector whose fourth component
697  /// is 1 and ignores the fourth column of the matrix (i.e. assumes it is
698  /// (0, 0, 0, 1)).
699  GfVec3f TransformAffine(const GfVec3f &vec) const {
700  return GfVec3f(
701  vec[0] * _mtx[0][0] + vec[1] * _mtx[1][0] + vec[2] * _mtx[2][0] + _mtx[3][0],
702  vec[0] * _mtx[0][1] + vec[1] * _mtx[1][1] + vec[2] * _mtx[2][1] + _mtx[3][1],
703  vec[0] * _mtx[0][2] + vec[1] * _mtx[1][2] + vec[2] * _mtx[2][2] + _mtx[3][2]);
704  }
705  /// @}
706 
707 private:
708  /// Returns the determinant of the 3x3 submatrix specified by the three
709  /// given row and column indices (0-3 for each).
710  GF_API
711  double _GetDeterminant3(size_t row1, size_t row2, size_t row3,
712  size_t col1, size_t col2, size_t col3) const;
713 
714  /// Diagonalizes the upper 3x3 matrix of a matrix known to be symmetric.
715  void _Jacobi3(GfVec3d *eigenvalues, GfVec3d eigenvectors[3]) const;
716 
717  /// Set the 3x3 submatrix to the rotation given by a quaternion,
718  /// defined by the real component \p r and imaginary components \p i.
719  void _SetRotateFromQuat(float r, const GfVec3f& i);
720 
721 
722 private:
723  /// Matrix storage, in row-major order.
725 
726  // Friend declarations
727  friend class GfMatrix4d;
728 };
729 
730 
731 /// Tests for equality within a given tolerance, returning \c true if the
732 /// difference between each component of the matrix is less than or equal
733 /// to \p tolerance, or false otherwise.
734 GF_API
735 bool GfIsClose(GfMatrix4f const &m1, GfMatrix4f const &m2, double tolerance);
736 
737 /// Output a GfMatrix4f
738 /// \ingroup group_gf_DebuggingOutput
739 GF_API std::ostream& operator<<(std::ostream &, GfMatrix4f const &);
740 
742 
743 #endif // GF_MATRIX4F_H
bool HasOrthogonalRows3() const
Definition: matrix4f.h:375
GLdouble s
Definition: glew.h:1390
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:204
GF_API std::ostream & operator<<(std::ostream &, GfMatrix4f const &)
GfVec3f TransformDir(const GfVec3f &vec) const
Definition: matrix4f.h:677
GF_API friend GfMatrix4f operator-(const GfMatrix4f &m)
Returns the unary negation of matrix m.
static const size_t numRows
Definition: matrix4f.h:93
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:452
*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 IsLeftHanded() const
Definition: matrix4f.h:413
GF_API GfMatrix4f & operator+=(const GfMatrix4f &m)
Adds matrix m to this matrix.
float * data()
Definition: matrix4f.h:274
GF_API GfMatrix4f & SetRotate(const GfQuatf &rot)
GA_API const UT_StringHolder rot
GF_API GfMatrix4f & SetRotateOnly(const GfQuatf &rot)
Definition: vec3f.h:63
Definition: vec4d.h:63
GfHalf GfDot(GfHalf a, GfHalf b)
Definition: half.h:55
GfVec3d TransformDir(const GfVec3d &vec) const
Definition: matrix4f.h:664
const GLdouble * m
Definition: glew.h:9124
const GLdouble * v
Definition: glew.h:1391
GfVec4f GetColumn(int i) const
Gets a column of the matrix as a Vec4.
Definition: matrix4f.h:209
GF_API GfMatrix3f ExtractRotationMatrix() const
double GfAbs(double f)
Definition: math.h:112
Definition: quatf.h:60
GF_API GfMatrix4f & SetTranslateOnly(const GfVec3f &t)
void SetRow3(int i, const GfVec3f &v)
Definition: matrix4f.h:354
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:196
bool IsRightHanded() const
Definition: matrix4f.h:407
friend GfMatrix4f operator*(const GfMatrix4f &m1, double d)
Returns the product of a matrix and a float.
Definition: matrix4f.h:426
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:216
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:640
double GetDeterminant3() const
Definition: matrix4f.h:368
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:361
friend size_t hash_value(GfMatrix4f const &m)
Hash.
Definition: matrix4f.h:305
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:297
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)
GfMatrix4f & SetZero()
Sets the matrix to zero.
Definition: matrix4f.h:255
GF_API bool operator==(const GfMatrix4d &m) const
GLfloat GLfloat GLfloat GLfloat h
Definition: glew.h:8011
float ScalarType
Definition: matrix4f.h:91
GfMatrix4f(const GfVec4f &v)
Definition: matrix4f.h:126
Definition: vec4f.h:63
GfMatrix4f & SetIdentity()
Sets the matrix to the identity matrix.
Definition: matrix4f.h:250
GLfloat GLfloat p
Definition: glew.h:16321
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)
PXR_NAMESPACE_CLOSE_SCOPE PXR_NAMESPACE_OPEN_SCOPE
Definition: path.h:1245
GfMatrix4f & Set(const float m[4][4])
Definition: matrix4f.h:229
GfMatrix4f(const float m[4][4])
Definition: matrix4f.h:114
friend GfMatrix4f operator/(const GfMatrix4f &m1, const GfMatrix4f &m2)
Divides matrix m1 by m2 (that is, m1 * inv(m2)).
Definition: matrix4f.h:476
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:607
GLdouble GLdouble GLdouble r
Definition: glew.h:1406
Definition: vec3d.h:63
#define PXR_NAMESPACE_CLOSE_SCOPE
Definition: pxr.h:83
GfMatrix4f()=default
Default constructor. Leaves the matrix component values undefined.
GfVec3f TransformAffine(const GfVec3f &vec) const
Definition: matrix4f.h:699
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:102
GF_API GfRotation ExtractRotation() const
GfVec3f Transform(const GfVec3f &vec) const
Definition: matrix4f.h:652
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:94
GfMatrix4f(float s)
Definition: matrix4f.h:120
GF_API GfMatrix4f & operator-=(const GfMatrix4f &m)
Subtracts matrix m from this matrix.
GfVec3d TransformAffine(const GfVec3d &vec) const
Definition: matrix4f.h:688
void SetRow(int i, const GfVec4f &v)
Sets a row of the matrix from a Vec4.
Definition: matrix4f.h:188
GLsizei const GLfloat * value
Definition: glew.h:1849
GF_API GfMatrix4f GetOrthonormalized(bool issueWarning=true) const
Returns an orthonormalized copy of the matrix.
GLdouble GLdouble t
Definition: glew.h:1398
#define GF_MIN_ORTHO_TOLERANCE
Definition: limits.h:39
const float * data() const
Definition: matrix4f.h:280
#define GF_API
Definition: api.h:40
float * GetArray()
Returns vector components as an array of float values.
Definition: matrix4f.h:285
bool operator!=(const GfMatrix4d &m) const
Definition: matrix4f.h:326
const float * GetArray() const
Returns vector components as a const array of float values.
Definition: matrix4f.h:290