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qmatrix4x4.cpp
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1// Copyright (C) 2016 The Qt Company Ltd.
2// SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only
3
4#include "qmatrix4x4.h"
5#include <QtCore/qmath.h>
6#include <QtCore/qvariant.h>
7#include <QtGui/qtransform.h>
8
9#include <cmath>
10
11QT_BEGIN_NAMESPACE
12
13#ifndef QT_NO_MATRIX4X4
14
39static const float inv_dist_to_plane = 1.0f / 1024.0f;
40
67QMatrix4x4::QMatrix4x4(const float *values)
68{
69 for (int row = 0; row < 4; ++row)
70 for (int col = 0; col < 4; ++col)
71 m[col][row] = values[row * 4 + col];
72 flagBits = General;
73}
74
114QMatrix4x4::QMatrix4x4(const float *values, int cols, int rows)
115{
116 for (int col = 0; col < 4; ++col) {
117 for (int row = 0; row < 4; ++row) {
118 if (col < cols && row < rows)
119 m[col][row] = values[col * rows + row];
120 else if (col == row)
121 m[col][row] = 1.0f;
122 else
123 m[col][row] = 0.0f;
124 }
125 }
126 flagBits = General;
127}
128
140QMatrix4x4::QMatrix4x4(const QTransform& transform)
141{
142 m[0][0] = transform.m11();
143 m[0][1] = transform.m12();
144 m[0][2] = 0.0f;
145 m[0][3] = transform.m13();
146 m[1][0] = transform.m21();
147 m[1][1] = transform.m22();
148 m[1][2] = 0.0f;
149 m[1][3] = transform.m23();
150 m[2][0] = 0.0f;
151 m[2][1] = 0.0f;
152 m[2][2] = 1.0f;
153 m[2][3] = 0.0f;
154 m[3][0] = transform.dx();
155 m[3][1] = transform.dy();
156 m[3][2] = 0.0f;
157 m[3][3] = transform.m33();
158 flagBits = General;
159}
160
245static inline double matrixDet2(const double m[4][4], int col0, int col1, int row0, int row1)
246{
247 return m[col0][row0] * m[col1][row1] - m[col0][row1] * m[col1][row0];
248}
249
250
251// The 4x4 matrix inverse algorithm is based on that described at:
252// http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q24
253// Some optimization has been done to avoid making copies of 3x3
254// sub-matrices and to unroll the loops.
255
256// Calculate the determinant of a 3x3 sub-matrix.
257// | A B C |
258// M = | D E F | det(M) = A * (EI - HF) - B * (DI - GF) + C * (DH - GE)
259// | G H I |
260static inline double matrixDet3
261 (const double m[4][4], int col0, int col1, int col2,
262 int row0, int row1, int row2)
263{
264 return m[col0][row0] * matrixDet2(m, col1, col2, row1, row2)
265 - m[col1][row0] * matrixDet2(m, col0, col2, row1, row2)
266 + m[col2][row0] * matrixDet2(m, col0, col1, row1, row2);
267}
268
269// Calculate the determinant of a 4x4 matrix.
270static inline double matrixDet4(const double m[4][4])
271{
272 double det;
273 det = m[0][0] * matrixDet3(m, 1, 2, 3, 1, 2, 3);
274 det -= m[1][0] * matrixDet3(m, 0, 2, 3, 1, 2, 3);
275 det += m[2][0] * matrixDet3(m, 0, 1, 3, 1, 2, 3);
276 det -= m[3][0] * matrixDet3(m, 0, 1, 2, 1, 2, 3);
277 return det;
278}
279
280static inline void copyToDoubles(const float m[4][4], double mm[4][4])
281{
282 for (int i = 0; i < 4; ++i)
283 for (int j = 0; j < 4; ++j)
284 mm[i][j] = double(m[i][j]);
285}
286
290double QMatrix4x4::determinant() const
291{
292 if ((flagBits & ~(Translation | Rotation2D | Rotation)) == Identity)
293 return 1.0;
294
295 double mm[4][4];
296 copyToDoubles(m, mm);
297 if (flagBits < Rotation2D)
298 return mm[0][0] * mm[1][1] * mm[2][2]; // Translation | Scale
299 if (flagBits < Perspective)
300 return matrixDet3(mm, 0, 1, 2, 0, 1, 2);
301 return matrixDet4(mm);
302}
303
316QMatrix4x4 QMatrix4x4::inverted(bool *invertible) const
317{
318 // Handle some of the easy cases first.
319 if (flagBits == Identity) {
320 if (invertible)
321 *invertible = true;
322 return QMatrix4x4();
323 } else if (flagBits == Translation) {
324 QMatrix4x4 inv;
325 inv.m[3][0] = -m[3][0];
326 inv.m[3][1] = -m[3][1];
327 inv.m[3][2] = -m[3][2];
328 inv.flagBits = Translation;
329 if (invertible)
330 *invertible = true;
331 return inv;
332 } else if (flagBits < Rotation2D) {
333 // Translation | Scale
334 if (m[0][0] == 0 || m[1][1] == 0 || m[2][2] == 0) {
335 if (invertible)
336 *invertible = false;
337 return QMatrix4x4();
338 }
339 QMatrix4x4 inv;
340 inv.m[0][0] = 1.0f / m[0][0];
341 inv.m[1][1] = 1.0f / m[1][1];
342 inv.m[2][2] = 1.0f / m[2][2];
343 inv.m[3][0] = -m[3][0] * inv.m[0][0];
344 inv.m[3][1] = -m[3][1] * inv.m[1][1];
345 inv.m[3][2] = -m[3][2] * inv.m[2][2];
346 inv.flagBits = flagBits;
347
348 if (invertible)
349 *invertible = true;
350 return inv;
351 } else if ((flagBits & ~(Translation | Rotation2D | Rotation)) == Identity) {
352 if (invertible)
353 *invertible = true;
354 return orthonormalInverse();
355 } else if (flagBits < Perspective) {
356 QMatrix4x4 inv(Qt::Uninitialized);
357
358 double mm[4][4];
359 copyToDoubles(m, mm);
360
361 double det = matrixDet3(mm, 0, 1, 2, 0, 1, 2);
362 if (det == 0.0f) {
363 if (invertible)
364 *invertible = false;
365 return QMatrix4x4();
366 }
367 det = 1.0f / det;
368
369 inv.m[0][0] = matrixDet2(mm, 1, 2, 1, 2) * det;
370 inv.m[0][1] = -matrixDet2(mm, 0, 2, 1, 2) * det;
371 inv.m[0][2] = matrixDet2(mm, 0, 1, 1, 2) * det;
372 inv.m[0][3] = 0;
373 inv.m[1][0] = -matrixDet2(mm, 1, 2, 0, 2) * det;
374 inv.m[1][1] = matrixDet2(mm, 0, 2, 0, 2) * det;
375 inv.m[1][2] = -matrixDet2(mm, 0, 1, 0, 2) * det;
376 inv.m[1][3] = 0;
377 inv.m[2][0] = matrixDet2(mm, 1, 2, 0, 1) * det;
378 inv.m[2][1] = -matrixDet2(mm, 0, 2, 0, 1) * det;
379 inv.m[2][2] = matrixDet2(mm, 0, 1, 0, 1) * det;
380 inv.m[2][3] = 0;
381 inv.m[3][0] = -inv.m[0][0] * m[3][0] - inv.m[1][0] * m[3][1] - inv.m[2][0] * m[3][2];
382 inv.m[3][1] = -inv.m[0][1] * m[3][0] - inv.m[1][1] * m[3][1] - inv.m[2][1] * m[3][2];
383 inv.m[3][2] = -inv.m[0][2] * m[3][0] - inv.m[1][2] * m[3][1] - inv.m[2][2] * m[3][2];
384 inv.m[3][3] = 1;
385 inv.flagBits = flagBits;
386
387 if (invertible)
388 *invertible = true;
389 return inv;
390 }
391
392 QMatrix4x4 inv(Qt::Uninitialized);
393
394 double mm[4][4];
395 copyToDoubles(m, mm);
396
397 double det = matrixDet4(mm);
398 if (det == 0.0f) {
399 if (invertible)
400 *invertible = false;
401 return QMatrix4x4();
402 }
403 det = 1.0f / det;
404
405 inv.m[0][0] = matrixDet3(mm, 1, 2, 3, 1, 2, 3) * det;
406 inv.m[0][1] = -matrixDet3(mm, 0, 2, 3, 1, 2, 3) * det;
407 inv.m[0][2] = matrixDet3(mm, 0, 1, 3, 1, 2, 3) * det;
408 inv.m[0][3] = -matrixDet3(mm, 0, 1, 2, 1, 2, 3) * det;
409 inv.m[1][0] = -matrixDet3(mm, 1, 2, 3, 0, 2, 3) * det;
410 inv.m[1][1] = matrixDet3(mm, 0, 2, 3, 0, 2, 3) * det;
411 inv.m[1][2] = -matrixDet3(mm, 0, 1, 3, 0, 2, 3) * det;
412 inv.m[1][3] = matrixDet3(mm, 0, 1, 2, 0, 2, 3) * det;
413 inv.m[2][0] = matrixDet3(mm, 1, 2, 3, 0, 1, 3) * det;
414 inv.m[2][1] = -matrixDet3(mm, 0, 2, 3, 0, 1, 3) * det;
415 inv.m[2][2] = matrixDet3(mm, 0, 1, 3, 0, 1, 3) * det;
416 inv.m[2][3] = -matrixDet3(mm, 0, 1, 2, 0, 1, 3) * det;
417 inv.m[3][0] = -matrixDet3(mm, 1, 2, 3, 0, 1, 2) * det;
418 inv.m[3][1] = matrixDet3(mm, 0, 2, 3, 0, 1, 2) * det;
419 inv.m[3][2] = -matrixDet3(mm, 0, 1, 3, 0, 1, 2) * det;
420 inv.m[3][3] = matrixDet3(mm, 0, 1, 2, 0, 1, 2) * det;
421 inv.flagBits = flagBits;
422
423 if (invertible)
424 *invertible = true;
425 return inv;
426}
427
436QMatrix3x3 QMatrix4x4::normalMatrix() const
437{
438 QMatrix3x3 inv;
439
440 // Handle the simple cases first.
