summaryrefslogtreecommitdiffstats
path: root/src/gui/painting/qstroker.cpp
blob: 90639458be2870a33af89c1d1bb45bf199e09821 (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
/****************************************************************************
**
** 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 "private/qstroker_p.h"
#include "private/qbezier_p.h"
#include "private/qmath_p.h"
#include "qline.h"
#include "qtransform.h"
#include <qmath.h>

QT_BEGIN_NAMESPACE

// #define QPP_STROKE_DEBUG

class QSubpathForwardIterator
{
public:
    QSubpathForwardIterator(const QDataBuffer<QStrokerOps::Element> *path)
        : m_path(path), m_pos(0) { }
    inline int position() const { return m_pos; }
    inline bool hasNext() const { return m_pos < m_path->size(); }
    inline QStrokerOps::Element next() { Q_ASSERT(hasNext()); return m_path->at(m_pos++); }

private:
    const QDataBuffer<QStrokerOps::Element> *m_path;
    int m_pos;
};

class QSubpathBackwardIterator
{
public:
    QSubpathBackwardIterator(const QDataBuffer<QStrokerOps::Element> *path)
        : m_path(path), m_pos(path->size() - 1) { }

    inline int position() const { return m_pos; }

    inline bool hasNext() const { return m_pos >= 0; }

    inline QStrokerOps::Element next()
    {
        Q_ASSERT(hasNext());

        QStrokerOps::Element ce = m_path->at(m_pos);   // current element

        if (m_pos == m_path->size() - 1) {
            --m_pos;
            ce.type = QPainterPath::MoveToElement;
            return ce;
        }

        const QStrokerOps::Element &pe = m_path->at(m_pos + 1); // previous element

        switch (pe.type) {
        case QPainterPath::LineToElement:
            ce.type = QPainterPath::LineToElement;
            break;
        case QPainterPath::CurveToDataElement:
            // First control point?
            if (ce.type == QPainterPath::CurveToElement) {
                ce.type = QPainterPath::CurveToDataElement;
            } else { // Second control point then
                ce.type = QPainterPath::CurveToElement;
            }
            break;
        case QPainterPath::CurveToElement:
            ce.type = QPainterPath::CurveToDataElement;
            break;
        default:
            qWarning("QSubpathReverseIterator::next: Case %d unhandled", ce.type);
            break;
        }
        --m_pos;

        return ce;
    }

private:
    const QDataBuffer<QStrokerOps::Element> *m_path;
    int m_pos;
};

class QSubpathFlatIterator
{
public:
    QSubpathFlatIterator(const QDataBuffer<QStrokerOps::Element> *path)
        : m_path(path), m_pos(0), m_curve_index(-1) { }

    inline bool hasNext() const { return m_curve_index >= 0 || m_pos < m_path->size(); }

    QStrokerOps::Element next()
    {
        Q_ASSERT(hasNext());

        if (m_curve_index >= 0) {
            QStrokerOps::Element e = { QPainterPath::LineToElement,
                                       qt_real_to_fixed(m_curve.at(m_curve_index).x()),
                                       qt_real_to_fixed(m_curve.at(m_curve_index).y())
                                       };
            ++m_curve_index;
            if (m_curve_index >= m_curve.size())
                m_curve_index = -1;
            return e;
        }

        QStrokerOps::Element e = m_path->at(m_pos);
        if (e.isCurveTo()) {
            Q_ASSERT(m_pos > 0);
            Q_ASSERT(m_pos < m_path->size());

            m_curve = QBezier::fromPoints(QPointF(qt_fixed_to_real(m_path->at(m_pos-1).x),
                                                  qt_fixed_to_real(m_path->at(m_pos-1).y)),
                                          QPointF(qt_fixed_to_real(e.x),
                                                  qt_fixed_to_real(e.y)),
                                          QPointF(qt_fixed_to_real(m_path->at(m_pos+1).x),
                                                  qt_fixed_to_real(m_path->at(m_pos+1).y)),
                                          QPointF(qt_fixed_to_real(m_path->at(m_pos+2).x),
                                                  qt_fixed_to_real(m_path->at(m_pos+2).y))).toPolygon();
            m_curve_index = 1;
            e.type = QPainterPath::LineToElement;
            e.x = m_curve.at(0).x();
            e.y = m_curve.at(0).y();
            m_pos += 2;
        }
        Q_ASSERT(e.isLineTo() || e.isMoveTo());
        ++m_pos;
        return e;
    }

private:
    const QDataBuffer<QStrokerOps::Element> *m_path;
    int m_pos;
    QPolygonF m_curve;
    int m_curve_index;
};

template <class Iterator> bool qt_stroke_side(Iterator *it, QStroker *stroker,
                                              bool capFirst, QLineF *startTangent);

/*******************************************************************************
 * QLineF::angle gives us the smalles angle between two lines. Here we
 * want to identify the line's angle direction on the unit circle.
 */
static inline qreal adapted_angle_on_x(const QLineF &line)
{
    qreal angle = line.angle(QLineF(0, 0, 1, 0));
    if (line.dy() > 0)
        angle = 360 - angle;
    return angle;
}

QStrokerOps::QStrokerOps()
    : m_customData(0), m_moveTo(0), m_lineTo(0), m_cubicTo(0)
{
}

QStrokerOps::~QStrokerOps()
{
}


/*!
    Prepares the stroker. Call this function once before starting a
    stroke by calling moveTo, lineTo or cubicTo.

