Simplify.cpp revision 9764cc6c109dba208592fe5f16447b8439375746
1/*
2 * Copyright 2012 Google Inc.
3 *
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
6 */
7#include "Simplify.h"
8
9#undef SkASSERT
10#define SkASSERT(cond) while (!(cond)) { sk_throw(); }
11
12// Terminology:
13// A Path contains one of more Contours
14// A Contour is made up of Segment array
15// A Segment is described by a Verb and a Point array with 2, 3, or 4 points
16// A Verb is one of Line, Quad(ratic), or Cubic
17// A Segment contains a Span array
18// A Span is describes a portion of a Segment using starting and ending T
19// T values range from 0 to 1, where 0 is the first Point in the Segment
20
21// FIXME: remove once debugging is complete
22#if 0 // set to 1 for no debugging whatsoever
23
24//const bool gxRunTestsInOneThread = false;
25
26#define DEBUG_ADD_INTERSECTING_TS 0
27#define DEBUG_BRIDGE 0
28#define DEBUG_CROSS 0
29#define DEBUG_DUMP 0
30#define DEBUG_PATH_CONSTRUCTION 0
31#define DEBUG_ACTIVE_SPANS 0
32#define DEBUG_WINDING 0
33#define DEBUG_UNUSED 0 // set to expose unused functions
34#define DEBUG_MARK_DONE 0
35
36#else
37
38//const bool gRunTestsInOneThread = true;
39
40#define DEBUG_ADD_INTERSECTING_TS 0
41#define DEBUG_BRIDGE 1
42#define DEBUG_CROSS 1
43#define DEBUG_DUMP 1
44#define DEBUG_PATH_CONSTRUCTION 1
45#define DEBUG_ACTIVE_SPANS 0
46#define DEBUG_WINDING 0
47#define DEBUG_UNUSED 0 // set to expose unused functions
48#define DEBUG_MARK_DONE 0
49
50#endif
51
52#if DEBUG_ACTIVE_SPANS && !DEBUG_DUMP
53#undef DEBUG_DUMP
54#define DEBUG_DUMP 1
55#endif
56
57#if DEBUG_DUMP
58static const char* kLVerbStr[] = {"", "line", "quad", "cubic"};
59// static const char* kUVerbStr[] = {"", "Line", "Quad", "Cubic"};
60static int gContourID;
61static int gSegmentID;
62#endif
63
64#ifndef DEBUG_TEST
65#define DEBUG_TEST 0
66#endif
67
68static int LineIntersect(const SkPoint a[2], const SkPoint b[2],
69        Intersections& intersections) {
70    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
71    const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
72    return intersect(aLine, bLine, intersections.fT[0], intersections.fT[1]);
73}
74
75static int QuadLineIntersect(const SkPoint a[3], const SkPoint b[2],
76        Intersections& intersections) {
77    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
78    const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
79    intersect(aQuad, bLine, intersections);
80    return intersections.fUsed;
81}
82
83static int CubicLineIntersect(const SkPoint a[2], const SkPoint b[3],
84        Intersections& intersections) {
85    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
86            {a[3].fX, a[3].fY}};
87    const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
88    return intersect(aCubic, bLine, intersections.fT[0], intersections.fT[1]);
89}
90
91static int QuadIntersect(const SkPoint a[3], const SkPoint b[3],
92        Intersections& intersections) {
93    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
94    const Quadratic bQuad = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}, {b[2].fX, b[2].fY}};
95    intersect(aQuad, bQuad, intersections);
96    return intersections.fUsed;
97}
98
99static int CubicIntersect(const SkPoint a[4], const SkPoint b[4],
100        Intersections& intersections) {
101    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
102            {a[3].fX, a[3].fY}};
103    const Cubic bCubic = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}, {b[2].fX, b[2].fY},
104            {b[3].fX, b[3].fY}};
105    intersect(aCubic, bCubic, intersections);
106    return intersections.fUsed;
107}
108
109static int HLineIntersect(const SkPoint a[2], SkScalar left, SkScalar right,
110        SkScalar y, bool flipped, Intersections& intersections) {
111    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
112    return horizontalIntersect(aLine, left, right, y, flipped, intersections);
113}
114
115static int HQuadIntersect(const SkPoint a[3], SkScalar left, SkScalar right,
116        SkScalar y, bool flipped, Intersections& intersections) {
117    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
118    return horizontalIntersect(aQuad, left, right, y, flipped, intersections);
119}
120
121static int HCubicIntersect(const SkPoint a[4], SkScalar left, SkScalar right,
122        SkScalar y, bool flipped, Intersections& intersections) {
123    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
124            {a[3].fX, a[3].fY}};
125    return horizontalIntersect(aCubic, left, right, y, flipped, intersections);
126}
127
128static int VLineIntersect(const SkPoint a[2], SkScalar top, SkScalar bottom,
129        SkScalar x, bool flipped, Intersections& intersections) {
130    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
131    return verticalIntersect(aLine, top, bottom, x, flipped, intersections);
132}
133
134static int VQuadIntersect(const SkPoint a[3], SkScalar top, SkScalar bottom,
135        SkScalar x, bool flipped, Intersections& intersections) {
136    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
137    return verticalIntersect(aQuad, top, bottom, x, flipped, intersections);
138}
139
140static int VCubicIntersect(const SkPoint a[4], SkScalar top, SkScalar bottom,
141        SkScalar x, bool flipped, Intersections& intersections) {
142    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
143            {a[3].fX, a[3].fY}};
144    return verticalIntersect(aCubic, top, bottom, x, flipped, intersections);
145}
146
147static int (* const VSegmentIntersect[])(const SkPoint [], SkScalar ,
148        SkScalar , SkScalar , bool , Intersections& ) = {
149    NULL,
150    VLineIntersect,
151    VQuadIntersect,
152    VCubicIntersect
153};
154
155static void LineXYAtT(const SkPoint a[2], double t, SkPoint* out) {
156    const _Line line = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
157    double x, y;
158    xy_at_t(line, t, x, y);
159    out->fX = SkDoubleToScalar(x);
160    out->fY = SkDoubleToScalar(y);
161}
162
163static void QuadXYAtT(const SkPoint a[3], double t, SkPoint* out) {
164    const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
165    double x, y;
166    xy_at_t(quad, t, x, y);
167    out->fX = SkDoubleToScalar(x);
168    out->fY = SkDoubleToScalar(y);
169}
170
171static void CubicXYAtT(const SkPoint a[4], double t, SkPoint* out) {
172    const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
173            {a[3].fX, a[3].fY}};
174    double x, y;
175    xy_at_t(cubic, t, x, y);
176    out->fX = SkDoubleToScalar(x);
177    out->fY = SkDoubleToScalar(y);
178}
179
180static void (* const SegmentXYAtT[])(const SkPoint [], double , SkPoint* ) = {
181    NULL,
182    LineXYAtT,
183    QuadXYAtT,
184    CubicXYAtT
185};
186
187static SkScalar LineXAtT(const SkPoint a[2], double t) {
188    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
189    double x;
190    xy_at_t(aLine, t, x, *(double*) 0);
191    return SkDoubleToScalar(x);
192}
193
194static SkScalar QuadXAtT(const SkPoint a[3], double t) {
195    const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
196    double x;
197    xy_at_t(quad, t, x, *(double*) 0);
198    return SkDoubleToScalar(x);
199}
200
201static SkScalar CubicXAtT(const SkPoint a[4], double t) {
202    const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
203            {a[3].fX, a[3].fY}};
204    double x;
205    xy_at_t(cubic, t, x, *(double*) 0);
206    return SkDoubleToScalar(x);
207}
208
209static SkScalar (* const SegmentXAtT[])(const SkPoint [], double ) = {
210    NULL,
211    LineXAtT,
212    QuadXAtT,
213    CubicXAtT
214};
215
216static SkScalar LineYAtT(const SkPoint a[2], double t) {
217    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
218    double y;
219    xy_at_t(aLine, t, *(double*) 0, y);
220    return SkDoubleToScalar(y);
221}
222
223static SkScalar QuadYAtT(const SkPoint a[3], double t) {
224    const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
225    double y;
226    xy_at_t(quad, t, *(double*) 0, y);
227    return SkDoubleToScalar(y);
228}
229
230static SkScalar CubicYAtT(const SkPoint a[4], double t) {
231    const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
232            {a[3].fX, a[3].fY}};
233    double y;
234    xy_at_t(cubic, t, *(double*) 0, y);
235    return SkDoubleToScalar(y);
236}
237
238static SkScalar (* const SegmentYAtT[])(const SkPoint [], double ) = {
239    NULL,
240    LineYAtT,
241    QuadYAtT,
242    CubicYAtT
243};
244
245static SkScalar LineDXAtT(const SkPoint a[2], double ) {
246    return a[1].fX - a[0].fX;
247}
248
249static SkScalar QuadDXAtT(const SkPoint a[3], double t) {
250    const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
251    double x;
252    dxdy_at_t(quad, t, x, *(double*) 0);
253    return SkDoubleToScalar(x);
254}
255
256static SkScalar CubicDXAtT(const SkPoint a[4], double t) {
257    const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
258            {a[3].fX, a[3].fY}};
259    double x;
260    dxdy_at_t(cubic, t, x, *(double*) 0);
261    return SkDoubleToScalar(x);
262}
263
264static SkScalar (* const SegmentDXAtT[])(const SkPoint [], double ) = {
265    NULL,
266    LineDXAtT,
267    QuadDXAtT,
268    CubicDXAtT
269};
270
271static void LineSubDivide(const SkPoint a[2], double startT, double endT,
272        SkPoint sub[2]) {
273    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
274    _Line dst;
275    sub_divide(aLine, startT, endT, dst);
276    sub[0].fX = SkDoubleToScalar(dst[0].x);
277    sub[0].fY = SkDoubleToScalar(dst[0].y);
278    sub[1].fX = SkDoubleToScalar(dst[1].x);
279    sub[1].fY = SkDoubleToScalar(dst[1].y);
280}
281
282static void QuadSubDivide(const SkPoint a[3], double startT, double endT,
283        SkPoint sub[3]) {
284    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
285            {a[2].fX, a[2].fY}};
286    Quadratic dst;
287    sub_divide(aQuad, startT, endT, dst);
288    sub[0].fX = SkDoubleToScalar(dst[0].x);
289    sub[0].fY = SkDoubleToScalar(dst[0].y);
290    sub[1].fX = SkDoubleToScalar(dst[1].x);
291    sub[1].fY = SkDoubleToScalar(dst[1].y);
292    sub[2].fX = SkDoubleToScalar(dst[2].x);
293    sub[2].fY = SkDoubleToScalar(dst[2].y);
294}
295
296static void CubicSubDivide(const SkPoint a[4], double startT, double endT,
297        SkPoint sub[4]) {
298    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