441 if (flagBits < Scale) {
442 // Translation
443 return inv;
444 } else if (flagBits < Rotation2D) {
445 // Translation | Scale
446 if (m[0][0] == 0.0f || m[1][1] == 0.0f || m[2][2] == 0.0f)
447 return inv;
448 inv.data()[0] = 1.0f / m[0][0];
449 inv.data()[4] = 1.0f / m[1][1];
450 inv.data()[8] = 1.0f / m[2][2];
451 return inv;
452 } else if ((flagBits & ~(Translation | Rotation2D | Rotation)) == Identity) {
453 float *invm = inv.data();
454 invm[0 + 0 * 3] = m[0][0];
455 invm[1 + 0 * 3] = m[0][1];
456 invm[2 + 0 * 3] = m[0][2];
457 invm[0 + 1 * 3] = m[1][0];
458 invm[1 + 1 * 3] = m[1][1];
459 invm[2 + 1 * 3] = m[1][2];
460 invm[0 + 2 * 3] = m[2][0];
461 invm[1 + 2 * 3] = m[2][1];
462 invm[2 + 2 * 3] = m[2][2];
463 return inv;
464 }
465
466 double mm[4][4];
467 copyToDoubles(m, mm);
468 double det = matrixDet3(mm, 0, 1, 2, 0, 1, 2);
469 if (det == 0.0f)
470 return inv;
471 det = 1.0f / det;
472
473 float *invm = inv.data();
474
475 // Invert and transpose in a single step.
476 invm[0 + 0 * 3] = (mm[1][1] * mm[2][2] - mm[2][1] * mm[1][2]) * det;
477 invm[1 + 0 * 3] = -(mm[1][0] * mm[2][2] - mm[1][2] * mm[2][0]) * det;
478 invm[2 + 0 * 3] = (mm[1][0] * mm[2][1] - mm[1][1] * mm[2][0]) * det;
479 invm[0 + 1 * 3] = -(mm[0][1] * mm[2][2] - mm[2][1] * mm[0][2]) * det;
480 invm[1 + 1 * 3] = (mm[0][0] * mm[2][2] - mm[0][2] * mm[2][0]) * det;
481 invm[2 + 1 * 3] = -(mm[0][0] * mm[2][1] - mm[0][1] * mm[2][0]) * det;
482 invm[0 + 2 * 3] = (mm[0][1] * mm[1][2] - mm[0][2] * mm[1][1]) * det;
483 invm[1 + 2 * 3] = -(mm[0][0] * mm[1][2] - mm[0][2] * mm[1][0]) * det;
484 invm[2 + 2 * 3] = (mm[0][0] * mm[1][1] - mm[1][0] * mm[0][1]) * det;
485
486 return inv;
487}
488
492QMatrix4x4 QMatrix4x4::transposed() const
493{
494 QMatrix4x4 result(Qt::Uninitialized);
495 for (int row = 0; row < 4; ++row) {
496 for (int col = 0; col < 4; ++col) {
497 result.m[col][row] = m[row][col];
498 }
499 }
500 // When a translation is transposed, it becomes a perspective transformation.
501 result.flagBits = (flagBits & Translation ? General : flagBits);
502 return result;
503}
504
535QMatrix4x4& QMatrix4x4::operator/=(float divisor)
536{
537 m[0][0] /= divisor;
538 m[0][1] /= divisor;
539 m[0][2] /= divisor;
540 m[0][3] /= divisor;
541 m[1][0] /= divisor;
542 m[1][1] /= divisor;
543 m[1][2] /= divisor;
544 m[1][3] /= divisor;
545 m[2][0] /= divisor;
546 m[2][1] /= divisor;
547 m[2][2] /= divisor;
548 m[2][3] /= divisor;
549 m[3][0] /= divisor;
550 m[3][1] /= divisor;
551 m[3][2] /= divisor;
552 m[3][3] /= divisor;
553 flagBits = General;
554 return *this;
555}
556
592#ifndef QT_NO_VECTOR3D
593
594#if QT_DEPRECATED_SINCE(6, 1)
595
617#endif
618
619#endif
620
621#ifndef QT_NO_VECTOR4D
622
639#endif
640
657#if QT_DEPRECATED_SINCE(6, 1)
658
679#endif
680
708QMatrix4x4 operator/(const QMatrix4x4& matrix, float divisor)
709{
710 QMatrix4x4 m(Qt::Uninitialized);
711 m.m[0][0] = matrix.m[0][0] / divisor;
712 m.m[0][1] = matrix.m[0][1] / divisor;
713 m.m[0][2] = matrix.m[0][2] / divisor;
714 m.m[0][3] = matrix.m[0][3] / divisor;
715 m.m[1][0] = matrix.m[1][0] / divisor;
716 m.m[1][1] = matrix.m[1][1] / divisor;
717 m.m[1][2] = matrix.m[1][2] / divisor;
718 m.m[1][3] = matrix.m[1][3] / divisor;
719 m.m[2][0] = matrix.m[2][0] / divisor;
720 m.m[2][1] = matrix.m[2][1] / divisor;
721 m.m[2][2] = matrix.m[2][2] / divisor;
722 m.m[2][3] = matrix.m[2][3] / divisor;
723 m.m[3][0] = matrix.m[3][0] / divisor;
724 m.m[3][1] = matrix.m[3][1] / divisor;
725 m.m[3][2] = matrix.m[3][2] / divisor;
726 m.m[3][3] = matrix.m[3][3] / divisor;
727 m.flagBits = QMatrix4x4::General;
728 return m;
729}
730
738bool qFuzzyCompare(const QMatrix4x4& m1, const QMatrix4x4& m2)
739{
740 return qFuzzyCompare(m1.m[0][0], m2.m[0][0]) &&
741 qFuzzyCompare(m1.m[0][1], m2.m[0][1]) &&
742 qFuzzyCompare(m1.m[0][2], m2.m[0][2]) &&
743 qFuzzyCompare(m1.m[0][3], m2.m[0][3]) &&
744 qFuzzyCompare(m1.m[1][0], m2.m[1][0]) &&
745 qFuzzyCompare(m1.m[1][1], m2.m[1][1]) &&
746 qFuzzyCompare(m1.m[1][2], m2.m[1][2]) &&
747 qFuzzyCompare(m1.m[1][3], m2.m[1][3]) &&
748 qFuzzyCompare(m1.m[2][0], m2.m[2][0]) &&
749 qFuzzyCompare(m1.m[2][1], m2.m[2][1]) &&
750 qFuzzyCompare(m1.m[2][2], m2.m[2][2]) &&
751 qFuzzyCompare(m1.m[2][3], m2.m[2][3]) &&
752 qFuzzyCompare(m1.m[3][0], m2.m[3][0]) &&
753 qFuzzyCompare(m1.m[3][1], m2.m[3][1]) &&
754 qFuzzyCompare(m1.m[3][2], m2.m[3][2]) &&
755 qFuzzyCompare(m1.m[3][3], m2.m[3][3]);
756}
757
758
759#ifndef QT_NO_VECTOR3D
760
767void QMatrix4x4::scale(const QVector3D& vector)
768{
769 float vx = vector.x();
770 float vy = vector.y();
771 float vz = vector.z();
772 if (flagBits < Scale) {
773 m[0][0] = vx;
774 m[1][1] = vy;
775 m[2][2] = vz;
776 } else if (flagBits < Rotation2D) {
777 m[0][0] *= vx;
778 m[1][1] *= vy;
779 m[2][2] *= vz;
780 } else if (flagBits < Rotation) {
781 m[0][0] *= vx;
782 m[0][1] *= vx;
783 m[1][0] *= vy;
784 m[1][1] *= vy;
785 m[2][2] *= vz;
786 } else {
787 m[0][0] *= vx;
788 m[0][1] *= vx;
789 m[0][2] *= vx;
790 m[0][3] *= vx;
791 m[1][0] *= vy;
792 m[1][1] *= vy;
793 m[1][2] *= vy;
794 m[1][3] *= vy;
795 m[2][0] *= vz;
796 m[2][1] *= vz;
797 m[2][2] *= vz;
798 m[2][3] *= vz;
799 }
800 flagBits |= Scale;
801}
802
803#endif
804
813void QMatrix4x4::scale(float x, float y)
814{
815 if (flagBits < Scale) {
816 m[0][0] = x;