    The \a customData is passed back through that callback functions
    and can be used by the user to for instance maintain state
    information.
*/
void QStrokerOps::begin(void *customData)
{
    m_customData = customData;
    m_elements.reset();
}


/*!
    Finishes the stroke. Call this function once when an entire
    primitive has been stroked.
*/
void QStrokerOps::end()
{
    if (m_elements.size() > 1)
        processCurrentSubpath();
    m_customData = 0;
}

/*!
    Convenience function that decomposes \a path into begin(),
    moveTo(), lineTo(), curevTo() and end() calls.

    The \a customData parameter is used in the callback functions

    The \a matrix is used to transform the points before input to the
    stroker.

    \sa begin()
*/
void QStrokerOps::strokePath(const QPainterPath &path, void *customData, const QTransform &matrix)
{
    if (path.isEmpty())
        return;

    begin(customData);
    int count = path.elementCount();
    if (matrix.isIdentity()) {
        for (int i=0; i<count; ++i) {
            const QPainterPath::Element &e = path.elementAt(i);
            switch (e.type) {
            case QPainterPath::MoveToElement:
                moveTo(qt_real_to_fixed(e.x), qt_real_to_fixed(e.y));
                break;
            case QPainterPath::LineToElement:
                lineTo(qt_real_to_fixed(e.x), qt_real_to_fixed(e.y));
                break;
            case QPainterPath::CurveToElement:
                {
                    const QPainterPath::Element &cp2 = path.elementAt(++i);
                    const QPainterPath::Element &ep = path.elementAt(++i);
                    cubicTo(qt_real_to_fixed(e.x), qt_real_to_fixed(e.y),
                            qt_real_to_fixed(cp2.x), qt_real_to_fixed(cp2.y),
                            qt_real_to_fixed(ep.x), qt_real_to_fixed(ep.y));
                }
                break;
            default:
                break;
            }
        }
    } else {
        for (int i=0; i<count; ++i) {
            const QPainterPath::Element &e = path.elementAt(i);
            QPointF pt = QPointF(e.x, e.y) * matrix;
            switch (e.type) {
            case QPainterPath::MoveToElement:
                moveTo(qt_real_to_fixed(pt.x()), qt_real_to_fixed(pt.y()));
                break;
            case QPainterPath::LineToElement:
                lineTo(qt_real_to_fixed(pt.x()), qt_real_to_fixed(pt.y()));
                break;
            case QPainterPath::CurveToElement:
                {
                    QPointF cp2 = ((QPointF) path.elementAt(++i)) * matrix;
                    QPointF ep = ((QPointF) path.elementAt(++i)) * matrix;
                    cubicTo(qt_real_to_fixed(pt.x()), qt_real_to_fixed(pt.y()),
                            qt_real_to_fixed(cp2.x()), qt_real_to_fixed(cp2.y()),
                            qt_real_to_fixed(ep.x()), qt_real_to_fixed(ep.y()));
                }
                break;
            default:
                break;
            }
        }
    }
    end();
}

/*!
    Convenience function for stroking a polygon of the \a pointCount
    first points in \a points. If \a implicit_close is set to true a
    line is implictly drawn between the first and last point in the
    polygon. Typically true for polygons and false for polylines.

    The \a matrix is used to transform the points before they enter the
    stroker.

    \sa begin()
*/

void QStrokerOps::strokePolygon(const QPointF *points, int pointCount, bool implicit_close,
                                void *data, const QTransform &matrix)
{
    if (!pointCount)
        return;
    begin(data);
    if (matrix.isIdentity()) {
        moveTo(qt_real_to_fixed(points[0].x()), qt_real_to_fixed(points[0].y()));
        for (int i=1; i<pointCount; ++i)
            lineTo(qt_real_to_fixed(points[i].x()),
                   qt_real_to_fixed(points[i].y()));
        if (implicit_close)
            lineTo(qt_real_to_fixed(points[0].x()), qt_real_to_fixed(points[0].y()));
    } else {
        QPointF start = points[0] * matrix;
        moveTo(qt_real_to_fixed(start.x()), qt_real_to_fixed(start.y()));
        for (int i=1; i<pointCount; ++i) {
            QPointF pt = points[i] * matrix;
            lineTo(qt_real_to_fixed(pt.x()), qt_real_to_fixed(pt.y()));
        }
        if (implicit_close)
            lineTo(qt_real_to_fixed(start.x()), qt_real_to_fixed(start.y()));
    }
    end();
}

/*!
    Convenience function for stroking an ellipse with bounding rect \a
    rect. The \a matrix is used to transform the coordinates before
    they enter the stroker.
*/
void QStrokerOps::strokeEllipse(const QRectF &rect, void *data, const QTransform &matrix)
{
    int count = 0;
    QPointF pts[12];
    QPointF start = qt_curves_for_arc(rect, 0, -360, pts, &count);
    Q_ASSERT(count == 12); // a perfect circle..

