summaryrefslogtreecommitdiffstats
path: root/src/gui/painting/qmatrix.cpp
blob: 0f0d4059fd4bbf076d9022cf573e9c2ab5b06220 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
/****************************************************************************
**
** Copyright (C) 2009 Nokia Corporation and/or its subsidiary(-ies).
** All rights reserved.
** Contact: Nokia Corporation (qt-info@nokia.com)
**
** This file is part of the QtGui module of the Qt Toolkit.
**
** $QT_BEGIN_LICENSE:LGPL$
** No Commercial Usage
** This file contains pre-release code and may not be distributed.
** You may use this file in accordance with the terms and conditions
** contained in the Technology Preview License Agreement accompanying
** this package.
**
** GNU Lesser General Public License Usage
** Alternatively, this file may be used under the terms of the GNU Lesser
** General Public License version 2.1 as published by the Free Software
** Foundation and appearing in the file LICENSE.LGPL included in the
** packaging of this file.  Please review the following information to
** ensure the GNU Lesser General Public License version 2.1 requirements
** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.
**
** In addition, as a special exception, Nokia gives you certain additional
** rights.  These rights are described in the Nokia Qt LGPL Exception
** version 1.1, included in the file LGPL_EXCEPTION.txt in this package.
**
** If you have questions regarding the use of this file, please contact
** Nokia at qt-info@nokia.com.
**
**
**
**
**
**
**
**
** $QT_END_LICENSE$
**
****************************************************************************/

#include "qdatastream.h"
#include "qdebug.h"
#include "qmatrix.h"
#include "qregion.h"
#include "qpainterpath.h"
#include "qvariant.h"
#include <qmath.h>

#include <limits.h>

QT_BEGIN_NAMESPACE

/*!
    \class QMatrix
    \brief The QMatrix class specifies 2D transformations of a
    coordinate system.
    \obsolete

    \ingroup painting

    A matrix specifies how to translate, scale, shear or rotate the
    coordinate system, and is typically used when rendering graphics.
    QMatrix, in contrast to QTransform, does not allow perspective
    transformations. QTransform is the recommended transformation
    class in Qt.

    A QMatrix object can be built using the setMatrix(), scale(),
    rotate(), translate() and shear() functions.  Alternatively, it
    can be built by applying \l {QMatrix#Basic Matrix
    Operations}{basic matrix operations}. The matrix can also be
    defined when constructed, and it can be reset to the identity
    matrix (the default) using the reset() function.

    The QMatrix class supports mapping of graphic primitives: A given
    point, line, polygon, region, or painter path can be mapped to the
    coordinate system defined by \e this matrix using the map()
    function. In case of a rectangle, its coordinates can be
    transformed using the mapRect() function. A rectangle can also be
    transformed into a \e polygon (mapped to the coordinate system
    defined by \e this matrix), using the mapToPolygon() function.

    QMatrix provides the isIdentity() function which returns true if
    the matrix is the identity matrix, and the isInvertible() function
    which returns true if the matrix is non-singular (i.e. AB = BA =
    I). The inverted() function returns an inverted copy of \e this
    matrix if it is invertible (otherwise it returns the identity
    matrix). In addition, QMatrix provides the det() function
    returning the matrix's determinant.

    Finally, the QMatrix class supports matrix multiplication, and
    objects of the class can be streamed as well as compared.

    \tableofcontents

    \section1 Rendering Graphics

    When rendering graphics, the matrix defines the transformations
    but the actual transformation is performed by the drawing routines
    in QPainter.

    By default, QPainter operates on the associated device's own
    coordinate system.  The standard coordinate system of a
    QPaintDevice has its origin located at the top-left position. The
    \e x values increase to the right; \e y values increase
    downward. For a complete description, see the \l {The Coordinate
    System}{coordinate system} documentation.

    QPainter has functions to translate, scale, shear and rotate the
    coordinate system without using a QMatrix. For example:

    \table 100%
    \row
    \o \inlineimage qmatrix-simpletransformation.png
    \o
    \snippet doc/src/snippets/matrix/matrix.cpp 0
    \endtable

    Although these functions are very convenient, it can be more
    efficient to build a QMatrix and call QPainter::setMatrix() if you
    want to perform more than a single transform operation. For
    example:

    \table 100%
    \row
    \o \inlineimage qmatrix-combinedtransformation.png
    \o
    \snippet doc/src/snippets/matrix/matrix.cpp 1
    \endtable

    \section1 Basic Matrix Operations

    \image qmatrix-representation.png

    A QMatrix object contains a 3 x 3 matrix.  The \c dx and \c dy
    elements specify horizontal and vertical translation. The \c m11
    and \c m22 elements specify horizontal and vertical scaling. And
    finally, the \c m21 and \c m12 elements specify horizontal and
    vertical \e shearing.