817 m[1][1] = y;
818 } else if (flagBits < Rotation2D) {
819 m[0][0] *= x;
820 m[1][1] *= y;
821 } else if (flagBits < Rotation) {
822 m[0][0] *= x;
823 m[0][1] *= x;
824 m[1][0] *= y;
825 m[1][1] *= y;
826 } else {
827 m[0][0] *= x;
828 m[0][1] *= x;
829 m[0][2] *= x;
830 m[0][3] *= x;
831 m[1][0] *= y;
832 m[1][1] *= y;
833 m[1][2] *= y;
834 m[1][3] *= y;
835 }
836 flagBits |= Scale;
837}
838
847void QMatrix4x4::scale(float x, float y, float z)
848{
849 if (flagBits < Scale) {
850 m[0][0] = x;
851 m[1][1] = y;
852 m[2][2] = z;
853 } else if (flagBits < Rotation2D) {
854 m[0][0] *= x;
855 m[1][1] *= y;
856 m[2][2] *= z;
857 } else if (flagBits < Rotation) {
858 m[0][0] *= x;
859 m[0][1] *= x;
860 m[1][0] *= y;
861 m[1][1] *= y;
862 m[2][2] *= z;
863 } else {
864 m[0][0] *= x;
865 m[0][1] *= x;
866 m[0][2] *= x;
867 m[0][3] *= x;
868 m[1][0] *= y;
869 m[1][1] *= y;
870 m[1][2] *= y;
871 m[1][3] *= y;
872 m[2][0] *= z;
873 m[2][1] *= z;
874 m[2][2] *= z;
875 m[2][3] *= z;
876 }
877 flagBits |= Scale;
878}
879
888void QMatrix4x4::scale(float factor)
889{
890 if (flagBits < Scale) {
891 m[0][0] = factor;
892 m[1][1] = factor;
893 m[2][2] = factor;
894 } else if (flagBits < Rotation2D) {
895 m[0][0] *= factor;
896 m[1][1] *= factor;
897 m[2][2] *= factor;
898 } else if (flagBits < Rotation) {
899 m[0][0] *= factor;
900 m[0][1] *= factor;
901 m[1][0] *= factor;
902 m[1][1] *= factor;
903 m[2][2] *= factor;
904 } else {
905 m[0][0] *= factor;
906 m[0][1] *= factor;
907 m[0][2] *= factor;
908 m[0][3] *= factor;
909 m[1][0] *= factor;
910 m[1][1] *= factor;
911 m[1][2] *= factor;
912 m[1][3] *= factor;
913 m[2][0] *= factor;
914 m[2][1] *= factor;
915 m[2][2] *= factor;
916 m[2][3] *= factor;
917 }
918 flagBits |= Scale;
919}
920
921#ifndef QT_NO_VECTOR3D
929void QMatrix4x4::translate(const QVector3D& vector)
930{
931 float vx = vector.x();
932 float vy = vector.y();
933 float vz = vector.z();
934 if (flagBits == Identity) {
935 m[3][0] = vx;
936 m[3][1] = vy;
937 m[3][2] = vz;
938 } else if (flagBits == Translation) {
939 m[3][0] += vx;
940 m[3][1] += vy;
941 m[3][2] += vz;
942 } else if (flagBits == Scale) {
943 m[3][0] = m[0][0] * vx;
944 m[3][1] = m[1][1] * vy;
945 m[3][2] = m[2][2] * vz;
946 } else if (flagBits == (Translation | Scale)) {
947 m[3][0] += m[0][0] * vx;
948 m[3][1] += m[1][1] * vy;
949 m[3][2] += m[2][2] * vz;
950 } else if (flagBits < Rotation) {
951 m[3][0] += m[0][0] * vx + m[1][0] * vy;
952 m[3][1] += m[0][1] * vx + m[1][1] * vy;
953 m[3][2] += m[2][2] * vz;
954 } else {
955 m[3][0] += m[0][0] * vx + m[1][0] * vy + m[2][0] * vz;
956 m[3][1] += m[0][1] * vx + m[1][1] * vy + m[2][1] * vz;
957 m[3][2] += m[0][2] * vx + m[1][2] * vy + m[2][2] * vz;
958 m[3][3] += m[0][3] * vx + m[1][3] * vy + m[2][3] * vz;
959 }
960 flagBits |= Translation;
961}
962#endif
963
972void QMatrix4x4::translate(float x, float y)
973{
974 if (flagBits == Identity) {
975 m[3][0] = x;
976 m[3][1] = y;
977 } else if (flagBits == Translation) {
978 m[3][0] += x;
979 m[3][1] += y;
980 } else if (flagBits == Scale) {
981 m[3][0] = m[0][0] * x;
982 m[3][1] = m[1][1] * y;
983 } else if (flagBits == (Translation | Scale)) {
984 m[3][0] += m[0][0] * x;
985 m[3][1] += m[1][1] * y;
986 } else if (flagBits < Rotation) {
987 m[3][0] += m[0][0] * x + m[1][0] * y;
988 m[3][1] += m[0][1] * x + m[1][1] * y;
989 } else {
990 m[3][0] += m[0][0] * x + m[1][0] * y;
991 m[3][1] += m[0][1] * x + m[1][1] * y;
992 m[3][2] += m[0][2] * x + m[1][2] * y;
993 m[3][3] += m[0][3] * x + m[1][3] * y;
994 }
995 flagBits |= Translation;
996}
997
1006void QMatrix4x4::translate(float x, float y, float z)
1007{
1008 if (flagBits == Identity) {
1009 m[3][0] = x;
1010 m[3][1] = y;
1011 m[3][2] = z;
1012 } else if (flagBits == Translation) {
1013 m[3][0] += x;
1014 m[3][1] += y;
1015 m[3][2] += z;
1016 } else if (flagBits == Scale) {
1017 m[3][0] = m[0][0] * x;
1018 m[3][1] = m[1][1] * y;
1019 m[3][2] = m[2][2] * z;
1020 } else if (flagBits == (Translation | Scale)) {
1021 m[3][0] += m[0][0] * x;
1022 m[3][1] += m[1][1] * y;
1023 m[3][2] += m[2][2] * z;
1024 } else if (flagBits < Rotation) {
1025 m[3][0] += m[0][0] * x + m[1][0] * y;
1026 m[3][1] += m[0][1] * x + m[1][1] * y;
1027 m[3][2] += m[2][2] * z;
1028 } else {
1029 m[3][0] += m[0][0] * x + m[1][0] * y + m[2][0] * z;
1030 m[3][1] += m[0][1] * x + m[1][1] * y + m[2][1] * z;
1031 m[3][2] += m[0][2] * x + m[1][2] * y + m[2][2] * z;
1032 m[3][3] += m[0][3] * x + m[1][3] * y + m[2][3] * z;
1033 }
1034 flagBits |= Translation;
1035}
1036
1037#ifndef QT_NO_VECTOR3D
1045void QMatrix4x4::rotate(float angle, const QVector3D& vector)
1046{
1047 rotate(angle, vector.x(), vector.y(), vector.z());
1048}
1049
1050#endif
1051
1060void QMatrix4x4::rotate(float angle, float x, float y, float z)
1061{
1062 if (angle == 0.0f)
1063 return;
1064 float c, s;
1065 if (angle == 90.0f || angle == -270.0f) {
1066 s = 1.0f;
1067 c = 0.0f;
1068 } else if (angle == -90.0f || angle == 270.0f) {
1069 s = -1.0f;
1070 c = 0.0f;
1071 } else if (angle == 180.0f || angle == -180.0f) {
1072 s = 0.0f;
1073 c = -1.0f;
1074 } else {
1075 float a = qDegreesToRadians(angle);
1076 c = std::cos(a);
1077 s = std::sin(a);
1078 }
1079 if (x == 0.0f) {
1080 if (y == 0.0f) {
1081 if (z != 0.0f) {
1082 // Rotate around the Z axis.