    if (!matrix.isIdentity()) {
        start = start * matrix;
        for (int i=0; i<12; ++i) {
            pts[i] = pts[i] * matrix;
        }
    }

    begin(data);
    moveTo(qt_real_to_fixed(start.x()), qt_real_to_fixed(start.y()));
    for (int i=0; i<12; i+=3) {
        cubicTo(qt_real_to_fixed(pts[i].x()), qt_real_to_fixed(pts[i].y()),
                qt_real_to_fixed(pts[i+1].x()), qt_real_to_fixed(pts[i+1].y()),
                qt_real_to_fixed(pts[i+2].x()), qt_real_to_fixed(pts[i+2].y()));
    }
    end();
}


QStroker::QStroker()
    : m_capStyle(SquareJoin), m_joinStyle(FlatJoin),
      m_back1X(0), m_back1Y(0),
      m_back2X(0), m_back2Y(0)
{
    m_strokeWidth = qt_real_to_fixed(1);
    m_miterLimit = qt_real_to_fixed(2);
    m_curveThreshold = qt_real_to_fixed(0.25);
}

QStroker::~QStroker()
{

}

Qt::PenCapStyle QStroker::capForJoinMode(LineJoinMode mode)
{
    if (mode == FlatJoin) return Qt::FlatCap;
    else if (mode == SquareJoin) return Qt::SquareCap;
    else return Qt::RoundCap;
}

QStroker::LineJoinMode QStroker::joinModeForCap(Qt::PenCapStyle style)
{
    if (style == Qt::FlatCap) return FlatJoin;
    else if (style == Qt::SquareCap) return SquareJoin;
    else return RoundCap;
}

Qt::PenJoinStyle QStroker::joinForJoinMode(LineJoinMode mode)
{
    if (mode == FlatJoin) return Qt::BevelJoin;
    else if (mode == MiterJoin) return Qt::MiterJoin;
    else if (mode == SvgMiterJoin) return Qt::SvgMiterJoin;
    else return Qt::RoundJoin;
}

QStroker::LineJoinMode QStroker::joinModeForJoin(Qt::PenJoinStyle joinStyle)
{
    if (joinStyle == Qt::BevelJoin) return FlatJoin;
    else if (joinStyle == Qt::MiterJoin) return MiterJoin;
    else if (joinStyle == Qt::SvgMiterJoin) return SvgMiterJoin;
    else return RoundJoin;
}


/*!
    This function is called to stroke the currently built up
    subpath. The subpath is cleared when the function completes.
*/
void QStroker::processCurrentSubpath()
{
    Q_ASSERT(!m_elements.isEmpty());
    Q_ASSERT(m_elements.first().type == QPainterPath::MoveToElement);
    Q_ASSERT(m_elements.size() > 1);

    QSubpathForwardIterator fwit(&m_elements);
    QSubpathBackwardIterator bwit(&m_elements);

    QLineF fwStartTangent, bwStartTangent;

    bool fwclosed = qt_stroke_side(&fwit, this, false, &fwStartTangent);
    bool bwclosed = qt_stroke_side(&bwit, this, !fwclosed, &bwStartTangent);

    if (!bwclosed)
        joinPoints(m_elements.at(0).x, m_elements.at(0).y, fwStartTangent, m_capStyle);
}


/*!
    \internal
*/
void QStroker::joinPoints(qfixed focal_x, qfixed focal_y, const QLineF &nextLine, LineJoinMode join)
{
#ifdef QPP_STROKE_DEBUG
    printf(" -----> joinPoints: around=(%.0f, %.0f), next_p1=(%.0f, %.f) next_p2=(%.0f, %.f)\n",
           qt_fixed_to_real(focal_x),
           qt_fixed_to_real(focal_y),
           nextLine.x1(), nextLine.y1(), nextLine.x2(), nextLine.y2());
#endif
    // points connected already, don't join

#if !defined (QFIXED_26_6) && !defined (Q_FIXED_32_32)
    if (qFuzzyCompare(m_back1X, nextLine.x1()) && qFuzzyCompare(m_back1Y, nextLine.y1()))
        return;
#else
    if (m_back1X == qt_real_to_fixed(nextLine.x1())
        && m_back1Y == qt_real_to_fixed(nextLine.y1())) {
        return;
    }
#endif

    if (join == FlatJoin) {
        emitLineTo(qt_real_to_fixed(nextLine.x1()),
                   qt_real_to_fixed(nextLine.y1()));

    } else {
        QLineF prevLine(qt_fixed_to_real(m_back2X), qt_fixed_to_real(m_back2Y),
                        qt_fixed_to_real(m_back1X), qt_fixed_to_real(m_back1Y));

        QPointF isect;
        QLineF::IntersectType type = prevLine.intersect(nextLine, &isect);

        if (join == MiterJoin) {
            qreal appliedMiterLimit = qt_fixed_to_real(m_strokeWidth * m_miterLimit);