299            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
300    Cubic dst;
301    sub_divide(aCubic, startT, endT, dst);
302    sub[0].fX = SkDoubleToScalar(dst[0].x);
303    sub[0].fY = SkDoubleToScalar(dst[0].y);
304    sub[1].fX = SkDoubleToScalar(dst[1].x);
305    sub[1].fY = SkDoubleToScalar(dst[1].y);
306    sub[2].fX = SkDoubleToScalar(dst[2].x);
307    sub[2].fY = SkDoubleToScalar(dst[2].y);
308    sub[3].fX = SkDoubleToScalar(dst[3].x);
309    sub[3].fY = SkDoubleToScalar(dst[3].y);
310}
311
312static void (* const SegmentSubDivide[])(const SkPoint [], double , double ,
313        SkPoint []) = {
314    NULL,
315    LineSubDivide,
316    QuadSubDivide,
317    CubicSubDivide
318};
319
320#if DEBUG_UNUSED
321static void QuadSubBounds(const SkPoint a[3], double startT, double endT,
322        SkRect& bounds) {
323    SkPoint dst[3];
324    QuadSubDivide(a, startT, endT, dst);
325    bounds.fLeft = bounds.fRight = dst[0].fX;
326    bounds.fTop = bounds.fBottom = dst[0].fY;
327    for (int index = 1; index < 3; ++index) {
328        bounds.growToInclude(dst[index].fX, dst[index].fY);
329    }
330}
331
332static void CubicSubBounds(const SkPoint a[4], double startT, double endT,
333        SkRect& bounds) {
334    SkPoint dst[4];
335    CubicSubDivide(a, startT, endT, dst);
336    bounds.fLeft = bounds.fRight = dst[0].fX;
337    bounds.fTop = bounds.fBottom = dst[0].fY;
338    for (int index = 1; index < 4; ++index) {
339        bounds.growToInclude(dst[index].fX, dst[index].fY);
340    }
341}
342#endif
343
344static SkPath::Verb QuadReduceOrder(const SkPoint a[3],
345        SkTDArray<SkPoint>& reducePts) {
346    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
347            {a[2].fX, a[2].fY}};
348    Quadratic dst;
349    int order = reduceOrder(aQuad, dst);
350    if (order == 3) {
351        return SkPath::kQuad_Verb;
352    }
353    for (int index = 0; index < order; ++index) {
354        SkPoint* pt = reducePts.append();
355        pt->fX = SkDoubleToScalar(dst[index].x);
356        pt->fY = SkDoubleToScalar(dst[index].y);
357    }
358    return (SkPath::Verb) (order - 1);
359}
360
361static SkPath::Verb CubicReduceOrder(const SkPoint a[4],
362        SkTDArray<SkPoint>& reducePts) {
363    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
364            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
365    Cubic dst;
366    int order = reduceOrder(aCubic, dst, kReduceOrder_QuadraticsAllowed);
367    if (order == 4) {
368        return SkPath::kCubic_Verb;
369    }
370    for (int index = 0; index < order; ++index) {
371        SkPoint* pt = reducePts.append();
372        pt->fX = SkDoubleToScalar(dst[index].x);
373        pt->fY = SkDoubleToScalar(dst[index].y);
374    }
375    return (SkPath::Verb) (order - 1);
376}
377
378static bool QuadIsLinear(const SkPoint a[3]) {
379    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
380            {a[2].fX, a[2].fY}};
381    return isLinear(aQuad, 0, 2);
382}
383
384static bool CubicIsLinear(const SkPoint a[4]) {
385    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
386            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
387    return isLinear(aCubic, 0, 3);
388}
389
390static SkScalar LineLeftMost(const SkPoint a[2], double startT, double endT) {
391    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
392    double x[2];
393    xy_at_t(aLine, startT, x[0], *(double*) 0);
394    xy_at_t(aLine, endT, x[1], *(double*) 0);
395    return SkMinScalar((float) x[0], (float) x[1]);
396}
397
398static SkScalar QuadLeftMost(const SkPoint a[3], double startT, double endT) {
399    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
400            {a[2].fX, a[2].fY}};
401    return (float) leftMostT(aQuad, startT, endT);
402}
403
404static SkScalar CubicLeftMost(const SkPoint a[4], double startT, double endT) {
405    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
406            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
407    return (float) leftMostT(aCubic, startT, endT);
408}
409
410static SkScalar (* const SegmentLeftMost[])(const SkPoint [], double , double) = {
411    NULL,
412    LineLeftMost,
413    QuadLeftMost,
414    CubicLeftMost
415};
416
417#if DEBUG_UNUSED
418static bool IsCoincident(const SkPoint a[2], const SkPoint& above,
419        const SkPoint& below) {
420    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
421    const _Line bLine = {{above.fX, above.fY}, {below.fX, below.fY}};
422    return implicit_matches_ulps(aLine, bLine, 32);
423}
424#endif
425
426class Segment;
427
428// sorting angles
429// given angles of {dx dy ddx ddy dddx dddy} sort them
430class Angle {
431public:
432    // FIXME: this is bogus for quads and cubics
433    // if the quads and cubics' line from end pt to ctrl pt are coincident,
434    // there's no obvious way to determine the curve ordering from the
435    // derivatives alone. In particular, if one quadratic's coincident tangent
436    // is longer than the other curve, the final control point can place the
437    // longer curve on either side of the shorter one.
438    // Using Bezier curve focus http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf
439    // may provide some help, but nothing has been figured out yet.
440    bool operator<(const Angle& rh) const {
441        if ((fDy < 0) ^ (rh.fDy < 0)) {
442            return fDy < 0;
443        }
444        if (fDy == 0 && rh.fDy == 0 && fDx != rh.fDx) {
445            return fDx < rh.fDx;
446        }
447        SkScalar cmp = fDx * rh.fDy - rh.fDx * fDy;
448        if (cmp) {
449            return cmp < 0;
450        }
451        if ((fDDy < 0) ^ (rh.fDDy < 0)) {
452            return fDDy < 0;
453        }
454        if (fDDy == 0 && rh.fDDy == 0 && fDDx != rh.fDDx) {
455            return fDDx < rh.fDDx;
456        }
457        cmp = fDDx * rh.fDDy - rh.fDDx * fDDy;
458        if (cmp) {
459            return cmp < 0;
460        }
461        if ((fDDDy < 0) ^ (rh.fDDDy < 0)) {
462            return fDDDy < 0;
463        }
464        if (fDDDy == 0 && rh.fDDDy == 0) {
465            return fDDDx < rh.fDDDx;
466        }
467        return fDDDx * rh.fDDDy < rh.fDDDx * fDDDy;
468    }
469
470    int end() const {
471        return fEnd;
472    }
473
474    bool isHorizontal() const {
475        return fDy == 0 && fDDy == 0 && fDDDy == 0;
476    }
477
478    // since all angles share a point, this needs to know which point
479    // is the common origin, i.e., whether the center is at pts[0] or pts[verb]
480    // practically, this should only be called by addAngle
481    void set(const SkPoint* pts, SkPath::Verb verb, const Segment* segment,
482            int start, int end) {
483        SkASSERT(start != end);
484        fSegment = segment;
485        fStart = start;
486        fEnd = end;
487        fDx = pts[1].fX - pts[0].fX; // b - a
488        fDy = pts[1].fY - pts[0].fY;
489        if (verb == SkPath::kLine_Verb) {
490            fDDx = fDDy = fDDDx = fDDDy = 0;
491            return;
492        }
493        fDDx = pts[2].fX - pts[1].fX - fDx; // a - 2b + c
494        fDDy = pts[2].fY - pts[1].fY - fDy;
495        if (verb == SkPath::kQuad_Verb) {
496            fDDDx = fDDDy = 0;
497            return;
498        }
499        fDDDx = pts[3].fX + 3 * (pts[1].fX - pts[2].fX) - pts[0].fX;
500        fDDDy = pts[3].fY + 3 * (pts[1].fY - pts[2].fY) - pts[0].fY;
501    }
502
503    // noncoincident quads/cubics may have the same initial angle
504    // as lines, so must sort by derivatives as well
505    // if flatness turns out to be a reasonable way to sort, use the below:
506    void setFlat(const SkPoint* pts, SkPath::Verb verb, Segment* segment,
507            int start, int end) {
508        fSegment = segment;
509        fStart = start;
510        fEnd = end;
511        fDx = pts[1].fX - pts[0].fX; // b - a
512        fDy = pts[1].fY - pts[0].fY;
513        if (verb == SkPath::kLine_Verb) {
514            fDDx = fDDy = fDDDx = fDDDy = 0;
515            return;
516        }
517        if (verb == SkPath::kQuad_Verb) {
518            int uplsX = FloatAsInt(pts[2].fX - pts[1].fY - fDx);
519            int uplsY = FloatAsInt(pts[2].fY - pts[1].fY - fDy);
520            int larger = std::max(abs(uplsX), abs(uplsY));
521            int shift = 0;
522            double flatT;
523            SkPoint ddPt; // FIXME: get rid of copy (change fDD_ to point)
524            LineParameters implicitLine;
525            _Line tangent = {{pts[0].fX, pts[0].fY}, {pts[1].fX, pts[1].fY}};
526            implicitLine.lineEndPoints(tangent);
527            implicitLine.normalize();
528            while (larger > UlpsEpsilon * 1024) {
529                larger >>= 2;
530                ++shift;
531                flatT = 0.5 / (1 << shift);
532                QuadXYAtT(pts, flatT, &ddPt);
533                _Point _pt = {ddPt.fX, ddPt.fY};
534                double distance = implicitLine.pointDistance(_pt);
535                if (approximately_zero(distance)) {
536                    SkDebugf("%s ulps too small %1.9g\n", __FUNCTION__, distance);
537                    break;
538                }
539            }
540            flatT = 0.5 / (1 << shift);
541            QuadXYAtT(pts, flatT, &ddPt);
542            fDDx = ddPt.fX - pts[0].fX;
543            fDDy = ddPt.fY - pts[0].fY;
544            SkASSERT(fDDx != 0 || fDDy != 0);
545            fDDDx = fDDDy = 0;
546            return;
547        }
548        SkASSERT(0); // FIXME: add cubic case
549    }
550
551    Segment* segment() const {
552        return const_cast<Segment*>(fSegment);
553    }
554
555    int sign() const {
556        return SkSign32(fStart - fEnd);
557    }
558
559    int start() const {
560        return fStart;
561    }
562
563private:
564    SkScalar fDx;
565    SkScalar fDy;
566    SkScalar fDDx;
567    SkScalar fDDy;
568    SkScalar fDDDx;
569    SkScalar fDDDy;
570    const Segment* fSegment;
571    int fStart;
572    int fEnd;
573};
574
575static void sortAngles(SkTDArray<Angle>& angles, SkTDArray<Angle*>& angleList) {
576    int angleCount = angles.count();
577    int angleIndex;
578    angleList.setReserve(angleCount);
579    for (angleIndex = 0; angleIndex < angleCount; ++angleIndex) {
580        *angleList.append() = &angles[angleIndex];
581    }
582    QSort<Angle>(angleList.begin(), angleList.end() - 1);
583}
584
585// Bounds, unlike Rect, does not consider a line to be empty.