1083 if (z < 0)
1084 s = -s;
1085 float tmp;
1086 m[0][0] = (tmp = m[0][0]) * c + m[1][0] * s;
1087 m[1][0] = m[1][0] * c - tmp * s;
1088 m[0][1] = (tmp = m[0][1]) * c + m[1][1] * s;
1089 m[1][1] = m[1][1] * c - tmp * s;
1090 m[0][2] = (tmp = m[0][2]) * c + m[1][2] * s;
1091 m[1][2] = m[1][2] * c - tmp * s;
1092 m[0][3] = (tmp = m[0][3]) * c + m[1][3] * s;
1093 m[1][3] = m[1][3] * c - tmp * s;
1094
1095 flagBits |= Rotation2D;
1096 return;
1097 }
1098 } else if (z == 0.0f) {
1099 // Rotate around the Y axis.
1100 if (y < 0)
1101 s = -s;
1102 float tmp;
1103 m[2][0] = (tmp = m[2][0]) * c + m[0][0] * s;
1104 m[0][0] = m[0][0] * c - tmp * s;
1105 m[2][1] = (tmp = m[2][1]) * c + m[0][1] * s;
1106 m[0][1] = m[0][1] * c - tmp * s;
1107 m[2][2] = (tmp = m[2][2]) * c + m[0][2] * s;
1108 m[0][2] = m[0][2] * c - tmp * s;
1109 m[2][3] = (tmp = m[2][3]) * c + m[0][3] * s;
1110 m[0][3] = m[0][3] * c - tmp * s;
1111
1112 flagBits |= Rotation;
1113 return;
1114 }
1115 } else if (y == 0.0f && z == 0.0f) {
1116 // Rotate around the X axis.
1117 if (x < 0)
1118 s = -s;
1119 float tmp;
1120 m[1][0] = (tmp = m[1][0]) * c + m[2][0] * s;
1121 m[2][0] = m[2][0] * c - tmp * s;
1122 m[1][1] = (tmp = m[1][1]) * c + m[2][1] * s;
1123 m[2][1] = m[2][1] * c - tmp * s;
1124 m[1][2] = (tmp = m[1][2]) * c + m[2][2] * s;
1125 m[2][2] = m[2][2] * c - tmp * s;
1126 m[1][3] = (tmp = m[1][3]) * c + m[2][3] * s;
1127 m[2][3] = m[2][3] * c - tmp * s;
1128
1129 flagBits |= Rotation;
1130 return;
1131 }
1132
1133 double len = double(x) * double(x) +
1134 double(y) * double(y) +
1135 double(z) * double(z);
1136 if (!qFuzzyCompare(len, 1.0) && !qFuzzyIsNull(len)) {
1137 len = std::sqrt(len);
1138 x = float(double(x) / len);
1139 y = float(double(y) / len);
1140 z = float(double(z) / len);
1141 }
1142 float ic = 1.0f - c;
1143 QMatrix4x4 rot(Qt::Uninitialized);
1144 rot.m[0][0] = x * x * ic + c;
1145 rot.m[1][0] = x * y * ic - z * s;
1146 rot.m[2][0] = x * z * ic + y * s;
1147 rot.m[3][0] = 0.0f;
1148 rot.m[0][1] = y * x * ic + z * s;
1149 rot.m[1][1] = y * y * ic + c;
1150 rot.m[2][1] = y * z * ic - x * s;
1151 rot.m[3][1] = 0.0f;
1152 rot.m[0][2] = x * z * ic - y * s;
1153 rot.m[1][2] = y * z * ic + x * s;
1154 rot.m[2][2] = z * z * ic + c;
1155 rot.m[3][2] = 0.0f;
1156 rot.m[0][3] = 0.0f;
1157 rot.m[1][3] = 0.0f;
1158 rot.m[2][3] = 0.0f;
1159 rot.m[3][3] = 1.0f;
1160 rot.flagBits = Rotation;
1161 *this *= rot;
1162}
1163
1167void QMatrix4x4::projectedRotate(float angle, float x, float y, float z, float distanceToPlane)
1168{
1169 // Used by QGraphicsRotation::applyTo() to perform a rotation
1170 // and projection back to 2D in a single step.
1171 if (qIsNull(distanceToPlane))
1172 return rotate(angle, x, y, z);
1173 if (angle == 0.0f)
1174 return;
1175
1176 float c, s;
1177 if (angle == 90.0f || angle == -270.0f) {
1178 s = 1.0f;
1179 c = 0.0f;
1180 } else if (angle == -90.0f || angle == 270.0f) {
1181 s = -1.0f;
1182 c = 0.0f;
1183 } else if (angle == 180.0f || angle == -180.0f) {
1184 s = 0.0f;
1185 c = -1.0f;
1186 } else {
1187 float a = qDegreesToRadians(angle);
1188 c = std::cos(a);
1189 s = std::sin(a);
1190 }
1191
1192 const qreal d = 1.0 / distanceToPlane;
1193 if (x == 0.0f) {
1194 if (y == 0.0f) {
1195 if (z != 0.0f) {
1196 // Rotate around the Z axis.
1197 if (z < 0)
1198 s = -s;
1199 float tmp;
1200 m[0][0] = (tmp = m[0][0]) * c + m[1][0] * s;
1201 m[1][0] = m[1][0] * c - tmp * s;
1202 m[0][1] = (tmp = m[0][1]) * c + m[1][1] * s;
1203 m[1][1] = m[1][1] * c - tmp * s;
1204 m[0][2] = (tmp = m[0][2]) * c + m[1][2] * s;
1205 m[1][2] = m[1][2] * c - tmp * s;
1206 m[0][3] = (tmp = m[0][3]) * c + m[1][3] * s;
1207 m[1][3] = m[1][3] * c - tmp * s;
1208
1209 flagBits |= Rotation2D;
1210 return;
1211 }
1212 } else if (z == 0.0f) {
1213 // Rotate around the Y axis.
1214 if (y < 0)
1215 s = -s;
1216 s *= d;
1217 m[0][0] = m[0][0] * c + m[3][0] * s;
1218 m[0][1] = m[0][1] * c + m[3][1] * s;
1219 m[0][2] = m[0][2] * c + m[3][2] * s;
1220 m[0][3] = m[0][3] * c + m[3][3] * s;
1221 flagBits = General;
1222 return;
1223 }
1224 } else if (y == 0.0f && z == 0.0f) {
1225 // Rotate around the X axis.
1226 if (x < 0)
1227 s = -s;
1228 s *= d;
1229 m[1][0] = m[1][0] * c - m[3][0] * s;
1230 m[1][1] = m[1][1] * c - m[3][1] * s;
1231 m[1][2] = m[1][2] * c - m[3][2] * s;
1232 m[1][3] = m[1][3] * c - m[3][3] * s;
1233 flagBits = General;
1234 return;
1235 }
1236 double len = double(x) * double(x) +
1237 double(y) * double(y) +
1238 double(z) * double(z);
1239 if (!qFuzzyCompare(len, 1.0) && !qFuzzyIsNull(len)) {
1240 len = std::sqrt(len);
1241 x = float(double(x) / len);
1242 y = float(double(y) / len);
1243 z = float(double(z) / len);
1244 }
1245 const float ic = 1.0f - c;
1246 QMatrix4x4 rot(Qt::Uninitialized);
1247 rot.m[0][0] = x * x * ic + c;
1248 rot.m[1][0] = x * y * ic - z * s;
1249 rot.m[2][0] = 0.0f;
1250 rot.m[3][0] = 0.0f;
1251 rot.m[0][1] = y * x * ic + z * s;
1252 rot.m[1][1] = y * y * ic + c;
1253 rot.m[2][1] = 0.0f;
1254 rot.m[3][1] = 0.0f;
1255 rot.m[0][2] = 0.0f;
1256 rot.m[1][2] = 0.0f;
1257 rot.m[2][2] = 1.0f;
1258 rot.m[3][2] = 0.0f;
1259 rot.m[0][3] = (x * z * ic - y * s) * -d;
1260 rot.m[1][3] = (y * z * ic + x * s) * -d;
1261 rot.m[2][3] = 0.0f;
1262 rot.m[3][3] = 1.0f;
1263 rot.flagBits = General;
1264 *this *= rot;
1265}
1266
1267#if QT_VERSION < QT_VERSION_CHECK(7, 0, 0)
1271void QMatrix4x4::projectedRotate(float angle, float x, float y, float z)
1272{
1273 projectedRotate(angle, x, y, z, 1024.0);
1274}
1275#endif
1276
1294#ifndef QT_NO_QUATERNION
1295
1303void QMatrix4x4::rotate(const QQuaternion& quaternion)
1304{
1305 // Algorithm from:
1306 // http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q54
1307
1308 QMatrix4x4 m(Qt::Uninitialized);
1309
1310 const float f2x = quaternion.x() + quaternion.x();
1311 const float f2y = quaternion.y() + quaternion.y();
1312 const float f2z = quaternion.z() + quaternion.z();
1313 const float f2xw = f2x * quaternion.scalar();
1314 const float f2yw = f2y * quaternion.scalar();
1315 const float f2zw = f2z * quaternion.scalar();
1316 const float f2xx = f2x * quaternion.x();
1317 const float f2xy = f2x * quaternion.y();
1318 const float f2xz = f2x * quaternion.z();
1319 const float f2yy = f2y * quaternion.y();
1320 const float f2yz = f2y * quaternion.z();
1321 const float f2zz = f2z * quaternion.z();
1322
1323 m.m[0][0] = 1.0f - (f2yy + f2zz);
1324 m.m[1][0] = f2xy - f2zw;
1325 m.m[2][0] = f2xz + f2yw;
1326 m.m[3][0] = 0.0f;
1327 m.m[0][1] = f2xy + f2zw;
1328 m.m[1][1] = 1.0f - (f2xx + f2zz);
1329 m.m[2][1] = f2yz - f2xw;
1330 m.m[3][1] = 0.0f;
1331 m.m[0][2] = f2xz - f2yw;
1332 m.m[1][2] = f2yz + f2xw;
1333 m.m[2][2] = 1.0f - (f2xx + f2yy);
1334 m.m[3][2] = 0.0f;
1335 m.m[0][3] = 0.0f;
1336 m.m[1][3] = 0.0f;
1337 m.m[2][3] = 0.0f;
1338 m.m[3][3] = 1.0f;
1339 m.flagBits = Rotation;
1340 *this *= m;
1341}
1342
1343#endif
1344
1354void QMatrix4x4::ortho(const QRect& rect)
1355{
1356 // Note: rect.right() and rect.bottom() subtract 1 in QRect,
1357 // which gives the location of a pixel within the rectangle,
1358 // instead of the extent of the rectangle. We want the extent.