            // If we are on the inside, do the short cut...
            QLineF shortCut(prevLine.p2(), nextLine.p1());
            qreal angle = shortCut.angleTo(prevLine);

            if (type == QLineF::BoundedIntersection || (angle > 90 && !qFuzzyCompare(angle, (qreal)90))) {
                emitLineTo(qt_real_to_fixed(nextLine.x1()), qt_real_to_fixed(nextLine.y1()));
                return;
            }
            QLineF miterLine(QPointF(qt_fixed_to_real(m_back1X),
                                     qt_fixed_to_real(m_back1Y)), isect);
            if (type == QLineF::NoIntersection || miterLine.length() > appliedMiterLimit) {
                QLineF l1(prevLine);
                l1.setLength(appliedMiterLimit);
                l1.translate(prevLine.dx(), prevLine.dy());

                QLineF l2(nextLine);
                l2.setLength(appliedMiterLimit);
                l2.translate(-l2.dx(), -l2.dy());

                emitLineTo(qt_real_to_fixed(l1.x2()), qt_real_to_fixed(l1.y2()));
                emitLineTo(qt_real_to_fixed(l2.x1()), qt_real_to_fixed(l2.y1()));
                emitLineTo(qt_real_to_fixed(nextLine.x1()), qt_real_to_fixed(nextLine.y1()));
            } else {
                emitLineTo(qt_real_to_fixed(isect.x()), qt_real_to_fixed(isect.y()));
                emitLineTo(qt_real_to_fixed(nextLine.x1()), qt_real_to_fixed(nextLine.y1()));
            }

        } else if (join == SquareJoin) {
            qfixed offset = m_strokeWidth / 2;

            QLineF l1(prevLine);
            l1.translate(l1.dx(), l1.dy());
            l1.setLength(qt_fixed_to_real(offset));
            QLineF l2(nextLine.p2(), nextLine.p1());
            l2.translate(l2.dx(), l2.dy());
            l2.setLength(qt_fixed_to_real(offset));
            emitLineTo(qt_real_to_fixed(l1.x2()), qt_real_to_fixed(l1.y2()));
            emitLineTo(qt_real_to_fixed(l2.x2()), qt_real_to_fixed(l2.y2()));
            emitLineTo(qt_real_to_fixed(l2.x1()), qt_real_to_fixed(l2.y1()));

        } else if (join == RoundJoin) {
            qfixed offset = m_strokeWidth / 2;

            QLineF shortCut(prevLine.p2(), nextLine.p1());
            qreal angle = prevLine.angle(shortCut);
            if (type == QLineF::BoundedIntersection || (angle > 90 && !qFuzzyCompare(angle, (qreal)90))) {
                emitLineTo(qt_real_to_fixed(nextLine.x1()), qt_real_to_fixed(nextLine.y1()));
                return;
            }
            qreal l1_on_x = adapted_angle_on_x(prevLine);
            qreal l2_on_x = adapted_angle_on_x(nextLine);

            qreal sweepLength = qAbs(l2_on_x - l1_on_x);

            int point_count;
            QPointF curves[15];

            QPointF curve_start =
                qt_curves_for_arc(QRectF(qt_fixed_to_real(focal_x - offset),
                                         qt_fixed_to_real(focal_y - offset),
                                         qt_fixed_to_real(offset * 2),
                                         qt_fixed_to_real(offset * 2)),
                                  l1_on_x + 90, -sweepLength,
                                  curves, &point_count);

//             // line to the beginning of the arc segment, (should not be needed).
//             emitLineTo(qt_real_to_fixed(curve_start.x()), qt_real_to_fixed(curve_start.y()));

            for (int i=0; i<point_count; i+=3) {
                emitCubicTo(qt_real_to_fixed(curves[i].x()),
                            qt_real_to_fixed(curves[i].y()),
                            qt_real_to_fixed(curves[i+1].x()),
                            qt_real_to_fixed(curves[i+1].y()),
                            qt_real_to_fixed(curves[i+2].x()),
                            qt_real_to_fixed(curves[i+2].y()));
            }

            // line to the end of the arc segment, (should also not be needed).
            emitLineTo(qt_real_to_fixed(nextLine.x1()), qt_real_to_fixed(nextLine.y1()));

        // Same as round join except we know its 180 degrees. Can also optimize this
        // later based on the addEllipse logic
        } else if (join == RoundCap) {
            qfixed offset = m_strokeWidth / 2;

            // first control line
            QLineF l1 = prevLine;
            l1.translate(l1.dx(), l1.dy());
            l1.setLength(QT_PATH_KAPPA * offset);

            // second control line, find through normal between prevLine and focal.
            QLineF l2(qt_fixed_to_real(focal_x), qt_fixed_to_real(focal_y),
                      prevLine.x2(), prevLine.y2());
            l2.translate(-l2.dy(), l2.dx());
            l2.setLength(QT_PATH_KAPPA * offset);

            emitCubicTo(qt_real_to_fixed(l1.x2()),
                        qt_real_to_fixed(l1.y2()),
                        qt_real_to_fixed(l2.x2()),
                        qt_real_to_fixed(l2.y2()),
                        qt_real_to_fixed(l2.x1()),
                        qt_real_to_fixed(l2.y1()));

            // move so that it matches
            l2 = QLineF(l2.x1(), l2.y1(), l2.x1()-l2.dx(), l2.y1()-l2.dy());