586struct Bounds : public SkRect {
587    static bool Intersects(const Bounds& a, const Bounds& b) {
588        return a.fLeft <= b.fRight && b.fLeft <= a.fRight &&
589                a.fTop <= b.fBottom && b.fTop <= a.fBottom;
590    }
591
592    void add(SkScalar left, SkScalar top, SkScalar right, SkScalar bottom) {
593        if (left < fLeft) {
594            fLeft = left;
595        }
596        if (top < fTop) {
597            fTop = top;
598        }
599        if (right > fRight) {
600            fRight = right;
601        }
602        if (bottom > fBottom) {
603            fBottom = bottom;
604        }
605    }
606
607    void add(const Bounds& toAdd) {
608        add(toAdd.fLeft, toAdd.fTop, toAdd.fRight, toAdd.fBottom);
609    }
610
611    bool isEmpty() {
612        return fLeft > fRight || fTop > fBottom
613                || fLeft == fRight && fTop == fBottom
614                || isnan(fLeft) || isnan(fRight)
615                || isnan(fTop) || isnan(fBottom);
616    }
617
618    void setCubicBounds(const SkPoint a[4]) {
619        _Rect dRect;
620        Cubic cubic  = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
621            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
622        dRect.setBounds(cubic);
623        set((float) dRect.left, (float) dRect.top, (float) dRect.right,
624                (float) dRect.bottom);
625    }
626
627    void setQuadBounds(const SkPoint a[3]) {
628        const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
629                {a[2].fX, a[2].fY}};
630        _Rect dRect;
631        dRect.setBounds(quad);
632        set((float) dRect.left, (float) dRect.top, (float) dRect.right,
633                (float) dRect.bottom);
634    }
635};
636
637struct Span {
638    Segment* fOther;
639    mutable SkPoint const* fPt; // lazily computed as needed
640    double fT;
641    double fOtherT; // value at fOther[fOtherIndex].fT
642    int fOtherIndex;  // can't be used during intersection
643    int fWindSum; // accumulated from contours surrounding this one
644    int fWindValue; // 0 == canceled; 1 == normal; >1 == coincident
645    bool fDone; // if set, this span to next higher T has been processed
646};
647
648class Segment {
649public:
650    Segment() {
651#if DEBUG_DUMP
652        fID = ++gSegmentID;
653#endif
654    }
655
656    bool activeAngle(int index, int& done, SkTDArray<Angle>& angles) const {
657        if (activeAngleInner(index, done, angles)) {
658            return true;
659        }
660        double referenceT = fTs[index].fT;
661        int lesser = index;
662        while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
663            if (activeAngleOther(lesser, done, angles)) {
664                return true;
665            }
666        }
667        do {
668            if (activeAngleOther(index, done, angles)) {
669                return true;
670            }
671        } while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
672        return false;
673    }
674
675    bool activeAngleOther(int index, int& done, SkTDArray<Angle>& angles) const {
676        Span* span = &fTs[index];
677        Segment* other = span->fOther;
678        int oIndex = span->fOtherIndex;
679        return other->activeAngleInner(oIndex, done, angles);
680    }
681
682    bool activeAngleInner(int index, int& done, SkTDArray<Angle>& angles) const {
683        int next = nextSpan(index, 1);
684        if (next > 0) {
685            addAngle(angles, index, next);
686            const Span& upSpan = fTs[index];
687            if (upSpan.fDone) {
688                done++;
689            } else if (upSpan.fWindSum != SK_MinS32) {
690                return true;
691            }
692        }
693        int prev = nextSpan(index, -1);
694        // edge leading into junction
695        if (prev >= 0) {
696            addAngle(angles, index, prev);
697            const Span& downSpan = fTs[prev];
698            if (downSpan.fDone) {
699                done++;
700             } else if (downSpan.fWindSum != SK_MinS32) {
701                return true;
702            }
703        }
704        return false;
705    }
706
707    SkScalar activeTop() const {
708        SkASSERT(!done());
709        int count = fTs.count();
710        SkScalar result = SK_ScalarMax;
711        bool lastDone = true;
712        for (int index = 0; index < count; ++index) {
713            bool done = fTs[index].fDone;
714            if (!done || !lastDone) {
715                SkScalar y = yAtT(index);
716                if (result > y) {
717                    result = y;
718                }
719            }
720            lastDone = done;
721        }
722        SkASSERT(result < SK_ScalarMax);
723        return result;
724    }
725
726    void addAngle(SkTDArray<Angle>& angles, int start, int end) const {
727        SkASSERT(start != end);
728        SkPoint edge[4];
729        (*SegmentSubDivide[fVerb])(fPts, fTs[start].fT, fTs[end].fT, edge);
730        Angle* angle = angles.append();
731        angle->set(edge, fVerb, this, start, end);
732    }
733
734    void addCubic(const SkPoint pts[4]) {
735        init(pts, SkPath::kCubic_Verb);
736        fBounds.setCubicBounds(pts);
737    }
738
739    // FIXME: this needs to defer add for aligned consecutive line segments
740    SkPoint addCurveTo(int start, int end, SkPath& path, bool active) {
741        SkPoint edge[4];
742        // OPTIMIZE? if not active, skip remainder and return xy_at_t(end)
743        (*SegmentSubDivide[fVerb])(fPts, fTs[start].fT, fTs[end].fT, edge);
744        if (active) {
745    #if DEBUG_PATH_CONSTRUCTION
746            SkDebugf("%s %s (%1.9g,%1.9g)", __FUNCTION__,
747                    kLVerbStr[fVerb], edge[1].fX, edge[1].fY);
748            if (fVerb > 1) {
749                SkDebugf(" (%1.9g,%1.9g)", edge[2].fX, edge[2].fY);
750            }
751            if (fVerb > 2) {
752                SkDebugf(" (%1.9g,%1.9g)", edge[3].fX, edge[3].fY);
753            }
754            SkDebugf("\n");
755    #endif
756            switch (fVerb) {
757                case SkPath::kLine_Verb:
758                    path.lineTo(edge[1].fX, edge[1].fY);
759                    break;
760                case SkPath::kQuad_Verb:
761                    path.quadTo(edge[1].fX, edge[1].fY, edge[2].fX, edge[2].fY);
762                    break;
763                case SkPath::kCubic_Verb:
764                    path.cubicTo(edge[1].fX, edge[1].fY, edge[2].fX, edge[2].fY,
765                            edge[3].fX, edge[3].fY);
766                    break;
767            }
768        }
769        return edge[fVerb];
770    }
771
772    void addLine(const SkPoint pts[2]) {
773        init(pts, SkPath::kLine_Verb);
774        fBounds.set(pts, 2);
775    }
776
777    const SkPoint& addMoveTo(int tIndex, SkPath& path, bool active) {
778        const SkPoint& pt = xyAtT(tIndex);
779        if (active) {
780    #if DEBUG_PATH_CONSTRUCTION
781            SkDebugf("%s (%1.9g,%1.9g)\n", __FUNCTION__, pt.fX, pt.fY);
782    #endif
783            path.moveTo(pt.fX, pt.fY);
784        }
785        return pt;
786    }
787
788    // add 2 to edge or out of range values to get T extremes
789    void addOtherT(int index, double otherT, int otherIndex) {
790        Span& span = fTs[index];
791        span.fOtherT = otherT;
792        span.fOtherIndex = otherIndex;
793    }
794
795    void addQuad(const SkPoint pts[3]) {
796        init(pts, SkPath::kQuad_Verb);
797        fBounds.setQuadBounds(pts);
798    }
799
800    // Defer all coincident edge processing until
801    // after normal intersections have been computed
802
803// no need to be tricky; insert in normal T order
804// resolve overlapping ts when considering coincidence later
805
806    // add non-coincident intersection. Resulting edges are sorted in T.