1359 // QRectF expresses the extent properly.
1360 ortho(rect.x(), rect.x() + rect.width(), rect.y() + rect.height(), rect.y(), -1.0f, 1.0f);
1361}
1362
1372void QMatrix4x4::ortho(const QRectF& rect)
1373{
1374 ortho(rect.left(), rect.right(), rect.bottom(), rect.top(), -1.0f, 1.0f);
1375}
1376
1385void QMatrix4x4::ortho(float left, float right, float bottom, float top, float nearPlane, float farPlane)
1386{
1387 // Bail out if the projection volume is zero-sized.
1388 if (left == right || bottom == top || nearPlane == farPlane)
1389 return;
1390
1391 // Construct the projection.
1392 const float width = right - left;
1393 const float invheight = top - bottom;
1394 const float clip = farPlane - nearPlane;
1395 QMatrix4x4 m(Qt::Uninitialized);
1396 m.m[0][0] = 2.0f / width;
1397 m.m[1][0] = 0.0f;
1398 m.m[2][0] = 0.0f;
1399 m.m[3][0] = -(left + right) / width;
1400 m.m[0][1] = 0.0f;
1401 m.m[1][1] = 2.0f / invheight;
1402 m.m[2][1] = 0.0f;
1403 m.m[3][1] = -(top + bottom) / invheight;
1404 m.m[0][2] = 0.0f;
1405 m.m[1][2] = 0.0f;
1406 m.m[2][2] = -2.0f / clip;
1407 m.m[3][2] = -(nearPlane + farPlane) / clip;
1408 m.m[0][3] = 0.0f;
1409 m.m[1][3] = 0.0f;
1410 m.m[2][3] = 0.0f;
1411 m.m[3][3] = 1.0f;
1412 m.flagBits = Translation | Scale;
1413
1414 // Apply the projection.
1415 *this *= m;
1416}
1417
1426void QMatrix4x4::frustum(float left, float right, float bottom, float top, float nearPlane, float farPlane)
1427{
1428 // Bail out if the projection volume is zero-sized.
1429 if (left == right || bottom == top || nearPlane == farPlane)
1430 return;
1431
1432 // Construct the projection.
1433 QMatrix4x4 m(Qt::Uninitialized);
1434 const float width = right - left;
1435 const float invheight = top - bottom;
1436 const float clip = farPlane - nearPlane;
1437 m.m[0][0] = 2.0f * nearPlane / width;
1438 m.m[1][0] = 0.0f;
1439 m.m[2][0] = (left + right) / width;
1440 m.m[3][0] = 0.0f;
1441 m.m[0][1] = 0.0f;
1442 m.m[1][1] = 2.0f * nearPlane / invheight;
1443 m.m[2][1] = (top + bottom) / invheight;
1444 m.m[3][1] = 0.0f;
1445 m.m[0][2] = 0.0f;
1446 m.m[1][2] = 0.0f;
1447 m.m[2][2] = -(nearPlane + farPlane) / clip;
1448 m.m[3][2] = -2.0f * nearPlane * farPlane / clip;
1449 m.m[0][3] = 0.0f;
1450 m.m[1][3] = 0.0f;
1451 m.m[2][3] = -1.0f;
1452 m.m[3][3] = 0.0f;
1453 m.flagBits = General;
1454
1455 // Apply the projection.
1456 *this *= m;
1457}
1458
1469void QMatrix4x4::perspective(float verticalAngle, float aspectRatio, float nearPlane, float farPlane)
1470{
1471 // Bail out if the projection volume is zero-sized.
1472 if (nearPlane == farPlane || aspectRatio == 0.0f)
1473 return;
1474
1475 // Construct the projection.
1476 QMatrix4x4 m(Qt::Uninitialized);
1477 const float radians = qDegreesToRadians(verticalAngle / 2.0f);
1478 const float sine = std::sin(radians);
1479 if (sine == 0.0f)
1480 return;
1481 float cotan = std::cos(radians) / sine;
1482 float clip = farPlane - nearPlane;
1483 m.m[0][0] = cotan / aspectRatio;
1484 m.m[1][0] = 0.0f;
1485 m.m[2][0] = 0.0f;
1486 m.m[3][0] = 0.0f;
1487 m.m[0][1] = 0.0f;
1488 m.m[1][1] = cotan;
1489 m.m[2][1] = 0.0f;
1490 m.m[3][1] = 0.0f;
1491 m.m[0][2] = 0.0f;
1492 m.m[1][2] = 0.0f;
1493 m.m[2][2] = -(nearPlane + farPlane) / clip;
1494 m.m[3][2] = -(2.0f * nearPlane * farPlane) / clip;
1495 m.m[0][3] = 0.0f;
1496 m.m[1][3] = 0.0f;
1497 m.m[2][3] = -1.0f;
1498 m.m[3][3] = 0.0f;
1499 m.flagBits = General;
1500
1501 // Apply the projection.
1502 *this *= m;
1503}
1504
1505#ifndef QT_NO_VECTOR3D
1506
1516void QMatrix4x4::lookAt(const QVector3D& eye, const QVector3D& center, const QVector3D& up)
1517{
1518 QVector3D forward = center - eye;
1519 if (qFuzzyIsNull(forward.x()) && qFuzzyIsNull(forward.y()) && qFuzzyIsNull(forward.z()))
1520 return;
1521
1522 forward.normalize();
1523 QVector3D side = QVector3D::crossProduct(forward, up).normalized();
1524 QVector3D upVector = QVector3D::crossProduct(side, forward);
1525
1526 QMatrix4x4 m(Qt::Uninitialized);
1527 m.m[0][0] = side.x();
1528 m.m[1][0] = side.y();
1529 m.m[2][0] = side.z();
1530 m.m[3][0] = 0.0f;
1531 m.m[0][1] = upVector.x();
1532 m.m[1][1] = upVector.y();
1533 m.m[2][1] = upVector.z();
1534 m.m[3][1] = 0.0f;
1535 m.m[0][2] = -forward.x();
1536 m.m[1][2] = -forward.y();
1537 m.m[2][2] = -forward.z();
1538 m.m[3][2] = 0.0f;
1539 m.m[0][3] = 0.0f;
1540 m.m[1][3] = 0.0f;
1541 m.m[2][3] = 0.0f;
1542 m.m[3][3] = 1.0f;
1543 m.flagBits = Rotation;
1544
1545 *this *= m;
1546 translate(-eye);
1547}
1548
1549#endif
1550
1570void QMatrix4x4::viewport(float left, float bottom, float width, float height, float nearPlane, float farPlane)
1571{
1572 const float w2 = width / 2.0f;
1573 const float h2 = height / 2.0f;
1574
1575 QMatrix4x4 m(Qt::Uninitialized);
1576 m.m[0][0] = w2;
1577 m.m[1][0] = 0.0f;
1578 m.m[2][0] = 0.0f;
1579 m.m[3][0] = left + w2;
1580 m.m[0][1] = 0.0f;
1581 m.m[1][1] = h2;
1582 m.m[2][1] = 0.0f;
1583 m.m[3][1] = bottom + h2;
1584 m.m[0][2] = 0.0f;
1585 m.m[1][2] = 0.0f;
1586 m.m[2][2] = (farPlane - nearPlane) / 2.0f;
1587 m.m[3][2] = (nearPlane + farPlane) / 2.0f;
1588 m.m[0][3] = 0.0f;
1589 m.m[1][3] = 0.0f;
1590 m.m[2][3] = 0.0f;
1591 m.m[3][3] = 1.0f;
1592 m.flagBits = General;
1593
1594 *this *= m;
1595}
1596
1607void QMatrix4x4::flipCoordinates()
1608{
1609 // Multiplying the y and z coordinates with -1 does NOT flip between right-handed and
1610 // left-handed coordinate systems, it just rotates 180 degrees around the x axis, so
1611 // I'm deprecating this function.