    QMatrix transforms a point in the plane to another point using the
    following formulas:

    \snippet doc/src/snippets/code/src_gui_painting_qmatrix.cpp 0

    The point \e (x, y) is the original point, and \e (x', y') is the
    transformed point. \e (x', y') can be transformed back to \e (x,
    y) by performing the same operation on the inverted() matrix.

    The various matrix elements can be set when constructing the
    matrix, or by using the setMatrix() function later on. They can also
    be manipulated using the translate(), rotate(), scale() and
    shear() convenience functions, The currently set values can be
    retrieved using the m11(), m12(), m21(), m22(), dx() and dy()
    functions.

    Translation is the simplest transformation. Setting \c dx and \c
    dy will move the coordinate system \c dx units along the X axis
    and \c dy units along the Y axis.  Scaling can be done by setting
    \c m11 and \c m22. For example, setting \c m11 to 2 and \c m22 to
    1.5 will double the height and increase the width by 50%.  The
    identity matrix has \c m11 and \c m22 set to 1 (all others are set
    to 0) mapping a point to itself. Shearing is controlled by \c m12
    and \c m21. Setting these elements to values different from zero
    will twist the coordinate system. Rotation is achieved by
    carefully setting both the shearing factors and the scaling
    factors.

    Here's the combined transformations example using basic matrix
    operations:

    \table 100%
    \row
    \o \inlineimage qmatrix-combinedtransformation.png
    \o
    \snippet doc/src/snippets/matrix/matrix.cpp 2
    \endtable

    \sa QPainter, QTransform, {The Coordinate System}, 
    {demos/affine}{Affine Transformations Demo}, {Transformations Example}
*/


// some defines to inline some code
#define MAPDOUBLE(x, y, nx, ny) \
{ \
    qreal fx = x; \
    qreal fy = y; \
    nx = _m11*fx + _m21*fy + _dx; \
    ny = _m12*fx + _m22*fy + _dy; \
}

#define MAPINT(x, y, nx, ny) \
{ \
    qreal fx = x; \
    qreal fy = y; \
    nx = qRound(_m11*fx + _m21*fy + _dx); \
    ny = qRound(_m12*fx + _m22*fy + _dy); \
}

/*****************************************************************************
  QMatrix member functions
 *****************************************************************************/
/*!
    \fn QMatrix::QMatrix(Qt::Initialization)
    \internal
*/

/*!
    Constructs an identity matrix.

    All elements are set to zero except \c m11 and \c m22 (specifying
    the scale), which are set to 1.

    \sa reset()
*/

QMatrix::QMatrix()
    : _m11(1.)
    , _m12(0.)
    , _m21(0.)
    , _m22(1.)
    , _dx(0.)
    , _dy(0.)
{
}

/*!
    Constructs a matrix with the elements, \a m11, \a m12, \a m21, \a
    m22, \a dx and \a dy.

    \sa setMatrix()
*/

QMatrix::QMatrix(qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy)
    : _m11(m11)
    , _m12(m12)
    , _m21(m21)
    , _m22(m22)
    , _dx(dx)
    , _dy(dy)
{
}


/*!
     Constructs a matrix that is a copy of the given \a matrix.
 */
QMatrix::QMatrix(const QMatrix &matrix)
    : _m11(matrix._m11)
    , _m12(matrix._m12)
    , _m21(matrix._m21)
    , _m22(matrix._m22)
    , _dx(matrix._dx)
    , _dy(matrix._dy)
{
}

/*!
    Sets the matrix elements to the specified values, \a m11, \a m12,
    \a m21, \a m22, \a dx and \a dy.

    Note that this function replaces the previous values. QMatrix
    provide the translate(), rotate(), scale() and shear() convenience
    functions to manipulate the various matrix elements based on the
    currently defined coordinate system.

    \sa QMatrix()
*/

void QMatrix::setMatrix(qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy)
{
    _m11 = m11;
    _m12 = m12;
    _m21 = m21;
    _m22 = m22;
    _dx  = dx;
    _dy  = dy;
}


/*!
    \fn qreal QMatrix::m11() const

    Returns the horizontal scaling factor.

    \sa scale(), {QMatrix#Basic Matrix Operations}{Basic Matrix
    Operations}
*/

/*!
    \fn qreal QMatrix::m12() const

    Returns the vertical shearing factor.