807    int addT(double newT, Segment* other) {
808        // FIXME: in the pathological case where there is a ton of intercepts,
809        //  binary search?
810        int insertedAt = -1;
811        size_t tCount = fTs.count();
812        for (size_t index = 0; index < tCount; ++index) {
813            // OPTIMIZATION: if there are three or more identical Ts, then
814            // the fourth and following could be further insertion-sorted so
815            // that all the edges are clockwise or counterclockwise.
816            // This could later limit segment tests to the two adjacent
817            // neighbors, although it doesn't help with determining which
818            // circular direction to go in.
819            if (newT < fTs[index].fT) {
820                insertedAt = index;
821                break;
822            }
823        }
824        Span* span;
825        if (insertedAt >= 0) {
826            span = fTs.insert(insertedAt);
827        } else {
828            insertedAt = tCount;
829            span = fTs.append();
830        }
831        span->fT = newT;
832        span->fOther = other;
833        span->fPt = NULL;
834        span->fWindSum = SK_MinS32;
835        span->fWindValue = 1;
836        if ((span->fDone = newT == 1)) {
837            ++fDoneSpans;
838        }
839        return insertedAt;
840    }
841
842    // set spans from start to end to decrement by one
843    // note this walks other backwards
844    // FIMXE: there's probably an edge case that can be constructed where
845    // two span in one segment are separated by float epsilon on one span but
846    // not the other, if one segment is very small. For this
847    // case the counts asserted below may or may not be enough to separate the
848    // spans. Even if the counts work out, what if the spanw aren't correctly
849    // sorted? It feels better in such a case to match the span's other span
850    // pointer since both coincident segments must contain the same spans.
851    void addTCancel(double startT, double endT, Segment& other,
852            double oStartT, double oEndT) {
853        SkASSERT(endT - startT >= FLT_EPSILON);
854        SkASSERT(oEndT - oStartT >= FLT_EPSILON);
855        int index = 0;
856        while (startT - fTs[index].fT >= FLT_EPSILON) {
857            ++index;
858        }
859        int oIndex = other.fTs.count();
860        while (other.fTs[--oIndex].fT - oEndT > -FLT_EPSILON)
861            ;
862        Span* test = &fTs[index];
863        Span* oTest = &other.fTs[oIndex];
864        do {
865            bool decrement = test->fWindValue && oTest->fWindValue;
866            Span* end = test;
867            do {
868                if (decrement) {
869                    SkASSERT(end->fWindValue > 0);
870                    if (--(end->fWindValue) == 0) {
871                        end->fDone = true;
872                        ++fDoneSpans;
873                    }
874                }
875                end = &fTs[++index];
876            } while (end->fT - test->fT < FLT_EPSILON);
877            Span* oTestStart = oTest;
878            do {
879                if (decrement) {
880                    SkASSERT(oTestStart->fWindValue > 0);
881                    if (--(oTestStart->fWindValue) == 0) {
882                        oTestStart->fDone = true;
883                        ++other.fDoneSpans;
884                    }
885                }
886                if (!oIndex) {
887                    break;
888                }
889                oTestStart = &other.fTs[--oIndex];
890            } while (oTest->fT - oTestStart->fT < FLT_EPSILON);
891            test = end;
892            oTest = oTestStart;
893        } while (test->fT < endT - FLT_EPSILON);
894        SkASSERT(!oIndex || oTest->fT <= oStartT - FLT_EPSILON);
895    }
896
897    // set spans from start to end to increment the greater by one and decrement
898    // the lesser
899    void addTCoincident(double startT, double endT, Segment& other,
900            double oStartT, double oEndT) {
901        SkASSERT(endT - startT >= FLT_EPSILON);
902        SkASSERT(oEndT - oStartT >= FLT_EPSILON);
903        int index = 0;
904        while (startT - fTs[index].fT >= FLT_EPSILON) {
905            ++index;
906        }
907        int oIndex = 0;
908        while (oStartT - other.fTs[oIndex].fT >= FLT_EPSILON) {
909            ++oIndex;
910        }
911        Span* test = &fTs[index];
912        Span* oTest = &other.fTs[oIndex];
913        SkTDArray<double> outsideTs;
914        SkTDArray<double> oOutsideTs;
915        do {
916            bool transfer = test->fWindValue && oTest->fWindValue;
917            bool decrementOther = test->fWindValue >= oTest->fWindValue;
918            Span* end = test;
919            double startT = end->fT;
920            double oStartT = oTest->fT;
921            do {
922                if (transfer) {
923                    if (decrementOther) {
924                        ++(end->fWindValue);
925                    } else {
926                        SkASSERT(end->fWindValue > 0);
927                        if (--(end->fWindValue) == 0) {
928                            end->fDone = true;
929                            ++fDoneSpans;
930                            int outCount = outsideTs.count();
931                            if (outCount == 0 || end->fT - outsideTs[outCount - 2]
932                                    >= FLT_EPSILON) {
933                                *outsideTs.append() = end->fT;
934                                *outsideTs.append() = oStartT;
935                            }
936                        }
937                    }
938                }
939                end = &fTs[++index];
940            } while (end->fT - test->fT < FLT_EPSILON);
941            Span* oEnd = oTest;
942            do {
943                if (transfer) {
944                    if (decrementOther) {
945                        SkASSERT(oEnd->fWindValue > 0);
946                        if (--(oEnd->fWindValue) == 0) {
947                            oEnd->fDone = true;
948                            ++other.fDoneSpans;
949                            int oOutCount = oOutsideTs.count();
950                            if (oOutCount == 0 || oEnd->fT
951                                    - oOutsideTs[oOutCount - 2] >= FLT_EPSILON) {
952                                *oOutsideTs.append() = oEnd->fT;
953                                *oOutsideTs.append() = startT;
954                            }
955                        }
956                    } else {
957                        ++(oEnd->fWindValue);
958                    }
959                }
960                oEnd = &other.fTs[++oIndex];
961            } while (oEnd->fT - oTest->fT < FLT_EPSILON);
962            test = end;
963            oTest = oEnd;
964        } while (test->fT < endT - FLT_EPSILON);
965        SkASSERT(oTest->fT < oEndT + FLT_EPSILON);
966        SkASSERT(oTest->fT > oEndT - FLT_EPSILON);
967        if (!done() && outsideTs.count()) {
968            addTOutsides(outsideTs, other, oEndT);
969        }
970        if (!other.done() && oOutsideTs.count()) {
971            other.addTOutsides(oOutsideTs, *this, endT);
972        }
973    }
974
975    void addTOutsides(const SkTDArray<double>& outsideTs, Segment& other,
976            double otherEnd) {
977        int count = outsideTs.count();
978        double endT = 0;
979        int endSpan = 0;
980        for (int index = 0; index < count; index += 2) {
981            double t = outsideTs[index];
982            double otherT = outsideTs[index + 1];
983            if (t > 1 - FLT_EPSILON) {
984                return;
985            }
986            if (t - endT > FLT_EPSILON) {
987                endSpan = addTDonePair(t, other, otherT);
988            }
989            do {
990                endT = fTs[++endSpan].fT;
991            } while (endT - t < FLT_EPSILON);
992        }
993        addTPair(endT, other, otherEnd);
994    }
995
996    // match the other.fWindValue to its mates
997    int addTDonePair(double t, Segment& other, double otherT) {
998        int insertedAt = addTPair(t, other, otherT);
999        Span& end = fTs[insertedAt];
1000        SkASSERT(end.fWindValue == 1);
1001        end.fWindValue = 0;
1002        end.fDone = true;
1003        ++fDoneSpans;
1004        Span& otherEnd = other.fTs[end.fOtherIndex];
1005        Span* match = NULL;
1006        if (end.fOtherIndex > 0) {
1007            match = &other.fTs[end.fOtherIndex - 1];
1008        }
1009        if (!match || match->fT < otherT) {
1010            match = &other.fTs[end.fOtherIndex + 1];
1011        }
1012        otherEnd.fWindValue = match->fWindValue;
1013        return insertedAt;
1014    }
1015
1016    int addTPair(double t, Segment& other, double otherT) {
1017        int insertedAt = addT(t, &other);
1018        int otherInsertedAt = other.addT(otherT, this);
1019        addOtherT(insertedAt, otherT, otherInsertedAt);
1020        other.addOtherT(otherInsertedAt, t, insertedAt);
1021        return insertedAt;
1022    }
1023
1024    void addTwoAngles(int start, int end, SkTDArray<Angle>& angles) const {
1025        // add edge leading into junction
1026        if (fTs[SkMin32(end, start)].fWindValue > 0) {
1027            addAngle(angles, end, start);
1028        }
1029        // add edge leading away from junction
1030        int step = SkSign32(end - start);
1031        int tIndex = nextSpan(end, step);
1032        if (tIndex >= 0 && fTs[SkMin32(end, tIndex)].fWindValue > 0) {
1033            addAngle(angles, end, tIndex);
1034        }
1035    }
1036
1037    const Bounds& bounds() const {
1038        return fBounds;
1039    }
1040
1041    void buildAngles(int index, SkTDArray<Angle>& angles) const {
1042        double referenceT = fTs[index].fT;
1043        int lesser = index;
1044        while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
1045            buildAnglesInner(lesser, angles);
1046        }
1047        do {
1048            buildAnglesInner(index, angles);
1049        } while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
1050    }
1051
1052    void buildAnglesInner(int index, SkTDArray<Angle>& angles) const {
1053        Span* span = &fTs[index];