            // last line is parallel to l1 so just shift it down.
            l1.translate(nextLine.x1() - l1.x1(), nextLine.y1() - l1.y1());

            emitCubicTo(qt_real_to_fixed(l2.x2()),
                        qt_real_to_fixed(l2.y2()),
                        qt_real_to_fixed(l1.x2()),
                        qt_real_to_fixed(l1.y2()),
                        qt_real_to_fixed(l1.x1()),
                        qt_real_to_fixed(l1.y1()));
        } else if (join == SvgMiterJoin) {
            QLineF miterLine(QPointF(qt_fixed_to_real(focal_x),
                                     qt_fixed_to_real(focal_y)), isect);
            if (miterLine.length() > qt_fixed_to_real(m_strokeWidth * m_miterLimit) / 2) {
                emitLineTo(qt_real_to_fixed(nextLine.x1()),
                           qt_real_to_fixed(nextLine.y1()));
            } else {
                emitLineTo(qt_real_to_fixed(isect.x()), qt_real_to_fixed(isect.y()));
                emitLineTo(qt_real_to_fixed(nextLine.x1()), qt_real_to_fixed(nextLine.y1()));
            }
        } else {
            Q_ASSERT(!"QStroker::joinPoints(), bad join style...");
        }
    }
}


/*
   Strokes a subpath side using the \a it as source. Results are put into
   \a stroke. The function returns true if the subpath side was closed.
   If \a capFirst is true, we will use capPoints instead of joinPoints to
   connect the first segment, other segments will be joined using joinPoints.
   This is to put capping in order...
*/
template <class Iterator> bool qt_stroke_side(Iterator *it,
                                              QStroker *stroker,
                                              bool capFirst,
                                              QLineF *startTangent)
{
    // Used in CurveToElement section below.
    const int MAX_OFFSET = 16;
    QBezier offsetCurves[MAX_OFFSET];

    Q_ASSERT(it->hasNext()); // The initaial move to
    QStrokerOps::Element first_element = it->next();
    Q_ASSERT(first_element.isMoveTo());

    qfixed2d start = first_element;

#ifdef QPP_STROKE_DEBUG
    qDebug(" -> (side) [%.2f, %.2f], startPos=%d",
           qt_fixed_to_real(start.x),
           qt_fixed_to_real(start.y));
#endif

    qfixed2d prev = start;

    bool first = true;

    qfixed offset = stroker->strokeWidth() / 2;

    while (it->hasNext()) {
        QStrokerOps::Element e = it->next();

        // LineToElement
        if (e.isLineTo()) {
#ifdef QPP_STROKE_DEBUG
            qDebug("\n ---> (side) lineto [%.2f, %.2f]", e.x, e.y);
#endif
            QLineF line(qt_fixed_to_real(prev.x), qt_fixed_to_real(prev.y),
                        qt_fixed_to_real(e.x), qt_fixed_to_real(e.y));
            QLineF normal = line.normalVector();
            normal.setLength(offset);
            line.translate(normal.dx(), normal.dy());

            // If we are starting a new subpath, move to correct starting point.
            if (first) {
                if (capFirst)
                    stroker->joinPoints(prev.x, prev.y, line, stroker->capStyleMode());
                else
                    stroker->emitMoveTo(qt_real_to_fixed(line.x1()), qt_real_to_fixed(line.y1()));
                *startTangent = line;
                first = false;
            } else {
                stroker->joinPoints(prev.x, prev.y, line, stroker->joinStyleMode());
            }

            // Add the stroke for this line.
            stroker->emitLineTo(qt_real_to_fixed(line.x2()),
                                qt_real_to_fixed(line.y2()));
            prev = e;

        // CurveToElement
        } else if (e.isCurveTo()) {
            QStrokerOps::Element cp2 = it->next(); // control point 2
            QStrokerOps::Element ep = it->next();  // end point

#ifdef QPP_STROKE_DEBUG
            qDebug("\n ---> (side) cubicTo [%.2f, %.2f]",
                   qt_fixed_to_real(ep.x),
                   qt_fixed_to_real(ep.y));
#endif

            QBezier bezier =
                QBezier::fromPoints(QPointF(qt_fixed_to_real(prev.x), qt_fixed_to_real(prev.y)),
                                    QPointF(qt_fixed_to_real(e.x), qt_fixed_to_real(e.y)),
                                    QPointF(qt_fixed_to_real(cp2.x), qt_fixed_to_real(cp2.y)),
                                    QPointF(qt_fixed_to_real(ep.x), qt_fixed_to_real(ep.y)));

            int count = bezier.shifted(offsetCurves,
                                       MAX_OFFSET,
                                       offset,
                                       stroker->curveThreshold());

            if (count) {
                // If we are starting a new subpath, move to correct starting point
                QLineF tangent = bezier.startTangent();
                tangent.translate(offsetCurves[0].pt1() - bezier.pt1());
                if (first) {
                    QPointF pt = offsetCurves[0].pt1();
                    if (capFirst) {
                        stroker->joinPoints(prev.x, prev.y,
                                            tangent,
                                            stroker->capStyleMode());
                    } else {
                        stroker->emitMoveTo(qt_real_to_fixed(pt.x()),
                                            qt_real_to_fixed(pt.y()));
                    }
                    *startTangent = tangent;
                    first = false;
                } else {
                    stroker->joinPoints(prev.x, prev.y,
                                        tangent,
                                        stroker->joinStyleMode());
                }