    \sa shear(), {QMatrix#Basic Matrix Operations}{Basic Matrix
    Operations}
*/

/*!
    \fn qreal QMatrix::m21() const

    Returns the horizontal shearing factor.

    \sa shear(), {QMatrix#Basic Matrix Operations}{Basic Matrix
    Operations}
*/

/*!
    \fn qreal QMatrix::m22() const

    Returns the vertical scaling factor.

    \sa scale(), {QMatrix#Basic Matrix Operations}{Basic Matrix
    Operations}
*/

/*!
    \fn qreal QMatrix::dx() const

    Returns the horizontal translation factor.

    \sa translate(), {QMatrix#Basic Matrix Operations}{Basic Matrix
    Operations}
*/

/*!
    \fn qreal QMatrix::dy() const

    Returns the vertical translation factor.

    \sa translate(), {QMatrix#Basic Matrix Operations}{Basic Matrix
    Operations}
*/


/*!
    Maps the given coordinates \a x and \a y into the coordinate
    system defined by this matrix. The resulting values are put in *\a
    tx and *\a ty, respectively.

    The coordinates are transformed using the following formulas:

    \snippet doc/src/snippets/code/src_gui_painting_qmatrix.cpp 1

    The point (x, y) is the original point, and (x', y') is the
    transformed point.

    \sa {QMatrix#Basic Matrix Operations}{Basic Matrix Operations}
*/

void QMatrix::map(qreal x, qreal y, qreal *tx, qreal *ty) const
{
    MAPDOUBLE(x, y, *tx, *ty);
}



/*!
    \overload

    Maps the given coordinates \a x and \a y into the coordinate
    system defined by this matrix. The resulting values are put in *\a
    tx and *\a ty, respectively. Note that the transformed coordinates
    are rounded to the nearest integer.
*/

void QMatrix::map(int x, int y, int *tx, int *ty) const
{
    MAPINT(x, y, *tx, *ty);
}

QRect QMatrix::mapRect(const QRect &rect) const
{
    QRect result;
    if (_m12 == 0.0F && _m21 == 0.0F) {
        int x = qRound(_m11*rect.x() + _dx);
        int y = qRound(_m22*rect.y() + _dy);
        int w = qRound(_m11*rect.width());
        int h = qRound(_m22*rect.height());
        if (w < 0) {
            w = -w;
            x -= w;
        }
        if (h < 0) {
            h = -h;
            y -= h;
        }
        result = QRect(x, y, w, h);
    } else {
        // see mapToPolygon for explanations of the algorithm.
        qreal x0, y0;
        qreal x, y;
        MAPDOUBLE(rect.left(), rect.top(), x0, y0);
        qreal xmin = x0;
        qreal ymin = y0;
        qreal xmax = x0;
        qreal ymax = y0;
        MAPDOUBLE(rect.right() + 1, rect.top(), x, y);
        xmin = qMin(xmin, x);
        ymin = qMin(ymin, y);
        xmax = qMax(xmax, x);
        ymax = qMax(ymax, y);
        MAPDOUBLE(rect.right() + 1, rect.bottom() + 1, x, y);
        xmin = qMin(xmin, x);
        ymin = qMin(ymin, y);
        xmax = qMax(xmax, x);
        ymax = qMax(ymax, y);
        MAPDOUBLE(rect.left(), rect.bottom() + 1, x, y);
        xmin = qMin(xmin, x);
        ymin = qMin(ymin, y);
        xmax = qMax(xmax, x);
        ymax = qMax(ymax, y);
        result = QRect(qRound(xmin), qRound(ymin), qRound(xmax)-qRound(xmin), qRound(ymax)-qRound(ymin));
    }
    return result;
}

/*!
    \fn QRectF QMatrix::mapRect(const QRectF &rectangle) const

    Creates and returns a QRectF object that is a copy of the given \a
    rectangle, mapped into the coordinate system defined by this
    matrix.

    The rectangle's coordinates are transformed using the following
    formulas:

    \snippet doc/src/snippets/code/src_gui_painting_qmatrix.cpp 2

    If rotation or shearing has been specified, this function returns
    the \e bounding rectangle. To retrieve the exact region the given
    \a rectangle maps to, use the mapToPolygon() function instead.