1054        Segment* other = span->fOther;
1055    // if there is only one live crossing, and no coincidence, continue
1056    // in the same direction
1057    // if there is coincidence, the only choice may be to reverse direction
1058        // find edge on either side of intersection
1059        int oIndex = span->fOtherIndex;
1060        // if done == -1, prior span has already been processed
1061        int step = 1;
1062        int next = other->nextSpan(oIndex, step);
1063        if (next < 0) {
1064            step = -step;
1065            next = other->nextSpan(oIndex, step);
1066        }
1067        // add candidate into and away from junction
1068        other->addTwoAngles(next, oIndex, angles);
1069    }
1070
1071    bool cancels(const Segment& other) const {
1072        SkASSERT(fVerb == SkPath::kLine_Verb);
1073        SkASSERT(other.fVerb == SkPath::kLine_Verb);
1074        SkPoint dxy = fPts[0] - fPts[1];
1075        SkPoint odxy = other.fPts[0] - other.fPts[1];
1076        return dxy.fX * odxy.fX < 0 || dxy.fY * odxy.fY < 0;
1077    }
1078
1079    // figure out if the segment's ascending T goes clockwise or not
1080    // not enough context to write this as shown
1081    // instead, add all segments meeting at the top
1082    // sort them using buildAngleList
1083    // find the first in the sort
1084    // see if ascendingT goes to top
1085    bool clockwise(int /* tIndex */) const {
1086        SkASSERT(0); // incomplete
1087        return false;
1088    }
1089
1090    int crossedSpan(const SkPoint& basePt, SkScalar& bestY, double& hitT) const {
1091        int start = 0;
1092        int bestT = -1;
1093        SkScalar top = bounds().fTop;
1094        SkScalar bottom = bounds().fBottom;
1095        int end;
1096        do {
1097            end = nextSpan(start, 1);
1098            SkPoint edge[4];
1099            // OPTIMIZE: wrap this so that if start==0 end==fTCount-1 we can
1100            // work with the original data directly
1101            (*SegmentSubDivide[fVerb])(fPts, fTs[start].fT, fTs[end].fT, edge);
1102            // intersect ray starting at basePt with edge
1103            Intersections intersections;
1104            int pts = (*VSegmentIntersect[fVerb])(edge, top, bottom, basePt.fX,
1105                    false, intersections);
1106            if (pts == 0) {
1107                continue;
1108            }
1109            if (pts > 1 && fVerb == SkPath::kLine_Verb) {
1110            // if the intersection is edge on, wait for another one
1111                continue;
1112            }
1113            SkASSERT(pts == 1); // FIXME: more code required to disambiguate
1114            SkPoint pt;
1115            double foundT = intersections.fT[0][0];
1116            (*SegmentXYAtT[fVerb])(fPts, foundT, &pt);
1117            if (bestY < pt.fY) {
1118                bestY = pt.fY;
1119                bestT = foundT < 1 ? start : end;
1120                hitT = foundT;
1121            }
1122            start = end;
1123        } while (fTs[end].fT != 1);
1124        return bestT;
1125    }
1126
1127    bool done() const {
1128        SkASSERT(fDoneSpans <= fTs.count());
1129        return fDoneSpans == fTs.count();
1130    }
1131
1132    // so the span needs to contain the pairing info found here
1133    // this should include the winding computed for the edge, and
1134    //  what edge it connects to, and whether it is discarded
1135    //  (maybe discarded == abs(winding) > 1) ?
1136    // only need derivatives for duration of sorting, add a new struct
1137    // for pairings, remove extra spans that have zero length and
1138    //  reference an unused other
1139    // for coincident, the last span on the other may be marked done
1140    //  (always?)
1141
1142    // if loop is exhausted, contour may be closed.
1143    // FIXME: pass in close point so we can check for closure
1144
1145    // given a segment, and a sense of where 'inside' is, return the next
1146    // segment. If this segment has an intersection, or ends in multiple
1147    // segments, find the mate that continues the outside.
1148    // note that if there are multiples, but no coincidence, we can limit
1149    // choices to connections in the correct direction
1150
1151    // mark found segments as done
1152
1153    // start is the index of the beginning T of this edge
1154    // it is guaranteed to have an end which describes a non-zero length (?)
1155    // winding -1 means ccw, 1 means cw
1156    // firstFind allows coincident edges to be treated differently
1157    Segment* findNext(SkTDArray<Span*>& chase, int winding, const int startIndex,
1158            const int endIndex,
1159            int& nextStart, int& nextEnd, int& flipped, bool firstFind) {
1160        SkASSERT(startIndex != endIndex);
1161        int count = fTs.count();
1162        SkASSERT(startIndex < endIndex ? startIndex < count - 1
1163                : startIndex > 0);
1164        int step = SkSign32(endIndex - startIndex);
1165        int end = nextSpan(startIndex, step);
1166        SkASSERT(end >= 0);
1167        Span* endSpan = &fTs[end];
1168        Segment* other;
1169        if (isSimple(end)) {
1170        // mark the smaller of startIndex, endIndex done, and all adjacent
1171        // spans with the same T value (but not 'other' spans)
1172            markDone(SkMin32(startIndex, endIndex), winding);
1173            other = endSpan->fOther;
1174            nextStart = endSpan->fOtherIndex;
1175            nextEnd = nextStart + step;
1176            SkASSERT(step < 0 ? nextEnd >= 0 : nextEnd < other->fTs.count());
1177            return other;
1178        }
1179        // more than one viable candidate -- measure angles to find best
1180        SkTDArray<Angle> angles;
1181        SkASSERT(startIndex - endIndex != 0);
1182        SkASSERT((startIndex - endIndex < 0) ^ (step < 0));
1183        addTwoAngles(startIndex, end, angles);
1184        buildAngles(end, angles);
1185        SkTDArray<Angle*> sorted;
1186        sortAngles(angles, sorted);
1187        int angleCount = angles.count();
1188        int firstIndex = findStartingEdge(sorted, startIndex, end);
1189
1190        SkASSERT(firstIndex >= 0);
1191        int startWinding = winding;
1192        int nextIndex = firstIndex + 1;
1193        int lastIndex = firstIndex != 0 ? firstIndex : angleCount;
1194        const Angle* foundAngle = NULL;
1195        // iterate through the angle, and compute everyone's winding
1196        bool firstEdge = true;
1197        do {
1198            if (nextIndex == angleCount) {
1199                nextIndex = 0;
1200            }
1201            const Angle* nextAngle = sorted[nextIndex];
1202            int maxWinding = winding;
1203            Segment* nextSegment = nextAngle->segment();
1204            int windValue = nextSegment->windValue(nextAngle);
1205            SkASSERT(windValue > 0);
1206            winding -= nextAngle->sign() * windValue;
1207    #if DEBUG_WINDING
1208            SkDebugf("%s maxWinding=%d winding=%d\n", __FUNCTION__, maxWinding,
1209                    winding);
1210    #endif
1211            if (maxWinding * winding < 0) {
1212                flipped = -flipped;
1213                SkDebugf("flipped sign %d %d\n", maxWinding, winding);
1214            }
1215            firstEdge = false;
1216            if (!winding) {
1217                if (!foundAngle) {
1218                    foundAngle = nextAngle;
1219                }
1220                continue;
1221            }
1222            if (nextSegment->done()) {
1223                continue;
1224            }
1225            // if the winding is non-zero, nextAngle does not connect to
1226            // current chain. If we haven't done so already, mark the angle
1227            // as done, record the winding value, and mark connected unambiguous
1228            // segments as well.
1229            if (nextSegment->windSum(nextAngle) == SK_MinS32) {
1230                if (abs(maxWinding) < abs(winding)) {
1231                    maxWinding = winding;
1232                }
1233                Span* last;
1234                if (foundAngle) {
1235                    last = nextSegment->markAndChaseWinding(nextAngle, maxWinding);
1236                } else {
1237                    last = nextSegment->markAndChaseDone(nextAngle, maxWinding);
1238                }
1239                if (last) {
1240                    *chase.append() = last;
1241                }
1242            }
1243        } while (++nextIndex != lastIndex);
1244        sorted[firstIndex]->segment()->
1245            markDone(SkMin32(startIndex, endIndex), startWinding);
1246        if (!foundAngle) {
1247            return NULL;
1248        }
1249        nextStart = foundAngle->start();
1250        nextEnd = foundAngle->end();
1251        return foundAngle->segment();
1252    }
1253
1254    int findStartingEdge(SkTDArray<Angle*>& sorted, int start, int end) {
1255        int angleCount = sorted.count();
1256        int firstIndex = -1;
1257        for (int angleIndex = 0; angleIndex < angleCount; ++angleIndex) {
1258            const Angle* angle = sorted[angleIndex];
1259            if (angle->segment() == this && angle->start() == end &&
1260                    angle->end() == start) {
1261                firstIndex = angleIndex;
1262                break;
1263            }
1264        }
1265        return firstIndex;
1266    }
1267
1268    // FIXME: this is tricky code; needs its own unit test
1269    void findTooCloseToCall(int /* winding */ ) { // FIXME: winding should be considered
1270        int count = fTs.count();
1271        if (count < 3) { // require t=0, x, 1 at minimum
1272            return;
1273        }
1274        int matchIndex = 0;
1275        int moCount;
1276        Span* match;
1277        Segment* mOther;
1278        do {
1279            match = &fTs[matchIndex];
1280            mOther = match->fOther;
1281            moCount = mOther->fTs.count();
1282            if (moCount >= 3) {
1283                break;
1284            }
1285            if (++matchIndex >= count) {
1286                return;
1287            }
1288        } while (true); // require t=0, x, 1 at minimum
1289        // OPTIMIZATION: defer matchPt until qualifying toCount is found?