                // Add these beziers
                for (int i=0; i<count; ++i) {
                    QPointF cp1 = offsetCurves[i].pt2();
                    QPointF cp2 = offsetCurves[i].pt3();
                    QPointF ep = offsetCurves[i].pt4();
                    stroker->emitCubicTo(qt_real_to_fixed(cp1.x()), qt_real_to_fixed(cp1.y()),
                                         qt_real_to_fixed(cp2.x()), qt_real_to_fixed(cp2.y()),
                                         qt_real_to_fixed(ep.x()), qt_real_to_fixed(ep.y()));
                }
            }

            prev = ep;
        }
    }

    if (start == prev) {
        // closed subpath, join first and last point
#ifdef QPP_STROKE_DEBUG
        qDebug("\n ---> (side) closed subpath");
#endif
        stroker->joinPoints(prev.x, prev.y, *startTangent, stroker->joinStyleMode());
        return true;
    } else {
#ifdef QPP_STROKE_DEBUG
        qDebug("\n ---> (side) open subpath");
#endif
        return false;
    }
}

/*!
    \internal

    For a given angle in the range [0 .. 90], finds the corresponding parameter t
    of the prototype cubic bezier arc segment
    b = fromPoints(QPointF(1, 0), QPointF(1, KAPPA), QPointF(KAPPA, 1), QPointF(0, 1));

    From the bezier equation:
    b.pointAt(t).x() = (1-t)^3 + t*(1-t)^2 + t^2*(1-t)*KAPPA
    b.pointAt(t).y() = t*(1-t)^2 * KAPPA + t^2*(1-t) + t^3

    Third degree coefficients:
    b.pointAt(t).x() = at^3 + bt^2 + ct + d
    where a = 2-3*KAPPA, b = 3*(KAPPA-1), c = 0, d = 1

    b.pointAt(t).y() = at^3 + bt^2 + ct + d
    where a = 3*KAPPA-2, b = 6*KAPPA+3, c = 3*KAPPA, d = 0

    Newton's method to find the zero of a function:
    given a function f(x) and initial guess x_0
    x_1 = f(x_0) / f'(x_0)
    x_2 = f(x_1) / f'(x_1)
    etc...
*/

qreal qt_t_for_arc_angle(qreal angle)
{
    if (qFuzzyIsNull(angle))
        return 0;

    if (qFuzzyCompare(angle, qreal(90)))
        return 1;

    qreal radians = Q_PI * angle / 180;
    qreal cosAngle = qCos(radians);
    qreal sinAngle = qSin(radians);

    // initial guess
    qreal tc = angle / 90;
    // do some iterations of newton's method to approximate cosAngle
    // finds the zero of the function b.pointAt(tc).x() - cosAngle
    tc -= ((((2-3*QT_PATH_KAPPA) * tc + 3*(QT_PATH_KAPPA-1)) * tc) * tc + 1 - cosAngle) // value
         / (((6-9*QT_PATH_KAPPA) * tc + 6*(QT_PATH_KAPPA-1)) * tc); // derivative
    tc -= ((((2-3*QT_PATH_KAPPA) * tc + 3*(QT_PATH_KAPPA-1)) * tc) * tc + 1 - cosAngle) // value
         / (((6-9*QT_PATH_KAPPA) * tc + 6*(QT_PATH_KAPPA-1)) * tc); // derivative

    // initial guess
    qreal ts = tc;
    // do some iterations of newton's method to approximate sinAngle
    // finds the zero of the function b.pointAt(tc).y() - sinAngle
    ts -= ((((3*QT_PATH_KAPPA-2) * ts -  6*QT_PATH_KAPPA + 3) * ts + 3*QT_PATH_KAPPA) * ts - sinAngle)
         / (((9*QT_PATH_KAPPA-6) * ts + 12*QT_PATH_KAPPA - 6) * ts + 3*QT_PATH_KAPPA);
    ts -= ((((3*QT_PATH_KAPPA-2) * ts -  6*QT_PATH_KAPPA + 3) * ts + 3*QT_PATH_KAPPA) * ts - sinAngle)
         / (((9*QT_PATH_KAPPA-6) * ts + 12*QT_PATH_KAPPA - 6) * ts + 3*QT_PATH_KAPPA);

    // use the average of the t that best approximates cosAngle
    // and the t that best approximates sinAngle
    qreal t = 0.5 * (tc + ts);

#if 0
    printf("angle: %f, t: %f\n", angle, t);
    qreal a, b, c, d;
    bezierCoefficients(t, a, b, c, d);
    printf("cosAngle: %.10f, value: %.10f\n", cosAngle, a + b + c * QT_PATH_KAPPA);
    printf("sinAngle: %.10f, value: %.10f\n", sinAngle, b * QT_PATH_KAPPA + c + d);
#endif

    return t;
}

void qt_find_ellipse_coords(const QRectF &r, qreal angle, qreal length,
                            QPointF* startPoint, QPointF *endPoint);

/*!
    \internal

    Creates a number of curves for a given arc definition. The arc is
    defined an arc along the ellipses that fits into \a rect starting
    at \a startAngle and an arc length of \a sweepLength.