    \sa mapToPolygon(), {QMatrix#Basic Matrix Operations}{Basic Matrix
    Operations}
*/
QRectF QMatrix::mapRect(const QRectF &rect) const
{
    QRectF result;
    if (_m12 == 0.0F && _m21 == 0.0F) {
        qreal x = _m11*rect.x() + _dx;
        qreal y = _m22*rect.y() + _dy;
        qreal w = _m11*rect.width();
        qreal h = _m22*rect.height();
        if (w < 0) {
            w = -w;
            x -= w;
        }
        if (h < 0) {
            h = -h;
            y -= h;
        }
        result = QRectF(x, y, w, h);
    } else {
        qreal x0, y0;
        qreal x, y;
        MAPDOUBLE(rect.x(), rect.y(), x0, y0);
        qreal xmin = x0;
        qreal ymin = y0;
        qreal xmax = x0;
        qreal ymax = y0;
        MAPDOUBLE(rect.x() + rect.width(), rect.y(), x, y);
        xmin = qMin(xmin, x);
        ymin = qMin(ymin, y);
        xmax = qMax(xmax, x);
        ymax = qMax(ymax, y);
        MAPDOUBLE(rect.x() + rect.width(), rect.y() + rect.height(), x, y);
        xmin = qMin(xmin, x);
        ymin = qMin(ymin, y);
        xmax = qMax(xmax, x);
        ymax = qMax(ymax, y);
        MAPDOUBLE(rect.x(), rect.y() + rect.height(), x, y);
        xmin = qMin(xmin, x);
        ymin = qMin(ymin, y);
        xmax = qMax(xmax, x);
        ymax = qMax(ymax, y);
        result = QRectF(xmin, ymin, xmax-xmin, ymax - ymin);
    }
    return result;
}

/*!
    \fn QRect QMatrix::mapRect(const QRect &rectangle) const
    \overload

    Creates and returns a QRect object that is a copy of the given \a
    rectangle, mapped into the coordinate system defined by this
    matrix. Note that the transformed coordinates are rounded to the
    nearest integer.
*/


/*!
    \fn QPoint operator*(const QPoint &point, const QMatrix &matrix)
    \relates QMatrix

    This is the same as \a{matrix}.map(\a{point}).

    \sa QMatrix::map()
*/

QPoint QMatrix::map(const QPoint &p) const
{
    qreal fx = p.x();
    qreal fy = p.y();
    return QPoint(qRound(_m11*fx + _m21*fy + _dx),
                   qRound(_m12*fx + _m22*fy + _dy));
}

/*!
    \fn QPointF operator*(const QPointF &point, const QMatrix &matrix)
    \relates QMatrix

    Same as \a{matrix}.map(\a{point}).

    \sa QMatrix::map()
*/

/*!
    \overload

    Creates and returns a QPointF object that is a copy of the given
    \a point, mapped into the coordinate system defined by this
    matrix.
*/
QPointF QMatrix::map(const QPointF &point) const
{
    qreal fx = point.x();
    qreal fy = point.y();
    return QPointF(_m11*fx + _m21*fy + _dx, _m12*fx + _m22*fy + _dy);
}

/*!
    \fn QPoint QMatrix::map(const QPoint &point) const
    \overload

    Creates and returns a QPoint object that is a copy of the given \a
    point, mapped into the coordinate system defined by this
    matrix. Note that the transformed coordinates are rounded to the
    nearest integer.
*/

/*!
    \fn QLineF operator*(const QLineF &line, const QMatrix &matrix)
    \relates QMatrix

    This is the same as \a{matrix}.map(\a{line}).

    \sa QMatrix::map()
*/

/*!
    \fn QLine operator*(const QLine &line, const QMatrix &matrix)
    \relates QMatrix

    This is the same as \a{matrix}.map(\a{line}).

    \sa QMatrix::map()
*/

/*!
    \overload

    Creates and returns a QLineF object that is a copy of the given \a
    line, mapped into the coordinate system defined by this matrix.
*/
QLineF QMatrix::map(const QLineF &line) const
{
    return QLineF(map(line.p1()), map(line.p2()));
}

/*!
    \overload

    Creates and returns a QLine object that is a copy of the given \a
    line, mapped into the coordinate system defined by this matrix.
    Note that the transformed coordinates are rounded to the nearest
    integer.
*/
QLine QMatrix::map(const QLine &line) const
{
    return QLine(map(line.p1()), map(line.p2()));
}

/*!
    \fn QPolygonF operator *(const QPolygonF &polygon, const QMatrix &matrix)
    \relates QMatrix

    This is the same as \a{matrix}.map(\a{polygon}).

    \sa QMatrix::map()
*/

/*!
    \fn QPolygon operator*(const QPolygon &polygon, const QMatrix &matrix)
    \relates QMatrix

    This is the same as \a{matrix}.map(\a{polygon}).