1612 if (flagBits < Rotation2D) {
1613 // Translation | Scale
1614 m[1][1] = -m[1][1];
1615 m[2][2] = -m[2][2];
1616 } else {
1617 m[1][0] = -m[1][0];
1618 m[1][1] = -m[1][1];
1619 m[1][2] = -m[1][2];
1620 m[1][3] = -m[1][3];
1621 m[2][0] = -m[2][0];
1622 m[2][1] = -m[2][1];
1623 m[2][2] = -m[2][2];
1624 m[2][3] = -m[2][3];
1625 }
1626 flagBits |= Scale;
1627}
1628
1633void QMatrix4x4::copyDataTo(float *values) const
1634{
1635 for (int row = 0; row < 4; ++row)
1636 for (int col = 0; col < 4; ++col)
1637 values[row * 4 + col] = float(m[col][row]);
1638}
1639
1649QTransform QMatrix4x4::toTransform() const
1650{
1651 return QTransform(m[0][0], m[0][1], m[0][3],
1652 m[1][0], m[1][1], m[1][3],
1653 m[3][0], m[3][1], m[3][3]);
1654}
1655
1671QTransform QMatrix4x4::toTransform(float distanceToPlane) const
1672{
1673 if (distanceToPlane == 1024.0f) {
1674 // Optimize the common case with constants.
1675 return QTransform(m[0][0], m[0][1], m[0][3] - m[0][2] * inv_dist_to_plane,
1676 m[1][0], m[1][1], m[1][3] - m[1][2] * inv_dist_to_plane,
1677 m[3][0], m[3][1], m[3][3] - m[3][2] * inv_dist_to_plane);
1678 } else if (distanceToPlane != 0.0f) {
1679 // The following projection matrix is pre-multiplied with "matrix":
1680 // | 1 0 0 0 |
1681 // | 0 1 0 0 |
1682 // | 0 0 1 0 |
1683 // | 0 0 d 1 |
1684 // where d = -1 / distanceToPlane. After projection, row 3 and
1685 // column 3 are dropped to form the final QTransform.
1686 float d = 1.0f / distanceToPlane;
1687 return QTransform(m[0][0], m[0][1], m[0][3] - m[0][2] * d,
1688 m[1][0], m[1][1], m[1][3] - m[1][2] * d,
1689 m[3][0], m[3][1], m[3][3] - m[3][2] * d);
1690 } else {
1691 // Orthographic projection: drop row 3 and column 3.
1692 return QTransform(m[0][0], m[0][1], m[0][3],
1693 m[1][0], m[1][1], m[1][3],
1694 m[3][0], m[3][1], m[3][3]);
1695 }
1696}
1697
1716#ifndef QT_NO_VECTOR3D
1717
1741#endif
1742
1743#ifndef QT_NO_VECTOR4D
1744
1754#endif
1755
1764QRect QMatrix4x4::mapRect(const QRect& rect) const
1765{
1766 if (flagBits < Scale) {
1767 // Translation
1768 return QRect(qRound(rect.x() + m[3][0]),
1769 qRound(rect.y() + m[3][1]),
1770 rect.width(), rect.height());
1771 } else if (flagBits < Rotation2D) {
1772 // Translation | Scale
1773 float x = rect.x() * m[0][0] + m[3][0];
1774 float y = rect.y() * m[1][1] + m[3][1];
1775 float w = rect.width() * m[0][0];
1776 float h = rect.height() * m[1][1];
1777 if (w < 0) {
1778 w = -w;
1779 x -= w;
1780 }
1781 if (h < 0) {
1782 h = -h;
1783 y -= h;
1784 }
1785 return QRect(qRound(x), qRound(y), qRound(w), qRound(h));
1786 }
1787
1788 QPoint tl = map(rect.topLeft());
1789 QPoint tr = map(QPoint(rect.x() + rect.width(), rect.y()));
1790 QPoint bl = map(QPoint(rect.x(), rect.y() + rect.height()));
1791 QPoint br = map(QPoint(rect.x() + rect.width(),
1792 rect.y() + rect.height()));
1793
1794 int xmin = qMin(qMin(tl.x(), tr.x()), qMin(bl.x(), br.x()));
1795 int xmax = qMax(qMax(tl.x(), tr.x()), qMax(bl.x(), br.x()));
1796 int ymin = qMin(qMin(tl.y(), tr.y()), qMin(bl.y(), br.y()));
1797 int ymax = qMax(qMax(tl.y(), tr.y()), qMax(bl.y(), br.y()));
1798
1799 return QRect(xmin, ymin, xmax - xmin, ymax - ymin);
1800}
1801
1810QRectF QMatrix4x4::mapRect(const QRectF& rect) const
1811{
1812 if (flagBits < Scale) {
1813 // Translation
1814 return rect.translated(m[3][0], m[3][1]);
1815 } else if (flagBits < Rotation2D) {
1816 // Translation | Scale
1817 float x = rect.x() * m[0][0] + m[3][0];
1818 float y = rect.y() * m[1][1] + m[3][1];
1819 float w = rect.width() * m[0][0];
1820 float h = rect.height() * m[1][1];
1821 if (w < 0) {
1822 w = -w;
1823 x -= w;
1824 }
1825 if (h < 0) {
1826 h = -h;
1827 y -= h;
1828 }
1829 return QRectF(x, y, w, h);
1830 }
1831
1832 QPointF tl = map(rect.topLeft()); QPointF tr = map(rect.topRight());
1833 QPointF bl = map(rect.bottomLeft()); QPointF br = map(rect.bottomRight());
1834
1835 float xmin = qMin(qMin(tl.x(), tr.x()), qMin(bl.x(), br.x()));
1836 float xmax = qMax(qMax(tl.x(), tr.x()), qMax(bl.x(), br.x()));
1837 float ymin = qMin(qMin(tl.y(), tr.y()), qMin(bl.y(), br.y()));
1838 float ymax = qMax(qMax(tl.y(), tr.y()), qMax(bl.y(), br.y()));
1839
1840 return QRectF(QPointF(xmin, ymin), QPointF(xmax, ymax));
1841}
1842
1869// Helper routine for inverting orthonormal matrices that consist
1870// of just rotations and translations.
1871QMatrix4x4 QMatrix4x4::orthonormalInverse() const
1872{
1873 QMatrix4x4 result(Qt::Uninitialized);
1874
1875 result.m[0][0] = m[0][0];
1876 result.m[1][0] = m[0][1];
1877 result.m[2][0] = m[0][2];
1878
1879 result.m[0][1] = m[1][0];
1880 result.m[1][1] = m[1][1];
1881 result.m[2][1] = m[1][2];
1882
1883 result.m[0][2] = m[2][0];
1884 result.m[1][2] = m[2][1];
1885 result.m[2][2] = m[2][2];
1886
1887 result.m[0][3] = 0.0f;
1888 result.m[1][3] = 0.0f;
1889 result.m[2][3] = 0.0f;
1890
1891 result.m[3][0] = -(result.m[0][0] * m[3][0] + result.m[1][0] * m[3][1] + result.m[2][0] * m[3][2]);
1892 result.m[3][1] = -(result.m[0][1] * m[3][0] + result.m[1][1] * m[3][1] + result.m[2][1] * m[3][2]);
1893 result.m[3][2] = -(result.m[0][2] * m[3][0] + result.m[1][2] * m[3][1] + result.m[2][2] * m[3][2]);
1894 result.m[3][3] = 1.0f;
1895
1896 result.flagBits = flagBits;
1897
1898 return result;
1899}
1900
1921void QMatrix4x4::optimize()
1922{
1923 // If the last row is not (0, 0, 0, 1), the matrix is not a special type.
1924 flagBits = General;
1925 if (m[0][3] != 0 || m[1][3] != 0 || m[2][3] != 0 || m[3][3] != 1)
1926 return;
1927
1928 flagBits &= ~Perspective;
1929
1930 // If the last column is (0, 0, 0, 1), then there is no translation.