    The function has three out parameters. The return value is the
    starting point of the arc. The \a curves array represents the list
    of cubicTo elements up to a maximum of \a point_count. There are of course
    3 points pr curve.
*/
QPointF qt_curves_for_arc(const QRectF &rect, qreal startAngle, qreal sweepLength,
                       QPointF *curves, int *point_count)
{
    Q_ASSERT(point_count);
    Q_ASSERT(curves);

    *point_count = 0;
    if (qt_is_nan(rect.x()) || qt_is_nan(rect.y()) || qt_is_nan(rect.width()) || qt_is_nan(rect.height())
        || qt_is_nan(startAngle) || qt_is_nan(sweepLength)) {
        qWarning("QPainterPath::arcTo: Adding arc where a parameter is NaN, results are undefined");
        return QPointF();
    }

    if (rect.isNull()) {
        return QPointF();
    }

    qreal x = rect.x();
    qreal y = rect.y();

    qreal w = rect.width();
    qreal w2 = rect.width() / 2;
    qreal w2k = w2 * QT_PATH_KAPPA;

    qreal h = rect.height();
    qreal h2 = rect.height() / 2;
    qreal h2k = h2 * QT_PATH_KAPPA;

    QPointF points[16] =
    {
        // start point
        QPointF(x + w, y + h2),

        // 0 -> 270 degrees
        QPointF(x + w, y + h2 + h2k),
        QPointF(x + w2 + w2k, y + h),
        QPointF(x + w2, y + h),

        // 270 -> 180 degrees
        QPointF(x + w2 - w2k, y + h),
        QPointF(x, y + h2 + h2k),
        QPointF(x, y + h2),

        // 180 -> 90 degrees
        QPointF(x, y + h2 - h2k),
        QPointF(x + w2 - w2k, y),
        QPointF(x + w2, y),

        // 90 -> 0 degrees
        QPointF(x + w2 + w2k, y),
        QPointF(x + w, y + h2 - h2k),
        QPointF(x + w, y + h2)
    };

    if (sweepLength > 360) sweepLength = 360;
    else if (sweepLength < -360) sweepLength = -360;

    // Special case fast paths
    if (startAngle == 0.0) {
        if (sweepLength == 360.0) {
            for (int i = 11; i >= 0; --i)
                curves[(*point_count)++] = points[i];
            return points[12];
        } else if (sweepLength == -360.0) {
            for (int i = 1; i <= 12; ++i)
                curves[(*point_count)++] = points[i];
            return points[0];
        }
    }

    int startSegment = int(floor(startAngle / 90));
    int endSegment = int(floor((startAngle + sweepLength) / 90));

    qreal startT = (startAngle - startSegment * 90) / 90;
    qreal endT = (startAngle + sweepLength - endSegment * 90) / 90;

    int delta = sweepLength > 0 ? 1 : -1;
    if (delta < 0) {
        startT = 1 - startT;
        endT = 1 - endT;
    }

    // avoid empty start segment
    if (qFuzzyIsNull(startT - qreal(1))) {
        startT = 0;
        startSegment += delta;
    }

    // avoid empty end segment
    if (qFuzzyIsNull(endT)) {
        endT = 1;
        endSegment -= delta;
    }

    startT = qt_t_for_arc_angle(startT * 90);
    endT = qt_t_for_arc_angle(endT * 90);

    const bool splitAtStart = !qFuzzyIsNull(startT);
    const bool splitAtEnd = !qFuzzyIsNull(endT - qreal(1));

    const int end = endSegment + delta;

    // empty arc?
    if (startSegment == end) {
        const int quadrant = 3 - ((startSegment % 4) + 4) % 4;
        const int j = 3 * quadrant;
        return delta > 0 ? points[j + 3] : points[j];
    }

    QPointF startPoint, endPoint;
    qt_find_ellipse_coords(rect, startAngle, sweepLength, &startPoint, &endPoint);

    for (int i = startSegment; i != end; i += delta) {
        const int quadrant = 3 - ((i % 4) + 4) % 4;
        const int j = 3 * quadrant;

        QBezier b;
        if (delta > 0)
            b = QBezier::fromPoints(points[j + 3], points[j + 2], points[j + 1], points[j]);
        else
            b = QBezier::fromPoints(points[j], points[j + 1], points[j + 2], points[j + 3]);

        // empty arc?
        if (startSegment == endSegment && qFuzzyCompare(startT, endT))
            return startPoint;

        if (i == startSegment) {
            if (i == endSegment && splitAtEnd)
                b = b.bezierOnInterval(startT, endT);
            else if (splitAtStart)
                b = b.bezierOnInterval(startT, 1);
        } else if (i == endSegment && splitAtEnd) {
            b = b.bezierOnInterval(0, endT);
        }

        // push control points
        curves[(*point_count)++] = b.pt2();
        curves[(*point_count)++] = b.pt3();
        curves[(*point_count)++] = b.pt4();
    }

    Q_ASSERT(*point_count > 0);
    curves[*(point_count)-1] = endPoint;

    return startPoint;
}


/*******************************************************************************
 * QDashStroker members
 */
QDashStroker::QDashStroker(QStroker *stroker)
    : m_stroker(stroker), m_dashOffset(0)
{