    \sa QMatrix::map()
*/

QPolygon QMatrix::map(const QPolygon &a) const
{
    int size = a.size();
    int i;
    QPolygon p(size);
    const QPoint *da = a.constData();
    QPoint *dp = p.data();
    for(i = 0; i < size; i++) {
        MAPINT(da[i].x(), da[i].y(), dp[i].rx(), dp[i].ry());
    }
    return p;
}

/*!
    \fn QPolygonF QMatrix::map(const QPolygonF &polygon) const
    \overload

    Creates and returns a QPolygonF object that is a copy of the given
    \a polygon, mapped into the coordinate system defined by this
    matrix.
*/
QPolygonF QMatrix::map(const QPolygonF &a) const
{
    int size = a.size();
    int i;
    QPolygonF p(size);
    const QPointF *da = a.constData();
    QPointF *dp = p.data();
    for(i = 0; i < size; i++) {
        MAPDOUBLE(da[i].xp, da[i].yp, dp[i].xp, dp[i].yp);
    }
    return p;
}

/*!
    \fn QPolygon QMatrix::map(const QPolygon &polygon) const
    \overload

    Creates and returns a QPolygon object that is a copy of the given
    \a polygon, mapped into the coordinate system defined by this
    matrix. Note that the transformed coordinates are rounded to the
    nearest integer.
*/

/*!
    \fn QRegion operator*(const QRegion &region, const QMatrix &matrix)
    \relates QMatrix

    This is the same as \a{matrix}.map(\a{region}).

    \sa QMatrix::map()
*/

extern QPainterPath qt_regionToPath(const QRegion &region);

/*!
    \fn QRegion QMatrix::map(const QRegion &region) const
    \overload

    Creates and returns a QRegion object that is a copy of the given
    \a region, mapped into the coordinate system defined by this matrix.

    Calling this method can be rather expensive if rotations or
    shearing are used.
*/
QRegion QMatrix::map(const QRegion &r) const
{
    if (_m11 == 1.0 && _m22 == 1.0 && _m12 == 0.0 && _m21 == 0.0) { // translate or identity
        if (_dx == 0.0 && _dy == 0.0) // Identity
            return r;
        QRegion copy(r);
        copy.translate(qRound(_dx), qRound(_dy));
        return copy;
    }

    QPainterPath p = map(qt_regionToPath(r));
    return p.toFillPolygon().toPolygon();
}

/*!
    \fn QPainterPath operator *(const QPainterPath &path, const QMatrix &matrix)
    \relates QMatrix

    This is the same as \a{matrix}.map(\a{path}).

    \sa QMatrix::map()
*/

/*!
    \overload

    Creates and returns a QPainterPath object that is a copy of the
    given \a path, mapped into the coordinate system defined by this
    matrix.
*/
QPainterPath QMatrix::map(const QPainterPath &path) const
{
    if (path.isEmpty())
        return QPainterPath();

    QPainterPath copy = path;

    // Translate or identity
    if (_m11 == 1.0 && _m22 == 1.0 && _m12 == 0.0 && _m21 == 0.0) {

        // Translate
        if (_dx != 0.0 || _dy != 0.0) {
            copy.detach();
            for (int i=0; i<path.elementCount(); ++i) {
                QPainterPath::Element &e = copy.d_ptr->elements[i];
                e.x += _dx;
                e.y += _dy;
            }
        }

    // Full xform
    } else {
        copy.detach();
        for (int i=0; i<path.elementCount(); ++i) {
            QPainterPath::Element &e = copy.d_ptr->elements[i];
            qreal fx = e.x, fy = e.y;
            e.x = _m11*fx + _m21*fy + _dx;
            e.y =  _m12*fx + _m22*fy + _dy;
        }
    }

    return copy;
}

/*!
    \fn QRegion QMatrix::mapToRegion(const QRect &rectangle) const

    Returns the transformed rectangle \a rectangle as a QRegion
    object. A rectangle which has been rotated or sheared may result
    in a non-rectangular region being returned.

    Use the mapToPolygon() or map() function instead.
*/
#ifdef QT3_SUPPORT
QRegion QMatrix::mapToRegion(const QRect &rect) const
{
    QRegion result;
    if (isIdentity()) {
        result = rect;
    } else if (m12() == 0.0F && m21() == 0.0F) {
        int x = qRound(m11()*rect.x() + dx());
        int y = qRound(m22()*rect.y() + dy());
        int w = qRound(m11()*rect.width());
        int h = qRound(m22()*rect.height());
        if (w < 0) {
            w = -w;
            x -= w - 1;
        }
        if (h < 0) {
            h = -h;
            y -= h - 1;
        }
        result = QRect(x, y, w, h);
    } else {
        result = QRegion(mapToPolygon(rect));
    }
    return result;

}
#endif
/*!
    \fn QPolygon QMatrix::mapToPolygon(const QRect &rectangle) const

    Creates and returns a QPolygon representation of the given \a
    rectangle, mapped into the coordinate system defined by this
    matrix.