1931 if (m[3][0] == 0 && m[3][1] == 0 && m[3][2] == 0)
1932 flagBits &= ~Translation;
1933
1934 // If the two first elements of row 3 and column 3 are 0, then any rotation must be about Z.
1935 if (!m[0][2] && !m[1][2] && !m[2][0] && !m[2][1]) {
1936 flagBits &= ~Rotation;
1937 // If the six non-diagonal elements in the top left 3x3 matrix are 0, there is no rotation.
1938 if (!m[0][1] && !m[1][0]) {
1939 flagBits &= ~Rotation2D;
1940 // Check for identity.
1941 if (m[0][0] == 1 && m[1][1] == 1 && m[2][2] == 1)
1942 flagBits &= ~Scale;
1943 } else {
1944 // If the columns are orthonormal and form a right-handed system, then there is no scale.
1945 double mm[4][4];
1946 copyToDoubles(m, mm);
1947 double det = matrixDet2(mm, 0, 1, 0, 1);
1948 double lenX = mm[0][0] * mm[0][0] + mm[0][1] * mm[0][1];
1949 double lenY = mm[1][0] * mm[1][0] + mm[1][1] * mm[1][1];
1950 double lenZ = mm[2][2];
1951 if (qFuzzyCompare(det, 1.0) && qFuzzyCompare(lenX, 1.0)
1952 && qFuzzyCompare(lenY, 1.0) && qFuzzyCompare(lenZ, 1.0))
1953 {
1954 flagBits &= ~Scale;
1955 }
1956 }
1957 } else {
1958 // If the columns are orthonormal and form a right-handed system, then there is no scale.
1959 double mm[4][4];
1960 copyToDoubles(m, mm);
1961 double det = matrixDet3(mm, 0, 1, 2, 0, 1, 2);
1962 double lenX = mm[0][0] * mm[0][0] + mm[0][1] * mm[0][1] + mm[0][2] * mm[0][2];
1963 double lenY = mm[1][0] * mm[1][0] + mm[1][1] * mm[1][1] + mm[1][2] * mm[1][2];
1964 double lenZ = mm[2][0] * mm[2][0] + mm[2][1] * mm[2][1] + mm[2][2] * mm[2][2];
1965 if (qFuzzyCompare(det, 1.0) && qFuzzyCompare(lenX, 1.0)
1966 && qFuzzyCompare(lenY, 1.0) && qFuzzyCompare(lenZ, 1.0))
1967 {
1968 flagBits &= ~Scale;
1969 }
1970 }
1971}
1972
1976QMatrix4x4::operator QVariant() const
1977{
1978 return QVariant::fromValue(*this);
1979}
1980
1981#ifndef QT_NO_DEBUG_STREAM
1982
1983QDebug operator<<(QDebug dbg, const QMatrix4x4 &m)
1984{
1985 QDebugStateSaver saver(dbg);
1986 // Create a string that represents the matrix type.
1987 QByteArray bits;
1988 if (m.flagBits == QMatrix4x4::Identity) {
1989 bits = "Identity";
1990 } else if (m.flagBits == QMatrix4x4::General) {
1991 bits = "General";
1992 } else {
1993 if ((m.flagBits & QMatrix4x4::Translation) != 0)
1994 bits += "Translation,";
1995 if ((m.flagBits & QMatrix4x4::Scale) != 0)
1996 bits += "Scale,";
1997 if ((m.flagBits & QMatrix4x4::Rotation2D) != 0)
1998 bits += "Rotation2D,";
1999 if ((m.flagBits & QMatrix4x4::Rotation) != 0)
2000 bits += "Rotation,";
2001 if ((m.flagBits & QMatrix4x4::Perspective) != 0)
2002 bits += "Perspective,";
2003 bits.chop(1);
2004 }
2005
2006 // Output in row-major order because it is more human-readable.
2007 dbg.nospace() << "QMatrix4x4(type:" << bits.constData() << Qt::endl
2008 << qSetFieldWidth(10)
2009 << m(0, 0) << m(0, 1) << m(0, 2) << m(0, 3) << Qt::endl
2010 << m(1, 0) << m(1, 1) << m(1, 2) << m(1, 3) << Qt::endl
2011 << m(2, 0) << m(2, 1) << m(2, 2) << m(2, 3) << Qt::endl
2012 << m(3, 0) << m(3, 1) << m(3, 2) << m(3, 3) << Qt::endl
2013 << qSetFieldWidth(0) << ')';
2014 return dbg;
2015}
2016
2017#endif
2018
2019#ifndef QT_NO_DATASTREAM
2020
2031QDataStream &operator<<(QDataStream &stream, const QMatrix4x4 &matrix)
2032{
2033 for (int row = 0; row < 4; ++row)
2034 for (int col = 0; col < 4; ++col)
2035 stream << matrix(row, col);
2036 return stream;
2037}
2038
2049QDataStream &operator>>(QDataStream &stream, QMatrix4x4 &matrix)
2050{
2051 float x;
2052 for (int row = 0; row < 4; ++row) {
2053 for (int col = 0; col < 4; ++col) {
2054 stream >> x;
2055 matrix(row, col) = x;
2056 }
2057 }
2058 matrix.optimize();
2059 return stream;
2060}
2061
2062#endif // QT_NO_DATASTREAM
2063
2064#endif // QT_NO_MATRIX4X4
2065
2066QT_END_NAMESPACE
QByteArray
\inmodule QtCore
Definition qbytearray.h:57
QDataStream
\inmodule QtCore\reentrant
Definition qdatastream.h:30
QDebugStateSaver
\inmodule QtCore
QDebug
\inmodule QtCore
QGenericMatrix::data
T * data()
Returns a pointer to the raw data of this matrix.
Definition qgenericmatrix.h:42
QMatrix4x4
The QMatrix4x4 class represents a 4x4 transformation matrix in 3D space.
Definition qmatrix4x4.h:25
QMatrix4x4::flipCoordinates
void flipCoordinates()
Definition qmatrix4x4.cpp:1607
QMatrix4x4::normalMatrix
QMatrix3x3 normalMatrix() const
Returns the normal matrix corresponding to this 4x4 transformation.
Definition qmatrix4x4.cpp:436
QMatrix4x4::frustum
void frustum(float left, float right, float bottom, float top, float nearPlane, float farPlane)
Multiplies this matrix by another that applies a perspective frustum projection for a window with low...
Definition qmatrix4x4.cpp:1426
QMatrix4x4::lookAt
void lookAt(const QVector3D &eye, const QVector3D &center, const QVector3D &up)
Multiplies this matrix by a viewing matrix derived from an eye point.
Definition qmatrix4x4.cpp:1516
QMatrix4x4::copyDataTo
void copyDataTo(float *values) const
Retrieves the 16 items in this matrix and copies them to values in row-major order.
Definition qmatrix4x4.cpp:1633
QMatrix4x4::QMatrix4x4
QMatrix4x4()
Constructs an identity matrix.
Definition qmatrix4x4.h:27
QMatrix4x4::rotate
void rotate(float angle, const QVector3D &vector)
Multiples this matrix by another that rotates coordinates through angle degrees about vector.
Definition qmatrix4x4.cpp:1045
QMatrix4x4::scale
void scale(const QVector3D &vector)
Multiplies this matrix by another that scales coordinates by the components of vector.
Definition qmatrix4x4.cpp:767
QMatrix4x4::projectedRotate
void projectedRotate(float angle, float x, float y, float z, float distanceToPlane=1024.0)
Definition qmatrix4x4.cpp:1167
QMatrix4x4::operator/=
QMatrix4x4 & operator/=(float divisor)
This is an overloaded member function, provided for convenience. It differs from the above function o...
Definition qmatrix4x4.cpp:535
QMatrix4x4::transposed
QMatrix4x4 transposed() const
Returns this matrix, transposed about its diagonal.
Definition qmatrix4x4.cpp:492
QMatrix4x4::ortho
void ortho(const QRect &rect)
This is an overloaded member function, provided for convenience. It differs from the above function o...
Definition qmatrix4x4.cpp:1354
QMatrix4x4::toTransform
QTransform toTransform() const
Returns the conventional Qt 2D transformation matrix that corresponds to this matrix.
Definition qmatrix4x4.cpp:1649
QMatrix4x4::qFuzzyCompare
friend Q_GUI_EXPORT bool qFuzzyCompare(const QMatrix4x4 &m1, const QMatrix4x4 &m2)
Returns true if m1 and m2 are equal, allowing for a small fuzziness factor for floating-point compari...
Definition qmatrix4x4.cpp:738
QMatrix4x4::perspective
void perspective(float verticalAngle, float aspectRatio, float nearPlane, float farPlane)
Multiplies this matrix by another that applies a perspective projection.
Definition qmatrix4x4.cpp:1469
QMatrix4x4::mapRect
QRect mapRect(const QRect &rect) const
Maps rect by multiplying this matrix by the corners of rect and then forming a new rectangle from the...