}

QVector<qfixed> QDashStroker::patternForStyle(Qt::PenStyle style)
{
    const qfixed space = 2;
    const qfixed dot = 1;
    const qfixed dash = 4;

    QVector<qfixed> pattern;

    switch (style) {
    case Qt::DashLine:
        pattern << dash << space;
        break;
    case Qt::DotLine:
        pattern << dot << space;
        break;
    case Qt::DashDotLine:
        pattern << dash << space << dot << space;
        break;
    case Qt::DashDotDotLine:
        pattern << dash << space << dot << space << dot << space;
        break;
    default:
        break;
    }

    return pattern;
}


void QDashStroker::processCurrentSubpath()
{
    int dashCount = qMin(m_dashPattern.size(), 32);
    qfixed dashes[32];

    qreal longestLength = 0;
    qreal sumLength = 0;
    for (int i=0; i<dashCount; ++i) {
        dashes[i] = qMax(m_dashPattern.at(i), qreal(0)) * m_stroker->strokeWidth();
        sumLength += dashes[i];
        if (dashes[i] > longestLength)
            longestLength = dashes[i];
    }

    if (qFuzzyIsNull(sumLength))
        return;

    Q_ASSERT(dashCount > 0);

    dashCount = (dashCount / 2) * 2; // Round down to even number

    int idash = 0; // Index to current dash
    qreal pos = 0; // The position on the curve, 0 <= pos <= path.length
    qreal elen = 0; // element length
    qreal doffset = m_dashOffset * m_stroker->strokeWidth();

    // make sure doffset is in range [0..sumLength)
    doffset -= qFloor(doffset / sumLength) * sumLength;

    while (doffset >= dashes[idash]) {
        doffset -= dashes[idash];
        idash = (idash + 1) % dashCount;
    }

    qreal estart = 0; // The elements starting position
    qreal estop = 0; // The element stop position

    QLineF cline;

    QPainterPath dashPath;

    QSubpathFlatIterator it(&m_elements);
    qfixed2d prev = it.next();

    bool clipping = !m_clip_rect.isEmpty();
    qfixed2d move_to_pos = prev;
    qfixed2d line_to_pos;

    // Pad to avoid clipping the borders of thick pens.
    qfixed padding = qt_real_to_fixed(qMax(m_stroker->strokeWidth(), m_stroker->miterLimit()) * longestLength);
    qfixed2d clip_tl = { qt_real_to_fixed(m_clip_rect.left()) - padding,
                         qt_real_to_fixed(m_clip_rect.top()) - padding };
    qfixed2d clip_br = { qt_real_to_fixed(m_clip_rect.right()) + padding ,
                         qt_real_to_fixed(m_clip_rect.bottom()) + padding };

    bool hasMoveTo = false;
    while (it.hasNext()) {
        QStrokerOps::Element e = it.next();

        Q_ASSERT(e.isLineTo());
        cline = QLineF(qt_fixed_to_real(prev.x),
                       qt_fixed_to_real(prev.y),
                       qt_fixed_to_real(e.x),
                       qt_fixed_to_real(e.y));
        elen = cline.length();

        estop = estart + elen;

        bool done = pos >= estop;
        // Dash away...
        while (!done) {
            QPointF p2;

            int idash_incr = 0;
            bool has_offset = doffset > 0;
            qreal dpos = pos + dashes[idash] - doffset - estart;

            Q_ASSERT(dpos >= 0);

            if (dpos > elen) { // dash extends this line
                doffset = dashes[idash] - (dpos - elen); // subtract the part already used
                pos = estop; // move pos to next path element
                done = true;
                p2 = cline.p2();
            } else { // Dash is on this line
                p2 = cline.pointAt(dpos/elen);
                pos = dpos + estart;
                done = pos >= estop;
                idash_incr = 1;
                doffset = 0; // full segment so no offset on next.
            }

            if (idash % 2 == 0) {
                line_to_pos.x = qt_real_to_fixed(p2.x());
                line_to_pos.y = qt_real_to_fixed(p2.y());

                // If we have an offset, we're continuing a dash
                // from a previous element and should only
                // continue the current dash, without starting a
                // new subpath.
                if (!has_offset || !hasMoveTo) {
                    m_stroker->moveTo(move_to_pos.x, move_to_pos.y);
                    hasMoveTo = true;
                }

                if (!clipping
                    // if move_to is inside...
                    || (move_to_pos.x > clip_tl.x && move_to_pos.x < clip_br.x
                     && move_to_pos.y > clip_tl.y && move_to_pos.y < clip_br.y)
                    // Or if line_to is inside...
                    || (line_to_pos.x > clip_tl.x && line_to_pos.x < clip_br.x
                     && line_to_pos.y > clip_tl.y && line_to_pos.y < clip_br.y))
                {
                    m_stroker->lineTo(line_to_pos.x, line_to_pos.y);
                }
            } else {
                move_to_pos.x = qt_real_to_fixed(p2.x());
                move_to_pos.y = qt_real_to_fixed(p2.y());
            }

            idash = (idash + idash_incr) % dashCount;
        }

        // Shuffle to the next cycle...
        estart = estop;
        prev = e;
    }
}

QT_END_NAMESPACE