    The rectangle's coordinates are transformed using the following
    formulas:

    \snippet doc/src/snippets/code/src_gui_painting_qmatrix.cpp 3

    Polygons and rectangles behave slightly differently when
    transformed (due to integer rounding), so
    \c{matrix.map(QPolygon(rectangle))} is not always the same as
    \c{matrix.mapToPolygon(rectangle)}.

    \sa mapRect(), {QMatrix#Basic Matrix Operations}{Basic Matrix
    Operations}
*/
QPolygon QMatrix::mapToPolygon(const QRect &rect) const
{
    QPolygon a(4);
    qreal x[4], y[4];
    if (_m12 == 0.0F && _m21 == 0.0F) {
        x[0] = _m11*rect.x() + _dx;
        y[0] = _m22*rect.y() + _dy;
        qreal w = _m11*rect.width();
        qreal h = _m22*rect.height();
        if (w < 0) {
            w = -w;
            x[0] -= w;
        }
        if (h < 0) {
            h = -h;
            y[0] -= h;
        }
        x[1] = x[0]+w;
        x[2] = x[1];
        x[3] = x[0];
        y[1] = y[0];
        y[2] = y[0]+h;
        y[3] = y[2];
    } else {
        qreal right = rect.x() + rect.width();
        qreal bottom = rect.y() + rect.height();
        MAPDOUBLE(rect.x(), rect.y(), x[0], y[0]);
        MAPDOUBLE(right, rect.y(), x[1], y[1]);
        MAPDOUBLE(right, bottom, x[2], y[2]);
        MAPDOUBLE(rect.x(), bottom, x[3], y[3]);
    }
#if 0
    int i;
    for(i = 0; i< 4; i++)
        qDebug("coords(%d) = (%f/%f) (%d/%d)", i, x[i], y[i], qRound(x[i]), qRound(y[i]));
    qDebug("width=%f, height=%f", qSqrt((x[1]-x[0])*(x[1]-x[0]) + (y[1]-y[0])*(y[1]-y[0])),
            qSqrt((x[0]-x[3])*(x[0]-x[3]) + (y[0]-y[3])*(y[0]-y[3])));
#endif
    // all coordinates are correctly, tranform to a pointarray
    // (rounding to the next integer)
    a.setPoints(4, qRound(x[0]), qRound(y[0]),
                 qRound(x[1]), qRound(y[1]),
                 qRound(x[2]), qRound(y[2]),
                 qRound(x[3]), qRound(y[3]));
    return a;
}

/*!
    Resets the matrix to an identity matrix, i.e. all elements are set
    to zero, except \c m11 and \c m22 (specifying the scale) which are
    set to 1.

    \sa QMatrix(), isIdentity(), {QMatrix#Basic Matrix
    Operations}{Basic Matrix Operations}
*/

void QMatrix::reset()
{
    _m11 = _m22 = 1.0;
    _m12 = _m21 = _dx = _dy = 0.0;
}

/*!
    \fn bool QMatrix::isIdentity() const

    Returns true if the matrix is the identity matrix, otherwise
    returns false.

    \sa reset()
*/

/*!
    Moves the coordinate system \a dx along the x axis and \a dy along
    the y axis, and returns a reference to the matrix.

    \sa setMatrix()
*/

QMatrix &QMatrix::translate(qreal dx, qreal dy)
{
    _dx += dx*_m11 + dy*_m21;
    _dy += dy*_m22 + dx*_m12;
    return *this;
}

/*!
    \fn QMatrix &QMatrix::scale(qreal sx, qreal sy)

    Scales the coordinate system by \a sx horizontally and \a sy
    vertically, and returns a reference to the matrix.

    \sa setMatrix()
*/

QMatrix &QMatrix::scale(qreal sx, qreal sy)
{
    _m11 *= sx;
    _m12 *= sx;
    _m21 *= sy;
    _m22 *= sy;
    return *this;
}

/*!
    Shears the coordinate system by \a sh horizontally and \a sv
    vertically, and returns a reference to the matrix.