1290        const SkPoint* matchPt = &xyAtT(match);
1291        // look for a pair of nearby T values that map to the same (x,y) value
1292        // if found, see if the pair of other segments share a common point. If
1293        // so, the span from here to there is coincident.
1294        for (int index = matchIndex + 1; index < count; ++index) {
1295            Span* test = &fTs[index];
1296            if (test->fDone) {
1297                continue;
1298            }
1299            Segment* tOther = test->fOther;
1300            int toCount = tOther->fTs.count();
1301            if (toCount < 3) { // require t=0, x, 1 at minimum
1302                continue;
1303            }
1304            const SkPoint* testPt = &xyAtT(test);
1305            if (*matchPt != *testPt) {
1306                matchIndex = index;
1307                moCount = toCount;
1308                match = test;
1309                mOther = tOther;
1310                matchPt = testPt;
1311                continue;
1312            }
1313            int moStart = -1;
1314            int moEnd = -1;
1315            double moStartT, moEndT;
1316            for (int moIndex = 0; moIndex < moCount; ++moIndex) {
1317                Span& moSpan = mOther->fTs[moIndex];
1318                if (moSpan.fDone) {
1319                    continue;
1320                }
1321                if (moSpan.fOther == this) {
1322                    if (moSpan.fOtherT == match->fT) {
1323                        moStart = moIndex;
1324                        moStartT = moSpan.fT;
1325                    }
1326                    continue;
1327                }
1328                if (moSpan.fOther == tOther) {
1329                    SkASSERT(moEnd == -1);
1330                    moEnd = moIndex;
1331                    moEndT = moSpan.fT;
1332                }
1333            }
1334            if (moStart < 0 || moEnd < 0) {
1335                continue;
1336            }
1337            // FIXME: if moStartT, moEndT are initialized to NaN, can skip this test
1338            if (moStartT == moEndT) {
1339                continue;
1340            }
1341            int toStart = -1;
1342            int toEnd = -1;
1343            double toStartT, toEndT;
1344            for (int toIndex = 0; toIndex < toCount; ++toIndex) {
1345                Span& toSpan = tOther->fTs[toIndex];
1346                if (toSpan.fOther == this) {
1347                    if (toSpan.fOtherT == test->fT) {
1348                        toStart = toIndex;
1349                        toStartT = toSpan.fT;
1350                    }
1351                    continue;
1352                }
1353                if (toSpan.fOther == mOther && toSpan.fOtherT == moEndT) {
1354                    SkASSERT(toEnd == -1);
1355                    toEnd = toIndex;
1356                    toEndT = toSpan.fT;
1357                }
1358            }
1359            // FIXME: if toStartT, toEndT are initialized to NaN, can skip this test
1360            if (toStart <= 0 || toEnd <= 0) {
1361                continue;
1362            }
1363            if (toStartT == toEndT) {
1364                continue;
1365            }
1366            // test to see if the segment between there and here is linear
1367            if (!mOther->isLinear(moStart, moEnd)
1368                    || !tOther->isLinear(toStart, toEnd)) {
1369                continue;
1370            }
1371            // FIXME: defer implementation until the rest works
1372            // this may share code with regular coincident detection
1373            SkASSERT(0);
1374        #if 0
1375            if (flipped) {
1376                mOther->addTCancel(moStart, moEnd, tOther, tStart, tEnd);
1377            } else {
1378                mOther->addTCoincident(moStart, moEnd, tOther, tStart, tEnd);
1379            }
1380        #endif
1381        }
1382    }
1383
1384    // OPTIMIZATION : for a pair of lines, can we compute points at T (cached)
1385    // and use more concise logic like the old edge walker code?
1386    // FIXME: this needs to deal with coincident edges
1387    Segment* findTop(int& tIndex, int& endIndex) {
1388        // iterate through T intersections and return topmost
1389        // topmost tangent from y-min to first pt is closer to horizontal
1390        SkASSERT(!done());
1391        int firstT;
1392        int lastT;
1393        SkPoint topPt;
1394        topPt.fY = SK_ScalarMax;
1395        int count = fTs.count();
1396        // see if either end is not done since we want smaller Y of the pair
1397        bool lastDone = true;
1398        for (int index = 0; index < count; ++index) {
1399            const Span& span = fTs[index];
1400            if (!span.fDone || !lastDone) {
1401                const SkPoint& intercept = xyAtT(&span);
1402                if (topPt.fY > intercept.fY || (topPt.fY == intercept.fY
1403                        && topPt.fX > intercept.fX)) {
1404                    topPt = intercept;
1405                    firstT = lastT = index;
1406                } else if (topPt == intercept) {
1407                    lastT = index;
1408                }
1409            }
1410            lastDone = span.fDone;
1411        }
1412        // sort the edges to find the leftmost
1413        int step = 1;
1414        int end = nextSpan(firstT, step);
1415        if (end == -1) {
1416            step = -1;
1417            end = nextSpan(firstT, step);
1418            SkASSERT(end != -1);
1419        }
1420        // if the topmost T is not on end, or is three-way or more, find left
1421        // look for left-ness from tLeft to firstT (matching y of other)
1422        SkTDArray<Angle> angles;
1423        SkASSERT(firstT - end != 0);
1424        addTwoAngles(end, firstT, angles);
1425        buildAngles(firstT, angles);
1426        SkTDArray<Angle*> sorted;
1427        sortAngles(angles, sorted);
1428        // skip edges that have already been processed
1429        firstT = -1;
1430        Segment* leftSegment;
1431        do {
1432            const Angle* angle = sorted[++firstT];
1433            leftSegment = angle->segment();
1434            tIndex = angle->end();
1435            endIndex = angle->start();
1436        } while (leftSegment->fTs[SkMin32(tIndex, endIndex)].fDone);
1437        return leftSegment;
1438    }
1439
1440    // FIXME: not crazy about this
1441    // when the intersections are performed, the other index is into an
1442    // incomplete array. as the array grows, the indices become incorrect
1443    // while the following fixes the indices up again, it isn't smart about
1444    // skipping segments whose indices are already correct
1445    // assuming we leave the code that wrote the index in the first place
1446    void fixOtherTIndex() {
1447        int iCount = fTs.count();
1448        for (int i = 0; i < iCount; ++i) {
1449            Span& iSpan = fTs[i];
1450            double oT = iSpan.fOtherT;
1451            Segment* other = iSpan.fOther;
1452            int oCount = other->fTs.count();
1453            for (int o = 0; o < oCount; ++o) {
1454                Span& oSpan = other->fTs[o];
1455                if (oT == oSpan.fT && this == oSpan.fOther) {
1456                    iSpan.fOtherIndex = o;
1457                    break;
1458                }
1459            }
1460        }
1461    }
1462
1463    // OPTIMIZATION: uses tail recursion. Unwise?