Definition qmatrix4x4.cpp:1764
QMatrix4x4::inverted
QMatrix4x4 inverted(bool *invertible=nullptr) const
Returns the inverse of this matrix.
Definition qmatrix4x4.cpp:316
QMatrix4x4::determinant
double determinant() const
Returns the determinant of this matrix.
Definition qmatrix4x4.cpp:290
QMatrix4x4::viewport
void viewport(const QRectF &rect)
This is an overloaded member function, provided for convenience. It differs from the above function o...
Definition qmatrix4x4.h:1058
QMatrix4x4::optimize
void optimize()
Optimize the usage of this matrix from its current elements.
Definition qmatrix4x4.cpp:1921
QMatrix4x4::translate
void translate(const QVector3D &vector)
Multiplies this matrix by another that translates coordinates by the components of vector.
Definition qmatrix4x4.cpp:929
QPointF
\inmodule QtCore\reentrant
Definition qpoint.h:214
QPointF::x
constexpr qreal x() const noexcept
Returns the x coordinate of this point.
Definition qpoint.h:333
QPointF::y
constexpr qreal y() const noexcept
Returns the y coordinate of this point.
Definition qpoint.h:338
QPoint
\inmodule QtCore\reentrant
Definition qpoint.h:23
QPoint::x
constexpr int x() const noexcept
Returns the x coordinate of this point.
Definition qpoint.h:127
QPoint::y
constexpr int y() const noexcept
Returns the y coordinate of this point.
Definition qpoint.h:132
QQuaternion
The QQuaternion class represents a quaternion consisting of a vector and scalar.
Definition qquaternion.h:21
QQuaternion::z
float z() const
Returns the z coordinate of this quaternion's vector.
Definition qquaternion.h:158
QQuaternion::scalar
float scalar() const
Returns the scalar component of this quaternion.
Definition qquaternion.h:159
QQuaternion::x
float x() const
Returns the x coordinate of this quaternion's vector.
Definition qquaternion.h:156
QQuaternion::y
float y() const
Returns the y coordinate of this quaternion's vector.
Definition qquaternion.h:157
QRectF
\inmodule QtCore\reentrant
Definition qrect.h:483
QRect
\inmodule QtCore\reentrant
Definition qrect.h:30
QTransform
The QTransform class specifies 2D transformations of a coordinate system.
Definition qtransform.h:20
QVariant
\inmodule QtCore
Definition qvariant.h:64
QVariant::fromValue
static auto fromValue(T &&value) noexcept(std::is_nothrow_copy_constructible_v< T > &&Private::CanUseInternalSpace< T >) -> std::enable_if_t< std::conjunction_v< std::is_copy_constructible< T >, std::is_destructible< T > >, QVariant >
Definition qvariant.h:531
QVector3D
The QVector3D class represents a vector or vertex in 3D space.
Definition qvectornd.h:171
QVector3D::normalized
QVector3D normalized() const noexcept
Returns the normalized unit vector form of this vector.
Definition qvectornd.h:695
QVector3D::y
constexpr float y() const noexcept
Returns the y coordinate of this point.
Definition qvectornd.h:671
QVector3D::x
constexpr float x() const noexcept
Returns the x coordinate of this point.
Definition qvectornd.h:670
QVector3D::crossProduct
static constexpr QVector3D crossProduct(QVector3D v1, QVector3D v2) noexcept
Returns the cross-product of vectors v1 and v2, which is normal to the plane spanned by v1 and v2.
Definition qvectornd.h:775
QVector3D::normalize
void normalize() noexcept
Normalizes the current vector in place.
Definition qvectornd.h:702
QVector3D::z
constexpr float z() const noexcept
Returns the z coordinate of this point.
Definition qvectornd.h:672
j
int j
Definition doc_src_containers.cpp:273
i
i
[1]
Definition doc_src_containers.cpp:167
map
QMap< QString, QString > map
[6]
Definition doc_src_containers.cpp:94
rect
rect
[4]
Definition doc_src_styles.cpp:43
QT_BEGIN_NAMESPACE
Combined button and popup list for selecting options.
Definition qstandardpaths_haiku.cpp:21
QT_END_NAMESPACE
Definition qsharedpointer.cpp:1545
Qt::Uninitialized
constexpr Initialization Uninitialized
Definition qnamespace.h:1587
Qt::endl
QTextStream & endl(QTextStream &stream)
Writes '\n' to the stream and flushes the stream.
Definition qtextstream.cpp:2831
stream
EGLStreamKHR stream
Definition qeglstreamconvenience_p.h:67
qFuzzyIsNull
bool qFuzzyIsNull(qfloat16 f) noexcept
Definition qfloat16.h:303
qIsNull
bool qIsNull(qfloat16 f) noexcept
Definition qfloat16.h:308
qRound
int qRound(qfloat16 d) noexcept
Definition qfloat16.h:281
operator/
constexpr QMargins operator/(const QMargins &margins, int divisor)
Definition qmargins.h:189
qDegreesToRadians
constexpr float qDegreesToRadians(float degrees)
Definition qmath.h:260
matrixDet4
static double matrixDet4(const double m[4][4])
Definition qmatrix4x4.cpp:270
qFuzzyCompare
bool qFuzzyCompare(const QMatrix4x4 &m1, const QMatrix4x4 &m2)
Definition qmatrix4x4.cpp:738
copyToDoubles
static void copyToDoubles(const float m[4][4], double mm[4][4])
Definition qmatrix4x4.cpp:280
inv_dist_to_plane
static const float inv_dist_to_plane
Definition qmatrix4x4.cpp:39
operator>>
QDataStream & operator>>(QDataStream &stream, QMatrix4x4 &matrix)
Definition qmatrix4x4.cpp:2049
operator<<
QDebug operator<<(QDebug dbg, const QMatrix4x4 &m)
Definition qmatrix4x4.cpp:1983
matrixDet2
static double matrixDet2(const double m[4][4], int col0, int col1, int row0, int row1)
Definition qmatrix4x4.cpp:245
matrixDet3
static double matrixDet3(const double m[4][4], int col0, int col1, int col2, int row0, int row1, int row2)
Definition qmatrix4x4.cpp:261
qMin
constexpr const T & qMin(const T &a, const T &b)
Definition qminmax.h:40
qMax
constexpr const T & qMax(const T &a, const T &b)
Definition qminmax.h:42
values
GLenum GLsizei GLsizei GLint * values
[15]
Definition qopengles2ext.h:1032
z
GLuint GLfloat GLfloat GLfloat GLfloat GLfloat z
Definition qopengles2ext.h:2707
x
GLint GLint GLint GLint GLint x
[0]
Definition qopengles2ext.h:605
m
const GLfloat * m
Definition qopengles2ext.h:3203
w
GLfloat GLfloat GLfloat w
[0]
Definition qopengles2ext.h:789
height
GLint GLsizei GLsizei height
Definition qopengles2ext.h:206
a
GLboolean GLboolean GLboolean GLboolean a
[7]
Definition qopengles2ext.h:337
divisor
GLuint divisor
Definition qopengles2ext.h:915
top
GLdouble GLdouble GLdouble GLdouble top
Definition qopengles2ext.h:3218
right
GLdouble GLdouble right
Definition qopengles2ext.h:3218
width
GLint GLsizei width
Definition qopengles2ext.h:206
left
GLint left
Definition qopengles2ext.h:792
bottom
GLint GLint bottom
Definition qopengles2ext.h:792
angle
GLfloat angle
Definition qopengles2ext.h:3231
y
GLint y
Definition qopengles2ext.h:206
h
GLfloat GLfloat GLfloat GLfloat h
Definition qopengles2ext.h:789
transform
GLuint GLenum GLenum transform
Definition qopenglext.h:11564
w2
GLdouble GLdouble GLint GLint GLdouble GLdouble GLint GLint GLdouble GLdouble w2
Definition qopenglext.h:12395
c
const GLubyte * c
Definition qopenglext.h:12701
len
GLenum GLsizei len
Definition qopenglext.h:3292
matrix
GLuint GLenum matrix
Definition qopenglext.h:11564
bits
GLenum GLint GLenum GLsizei GLsizei GLsizei GLint GLsizei const void * bits
Definition qopenglext.h:6904
row
GLenum GLenum GLsizei void * row
Definition qopenglext.h:2747
result
GLuint64EXT * result
[6]
Definition qopenglext.h:10932
s
GLdouble s
[6]
Definition qopenglext.h:235
tr
#define tr(X)
Definition qtemporaryfile.cpp:21
qSetFieldWidth
QTextStreamManipulator qSetFieldWidth(int width)
Definition qtextstream.h:249
qreal
double qreal
Definition qtypes.h:92
vector
QList< int > vector
[14]
Definition src_concurrent_qtconcurrentmap.cpp:156
d
double d
Definition src_corelib_text_qlocale.cpp:9