    \sa setMatrix()
*/

QMatrix &QMatrix::shear(qreal sh, qreal sv)
{
    qreal tm11 = sv*_m21;
    qreal tm12 = sv*_m22;
    qreal tm21 = sh*_m11;
    qreal tm22 = sh*_m12;
    _m11 += tm11;
    _m12 += tm12;
    _m21 += tm21;
    _m22 += tm22;
    return *this;
}

const qreal deg2rad = qreal(0.017453292519943295769);        // pi/180

/*!
    \fn QMatrix &QMatrix::rotate(qreal degrees)

    Rotates the coordinate system the given \a degrees
    counterclockwise.

    Note that if you apply a QMatrix to a point defined in widget
    coordinates, the direction of the rotation will be clockwise
    because the y-axis points downwards.

    Returns a reference to the matrix.

    \sa setMatrix()
*/

QMatrix &QMatrix::rotate(qreal a)
{
    qreal sina = 0;
    qreal cosa = 0;
    if (a == 90. || a == -270.)
        sina = 1.;
    else if (a == 270. || a == -90.)
        sina = -1.;
    else if (a == 180.)
        cosa = -1.;
    else{
        qreal b = deg2rad*a;                        // convert to radians
        sina = qSin(b);               // fast and convenient
        cosa = qCos(b);
    }
    qreal tm11 = cosa*_m11 + sina*_m21;
    qreal tm12 = cosa*_m12 + sina*_m22;
    qreal tm21 = -sina*_m11 + cosa*_m21;
    qreal tm22 = -sina*_m12 + cosa*_m22;
    _m11 = tm11; _m12 = tm12;
    _m21 = tm21; _m22 = tm22;
    return *this;
}

/*!
    \fn bool QMatrix::isInvertible() const

    Returns true if the matrix is invertible, otherwise returns false.

    \sa inverted()
*/

/*!
    \fn qreal QMatrix::det() const

    Returns the matrix's determinant.
*/

/*!
    \fn QMatrix QMatrix::invert(bool *invertible) const

    Returns an inverted copy of this matrix.

    Use the inverted() function instead.
*/

/*!
    Returns an inverted copy of this matrix.

    If the matrix is singular (not invertible), the returned matrix is
    the identity matrix. If \a invertible is valid (i.e. not 0), its
    value is set to true if the matrix is invertible, otherwise it is
    set to false.

    \sa isInvertible()
*/

QMatrix QMatrix::inverted(bool *invertible) const
{
    qreal determinant = det();
    if (determinant == 0.0) {
        if (invertible)
            *invertible = false;                // singular matrix
        return QMatrix(true);
    }
    else {                                        // invertible matrix
        if (invertible)
            *invertible = true;
        qreal dinv = 1.0/determinant;
        return QMatrix((_m22*dinv),        (-_m12*dinv),
                       (-_m21*dinv), (_m11*dinv),
                       ((_m21*_dy - _m22*_dx)*dinv),
                       ((_m12*_dx - _m11*_dy)*dinv),
                       true);
    }
}


/*!
    \fn bool QMatrix::operator==(const QMatrix &matrix) const

    Returns true if this matrix is equal to the given \a matrix,
    otherwise returns false.
*/

bool QMatrix::operator==(const QMatrix &m) const
{
    return _m11 == m._m11 &&
           _m12 == m._m12 &&
           _m21 == m._m21 &&
           _m22 == m._m22 &&
           _dx == m._dx &&
           _dy == m._dy;
}

/*!
    \fn bool QMatrix::operator!=(const QMatrix &matrix) const

    Returns true if this matrix is not equal to the given \a matrix,
    otherwise returns false.
*/

bool QMatrix::operator!=(const QMatrix &m) const
{
    return _m11 != m._m11 ||
           _m12 != m._m12 ||
           _m21 != m._m21 ||
           _m22 != m._m22 ||
           _dx != m._dx ||
           _dy != m._dy;
}

/*!
    \fn QMatrix &QMatrix::operator *=(const QMatrix &matrix)
    \overload

    Returns the result of multiplying this matrix by the given \a
    matrix.
*/

QMatrix &QMatrix::operator *=(const QMatrix &m)
{
    qreal tm11 = _m11*m._m11 + _m12*m._m21;
    qreal tm12 = _m11*m._m12 + _m12*m._m22;
    qreal tm21 = _m21*m._m11 + _m22*m._m21;
    qreal tm22 = _m21*m._m12 + _m22*m._m22;

    qreal tdx  = _dx*m._m11  + _dy*m._m21 + m._dx;
    qreal tdy =  _dx*m._m12  + _dy*m._m22 + m._dy;

    _m11 = tm11; _m12 = tm12;
    _m21 = tm21; _m22 = tm22;
    _dx = tdx; _dy = tdy;
    return *this;
}

/*!
    \fn QMatrix QMatrix::operator *(const QMatrix &matrix) const

    Returns the result of multiplying this matrix by the given \a
    matrix.