1464    Span* innerChaseDone(int index, int step, int winding) {
1465        int end = nextSpan(index, step);
1466        SkASSERT(end >= 0);
1467        if (multipleSpans(end)) {
1468            return &fTs[end];
1469        }
1470        const Span& endSpan = fTs[end];
1471        Segment* other = endSpan.fOther;
1472        index = endSpan.fOtherIndex;
1473        int otherEnd = other->nextSpan(index, step);
1474        Span* last = other->innerChaseDone(index, step, winding);
1475        other->markDone(SkMin32(index, otherEnd), winding);
1476        return last;
1477    }
1478
1479    Span* innerChaseWinding(int index, int step, int winding) {
1480        int end = nextSpan(index, step);
1481        SkASSERT(end >= 0);
1482        if (multipleSpans(end)) {
1483            return &fTs[end];
1484        }
1485        const Span& endSpan = fTs[end];
1486        Segment* other = endSpan.fOther;
1487        index = endSpan.fOtherIndex;
1488        int otherEnd = other->nextSpan(index, step);
1489        int min = SkMin32(index, otherEnd);
1490        if (other->fTs[min].fWindSum != SK_MinS32) {
1491            SkASSERT(other->fTs[index].fWindSum == winding);
1492            return NULL;
1493        }
1494        Span* last = other->innerChaseWinding(index, step, winding);
1495        other->markWinding(min, winding);
1496        return last;
1497    }
1498
1499    void init(const SkPoint pts[], SkPath::Verb verb) {
1500        fPts = pts;
1501        fVerb = verb;
1502        fDoneSpans = 0;
1503    }
1504
1505    bool intersected() const {
1506        return fTs.count() > 0;
1507    }
1508
1509    bool isLinear(int start, int end) const {
1510        if (fVerb == SkPath::kLine_Verb) {
1511            return true;
1512        }
1513        if (fVerb == SkPath::kQuad_Verb) {
1514            SkPoint qPart[3];
1515            QuadSubDivide(fPts, fTs[start].fT, fTs[end].fT, qPart);
1516            return QuadIsLinear(qPart);
1517        } else {
1518            SkASSERT(fVerb == SkPath::kCubic_Verb);
1519            SkPoint cPart[4];
1520            CubicSubDivide(fPts, fTs[start].fT, fTs[end].fT, cPart);
1521            return CubicIsLinear(cPart);
1522        }
1523    }
1524
1525    // OPTIMIZE: successive calls could start were the last leaves off
1526    // or calls could specialize to walk forwards or backwards
1527    bool isMissing(double startT) const {
1528        size_t tCount = fTs.count();
1529        for (size_t index = 0; index < tCount; ++index) {
1530            if (fabs(startT - fTs[index].fT) < FLT_EPSILON) {
1531                return false;
1532            }
1533        }
1534        return true;
1535    }
1536
1537    bool isSimple(int end) const {
1538        int count = fTs.count();
1539        if (count == 2) {
1540            return true;
1541        }
1542        double t = fTs[end].fT;
1543        if (t < FLT_EPSILON) {
1544            return fTs[1].fT >= FLT_EPSILON;
1545        }
1546        if (t > 1 - FLT_EPSILON) {
1547            return fTs[count - 2].fT <= 1 - FLT_EPSILON;
1548        }
1549        return false;
1550    }
1551
1552    bool isHorizontal() const {
1553        return fBounds.fTop == fBounds.fBottom;
1554    }
1555
1556    bool isVertical() const {
1557        return fBounds.fLeft == fBounds.fRight;
1558    }
1559
1560    SkScalar leftMost(int start, int end) const {
1561        return (*SegmentLeftMost[fVerb])(fPts, fTs[start].fT, fTs[end].fT);
1562    }
1563
1564    // this span is excluded by the winding rule -- chase the ends
1565    // as long as they are unambiguous to mark connections as done
1566    // and give them the same winding value
1567    Span* markAndChaseDone(const Angle* angle, int winding) {
1568        int index = angle->start();
1569        int endIndex = angle->end();
1570        int step = SkSign32(endIndex - index);
1571        Span* last = innerChaseDone(index, step, winding);
1572        markDone(SkMin32(index, endIndex), winding);
1573        return last;
1574    }
1575
1576    Span* markAndChaseWinding(const Angle* angle, int winding) {
1577        int index = angle->start();
1578        int endIndex = angle->end();
1579        int min = SkMin32(index, endIndex);
1580        int step = SkSign32(endIndex - index);
1581        Span* last = innerChaseWinding(index, step, winding);
1582        markWinding(min, winding);
1583        return last;
1584    }
1585
1586    // FIXME: this should also mark spans with equal (x,y)
1587    // This may be called when the segment is already marked done. While this
1588    // wastes time, it shouldn't do any more than spin through the T spans.
1589    // OPTIMIZATION: abort on first done found (assuming that this code is
1590    // always called to mark segments done).
1591    void markDone(int index, int winding) {
1592      //  SkASSERT(!done());
1593        double referenceT = fTs[index].fT;
1594        int lesser = index;
1595        while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
1596            Span& span = fTs[lesser];
1597            if (span.fDone) {
1598                continue;
1599            }
1600        #if DEBUG_MARK_DONE
1601            const SkPoint& pt = xyAtT(&span);
1602            SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
1603                    __FUNCTION__, fID, lesser, span.fT, pt.fX, pt.fY, winding);
1604        #endif
1605            span.fDone = true;
1606            SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
1607            span.fWindSum = winding;
1608            fDoneSpans++;
1609        }
1610        do {
1611            Span& span = fTs[index];
1612     //       SkASSERT(!span.fDone);
1613            if (span.fDone) {
1614                continue;
1615            }
1616        #if DEBUG_MARK_DONE
1617            const SkPoint& pt = xyAtT(&span);
1618            SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
1619                    __FUNCTION__, fID, index, span.fT, pt.fX, pt.fY, winding);
1620        #endif
1621            span.fDone = true;
1622            SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
1623            span.fWindSum = winding;
1624            fDoneSpans++;
1625        } while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
1626    }
1627
1628    void markWinding(int index, int winding) {
1629        SkASSERT(!done());
1630        double referenceT = fTs[index].fT;
1631        int lesser = index;
1632        while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
1633            Span& span = fTs[lesser];
1634            if (span.fDone) {
1635                continue;
1636            }
1637            SkASSERT(span.fWindValue == 1 || winding == 0);
1638            SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
1639        #if DEBUG_MARK_DONE
1640            const SkPoint& pt = xyAtT(&span);
1641            SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
1642                    __FUNCTION__, fID, lesser, span.fT, pt.fX, pt.fY, winding);
1643        #endif
1644            span.fWindSum = winding;
1645        }
1646        do {
1647            Span& span = fTs[index];
1648     //       SkASSERT(!span.fDone || span.fCoincident);
1649            if (span.fDone) {
1650                continue;
1651            }
1652            SkASSERT(span.fWindValue == 1 || winding == 0);
1653            SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
1654        #if DEBUG_MARK_DONE
1655            const SkPoint& pt = xyAtT(&span);
1656            SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
1657                    __FUNCTION__, fID, index, span.fT, pt.fX, pt.fY, winding);
1658        #endif
1659            span.fWindSum = winding;
1660        } while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
1661    }
1662
1663    // return span if when chasing, two or more radiating spans are not done
1664    // OPTIMIZATION: ? multiple spans is detected when there is only one valid
1665    // candidate and the remaining spans have windValue == 0 (canceled by
1666    // coincidence). The coincident edges could either be removed altogether,
1667    // or this code could be more complicated in detecting this case. Worth it?
1668    bool multipleSpans(int end) const {
1669        return end > 0 && end < fTs.count() - 1;
1670    }
1671
1672    // This has callers for two different situations: one establishes the end
1673    // of the current span, and one establishes the beginning of the next span
1674    // (thus the name). When this is looking for the end of the current span,
1675    // coincidence is found when the beginning Ts contain -step and the end
1676    // contains step. When it is looking for the beginning of the next, the
1677    // first Ts found can be ignored and the last Ts should contain -step.
1678    // OPTIMIZATION: probably should split into two functions
1679    int nextSpan(int from, int step) const {
1680        const Span& fromSpan = fTs[from];
1681        int count = fTs.count();
1682        int to = from;
1683        while (step > 0 ? ++to < count : --to >= 0) {
1684            const Span& span = fTs[to];
1685            if ((step > 0 ? span.fT - fromSpan.fT : fromSpan.fT - span.fT) < FLT_EPSILON) {
1686                continue;
1687            }
1688            return to;
1689        }
1690        return -1;
1691    }
1692
1693    const SkPoint* pts() const {
1694        return fPts;
1695    }
1696
1697    void reset() {
1698        init(NULL, (SkPath::Verb) -1);
1699        fBounds.set(SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, SK_ScalarMax);
1700        fTs.reset();
1701    }
1702
1703    // OPTIMIZATION: mark as debugging only if used solely by tests
1704    const Span& span(int tIndex) const {
1705        return fTs[tIndex];
1706    }
1707
1708    int spanSign(int startIndex, int endIndex) const {
1709        return startIndex < endIndex ? -fTs[startIndex].fWindValue :
1710                fTs[endIndex].fWindValue;
1711    }
1712
1713    // OPTIMIZATION: mark as debugging only if used solely by tests
1714    double t(int tIndex) const {
1715        return fTs[tIndex].fT;
1716    }
1717
1718    void updatePts(const SkPoint pts[]) {
1719        fPts = pts;
1720    }
1721
1722    SkPath::Verb verb() const {
1723        return fVerb;
1724    }
1725
1726    int windSum(int tIndex) const {
1727        return fTs[tIndex].fWindSum;
1728    }
1729
1730    int windSum(const Angle* angle) const {
1731        int start = angle->start();
1732        int end = angle->end();
1733        int index = SkMin32(start, end);
1734        return windSum(index);
1735    }
1736