    Note that matrix multiplication is not commutative, i.e. a*b !=
    b*a.
*/

QMatrix QMatrix::operator *(const QMatrix &m) const
{
    qreal tm11 = _m11*m._m11 + _m12*m._m21;
    qreal tm12 = _m11*m._m12 + _m12*m._m22;
    qreal tm21 = _m21*m._m11 + _m22*m._m21;
    qreal tm22 = _m21*m._m12 + _m22*m._m22;

    qreal tdx  = _dx*m._m11  + _dy*m._m21 + m._dx;
    qreal tdy =  _dx*m._m12  + _dy*m._m22 + m._dy;
    return QMatrix(tm11, tm12, tm21, tm22, tdx, tdy, true);
}

/*!
    Assigns the given \a matrix's values to this matrix.
*/
QMatrix &QMatrix::operator=(const QMatrix &matrix)
{
    _m11 = matrix._m11;
    _m12 = matrix._m12;
    _m21 = matrix._m21;
    _m22 = matrix._m22;
    _dx  = matrix._dx;
    _dy  = matrix._dy;
    return *this;
}

/*!
    \since 4.2

    Returns the matrix as a QVariant.
*/
QMatrix::operator QVariant() const
{
    return QVariant(QVariant::Matrix, this);
}

Q_GUI_EXPORT QPainterPath operator *(const QPainterPath &p, const QMatrix &m)
{
    return m.map(p);
}


/*****************************************************************************
  QMatrix stream functions
 *****************************************************************************/
#ifndef QT_NO_DATASTREAM
/*!
    \fn QDataStream &operator<<(QDataStream &stream, const QMatrix &matrix)
    \relates QMatrix

    Writes the given \a matrix to the given \a stream and returns a
    reference to the stream.

    \sa {Format of the QDataStream Operators}
*/

QDataStream &operator<<(QDataStream &s, const QMatrix &m)
{
    if (s.version() == 1) {
        s << (float)m.m11() << (float)m.m12() << (float)m.m21()
          << (float)m.m22() << (float)m.dx()  << (float)m.dy();
    } else {
        s << double(m.m11())
          << double(m.m12())
          << double(m.m21())
          << double(m.m22())
          << double(m.dx())
          << double(m.dy());
    }
    return s;
}

/*!
    \fn QDataStream &operator>>(QDataStream &stream, QMatrix &matrix)
    \relates QMatrix

    Reads the given \a matrix from the given \a stream and returns a
    reference to the stream.

    \sa {Format of the QDataStream Operators}
*/

QDataStream &operator>>(QDataStream &s, QMatrix &m)
{
    if (s.version() == 1) {
        float m11, m12, m21, m22, dx, dy;
        s >> m11;  s >> m12;  s >> m21;  s >> m22;
        s >> dx;   s >> dy;
        m.setMatrix(m11, m12, m21, m22, dx, dy);
    }
    else {
        double m11, m12, m21, m22, dx, dy;
        s >> m11;
        s >> m12;
        s >> m21;
        s >> m22;
        s >> dx;
        s >> dy;
        m.setMatrix(m11, m12, m21, m22, dx, dy);
    }
    return s;
}
#endif // QT_NO_DATASTREAM

#ifndef QT_NO_DEBUG_STREAM
QDebug operator<<(QDebug dbg, const QMatrix &m)
{
    dbg.nospace() << "QMatrix("
                  << "11=" << m.m11()
                  << " 12=" << m.m12()
                  << " 21=" << m.m21()
                  << " 22=" << m.m22()
                  << " dx=" << m.dx()
                  << " dy=" << m.dy()
                  << ')';
    return dbg.space();
}
#endif

/*!
    \fn QRect QMatrix::map(const QRect &rect) const
    \compat

    Creates and returns a QRect object that is a copy of the given
    rectangle, mapped into the coordinate system defined by this
    matrix.

    Use the mapRect() function instead.
*/


/*!
    \fn bool qFuzzyCompare(const QMatrix& m1, const QMatrix& m2)

    \relates QMatrix
    \since 4.6

    Returns true if \a m1 and \a m2 are equal, allowing for a small
    fuzziness factor for floating-point comparisons; false otherwise.
*/

QT_END_NAMESPACE