1737    int windValue(int tIndex) const {
1738        return fTs[tIndex].fWindValue;
1739    }
1740
1741    int windValue(const Angle* angle) const {
1742        int start = angle->start();
1743        int end = angle->end();
1744        int index = SkMin32(start, end);
1745        return windValue(index);
1746    }
1747
1748    SkScalar xAtT(const Span* span) const {
1749        return xyAtT(span).fX;
1750    }
1751
1752    const SkPoint& xyAtT(int index) const {
1753        return xyAtT(&fTs[index]);
1754    }
1755
1756    const SkPoint& xyAtT(const Span* span) const {
1757        if (!span->fPt) {
1758            if (span->fT == 0) {
1759                span->fPt = &fPts[0];
1760            } else if (span->fT == 1) {
1761                span->fPt = &fPts[fVerb];
1762            } else {
1763                SkPoint* pt = fIntersections.append();
1764                (*SegmentXYAtT[fVerb])(fPts, span->fT, pt);
1765                span->fPt = pt;
1766            }
1767        }
1768        return *span->fPt;
1769    }
1770
1771    SkScalar yAtT(int index) const {
1772        return yAtT(&fTs[index]);
1773    }
1774
1775    SkScalar yAtT(const Span* span) const {
1776        return xyAtT(span).fY;
1777    }
1778
1779#if DEBUG_DUMP
1780    void dump() const {
1781        const char className[] = "Segment";
1782        const int tab = 4;
1783        for (int i = 0; i < fTs.count(); ++i) {
1784            SkPoint out;
1785            (*SegmentXYAtT[fVerb])(fPts, t(i), &out);
1786            SkDebugf("%*s [%d] %s.fTs[%d]=%1.9g (%1.9g,%1.9g) other=%d"
1787                    " otherT=%1.9g windSum=%d\n",
1788                    tab + sizeof(className), className, fID,
1789                    kLVerbStr[fVerb], i, fTs[i].fT, out.fX, out.fY,
1790                    fTs[i].fOther->fID, fTs[i].fOtherT, fTs[i].fWindSum);
1791        }
1792        SkDebugf("%*s [%d] fBounds=(l:%1.9g, t:%1.9g r:%1.9g, b:%1.9g)",
1793                tab + sizeof(className), className, fID,
1794                fBounds.fLeft, fBounds.fTop, fBounds.fRight, fBounds.fBottom);
1795    }
1796#endif
1797
1798#if DEBUG_ACTIVE_SPANS
1799    void debugShowActiveSpans(int contourID, int segmentIndex) {
1800        if (done()) {
1801            return;
1802        }
1803        for (int i = 0; i < fTs.count(); ++i) {
1804            if (fTs[i].fDone) {
1805                continue;
1806            }
1807            SkDebugf("%s contour=%d segment=%d (%d)", __FUNCTION__, contourID,
1808                     segmentIndex, fID);
1809            SkDebugf(" (%1.9g,%1.9g", fPts[0].fX, fPts[0].fY);
1810            for (int vIndex = 1; vIndex <= fVerb; ++vIndex) {
1811                SkDebugf(" %1.9g,%1.9g", fPts[vIndex].fX, fPts[vIndex].fY);
1812            }
1813            const Span* span = &fTs[i];
1814            SkDebugf(") fT=%d (%1.9g) (%1.9g,%1.9g)", i, fTs[i].fT,
1815                     xAtT(span), yAtT(i));
1816            const Segment* other = fTs[i].fOther;
1817            SkDebugf(" other=%d otherT=%1.9g otherIndex=%d", other->fID,
1818                     fTs[i].fOtherT, fTs[i].fOtherIndex);
1819            SkDebugf(" windSum=%d windValue=%d\n", fTs[i].fWindSum,
1820                     fTs[i].fWindValue);
1821        }
1822    }
1823#endif
1824
1825private:
1826    const SkPoint* fPts;
1827    SkPath::Verb fVerb;
1828    Bounds fBounds;
1829    SkTDArray<Span> fTs; // two or more (always includes t=0 t=1)
1830    // OPTIMIZATION:if intersections array is a pointer, the it could only
1831    // be allocated as needed instead of always initialized -- though maybe
1832    // the initialization is lightweight enough that it hardly matters
1833    mutable SkTDArray<SkPoint> fIntersections;
1834    int fDoneSpans; // used for quick check that segment is finished
1835#if DEBUG_DUMP
1836    int fID;
1837#endif
1838};
1839
1840class Contour;
1841
1842struct Coincidence {
1843    Contour* fContours[2];
1844    int fSegments[2];
1845    double fTs[2][2];
1846};
1847
1848class Contour {
1849public:
1850    Contour() {
1851        reset();
1852#if DEBUG_DUMP
1853        fID = ++gContourID;
1854#endif
1855    }
1856
1857    bool operator<(const Contour& rh) const {
1858        return fBounds.fTop == rh.fBounds.fTop
1859                ? fBounds.fLeft < rh.fBounds.fLeft
1860                : fBounds.fTop < rh.fBounds.fTop;
1861    }
1862
1863    void addCoincident(int index, Contour* other, int otherIndex,
1864            const Intersections& ts, bool swap) {
1865        Coincidence& coincidence = *fCoincidences.append();
1866        coincidence.fContours[0] = this;
1867        coincidence.fContours[1] = other;
1868        coincidence.fSegments[0] = index;
1869        coincidence.fSegments[1] = otherIndex;
1870        coincidence.fTs[swap][0] = ts.fT[0][0];
1871        coincidence.fTs[swap][1] = ts.fT[0][1];
1872        coincidence.fTs[!swap][0] = ts.fT[1][0];
1873        coincidence.fTs[!swap][1] = ts.fT[1][1];
1874    }
1875
1876    void addCross(const Contour* crosser) {
1877#ifdef DEBUG_CROSS
1878        for (int index = 0; index < fCrosses.count(); ++index) {
1879            SkASSERT(fCrosses[index] != crosser);
1880        }
1881#endif
1882        *fCrosses.append() = crosser;
1883    }
1884
1885    void addCubic(const SkPoint pts[4]) {
1886        fSegments.push_back().addCubic(pts);
1887        fContainsCurves = true;
1888    }
1889
1890    int addLine(const SkPoint pts[2]) {
1891        fSegments.push_back().addLine(pts);
1892        return fSegments.count();
1893    }
1894
1895    void addOtherT(int segIndex, int tIndex, double otherT, int otherIndex) {
1896        fSegments[segIndex].addOtherT(tIndex, otherT, otherIndex);
1897    }
1898
1899    int addQuad(const SkPoint pts[3]) {
1900        fSegments.push_back().addQuad(pts);
1901        fContainsCurves = true;
1902        return fSegments.count();
1903    }
1904
1905    int addT(int segIndex, double newT, Contour* other, int otherIndex) {
1906        containsIntercepts();
1907        return fSegments[segIndex].addT(newT, &other->fSegments[otherIndex]);
1908    }
1909
1910    const Bounds& bounds() const {
1911        return fBounds;
1912    }
1913
1914    void complete() {
1915        setBounds();
1916        fContainsIntercepts = false;
1917    }
1918
1919    void containsIntercepts() {
1920        fContainsIntercepts = true;
1921    }
1922
1923    const Segment* crossedSegment(const SkPoint& basePt, SkScalar& bestY,
1924            int &tIndex, double& hitT) {
1925        int segmentCount = fSegments.count();
1926        const Segment* bestSegment = NULL;
1927        for (int test = 0; test < segmentCount; ++test) {
1928            Segment* testSegment = &fSegments[test];
1929            const SkRect& bounds = testSegment->bounds();
1930            if (bounds.fTop < bestY) {
1931                continue;
1932            }
1933            if (bounds.fTop > basePt.fY) {
1934                continue;
1935            }
1936            if (bounds.fLeft > basePt.fX) {
1937                continue;
1938            }
1939            if (bounds.fRight < basePt.fX) {
1940                continue;
1941            }
1942            double testHitT;
1943            int testT = testSegment->crossedSpan(basePt, bestY, testHitT);
1944            if (testT >= 0) {
1945                bestSegment = testSegment;
1946                tIndex = testT;
1947                hitT = testHitT;
1948            }
1949        }
1950        return bestSegment;
1951    }
1952
1953    bool crosses(const Contour* crosser) const {
1954        if (this == crosser) {
1955            return true;
1956        }
1957        for (int index = 0; index < fCrosses.count(); ++index) {
1958            if (fCrosses[index] == crosser) {
1959                return true;
1960            }
1961        }
1962        return false;
1963    }
1964
1965    void findTooCloseToCall(int winding) {
1966        int segmentCount = fSegments.count();
1967        for (int sIndex = 0; sIndex < segmentCount; ++sIndex) {
1968            fSegments[sIndex].findTooCloseToCall(winding);
1969        }
1970    }
1971
1972    void fixOtherTIndex() {
1973        int segmentCount = fSegments.count();
1974        for (int sIndex = 0; sIndex < segmentCount; ++sIndex) {
1975            fSegments[sIndex].fixOtherTIndex();
1976        }
1977    }
1978
1979    void reset() {
1980        fSegments.reset();
1981        fBounds.set(SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, SK_ScalarMax);
1982        fContainsCurves = fContainsIntercepts = false;
1983        fWindingSum = SK_MinS32;
1984    }
1985
1986    void resolveCoincidence(int winding) {
1987        int count = fCoincidences.count();
1988        for (int index = 0; index < count; ++index) {
1989            Coincidence& coincidence = fCoincidences[index];
1990            Contour* thisContour = coincidence.fContours[0];
1991            Contour* otherContour = coincidence.fContours[1];
1992            int thisIndex = coincidence.fSegments[0];
1993            int otherIndex = coincidence.fSegments[1];
1994            Segment& thisOne = thisContour->fSegments[thisIndex];
1995            Segment& other = otherContour->fSegments[otherIndex];
1996            double startT = coincidence.fTs[0][0];
1997            double endT = coincidence.fTs[0][1];
1998            if (startT > endT) {
1999                SkTSwap<double>(startT, endT);
2000            }
2001            SkASSERT(endT - startT >= FLT_EPSILON);
2002            double oStartT = coincidence.fTs[1][0];
2003            double oEndT = coincidence.fTs[1][1];
2004            if (oStartT > oEndT) {
2005                SkTSwap<double>(oStartT, oEndT);
2006            }
2007            SkASSERT(oEndT - oStartT >= FLT_EPSILON);
2008            if (winding > 0 || thisOne.cancels(other)) {
2009                        // make sure startT and endT have t entries
2010                if (thisOne.isMissing(startT) || other.isMissing(oEndT)) {
2011                    thisOne.addTPair(startT, other, oEndT);
2012                }
2013                if (thisOne.isMissing(endT) || other.isMissing(oStartT)) {
2014                    other.addTPair(oStartT, thisOne, endT);
2015                }
2016                thisOne.addTCancel(startT, endT, other, oStartT, oEndT);
2017            } else {
2018                if (thisOne.isMissing(startT) || other.isMissing(oStartT)) {
2019                    thisOne.addTPair(startT, other, oStartT);
2020                }
2021                if (thisOne.isMissing(endT) || other.isMissing(oEndT)) {
2022                    other.addTPair(oEndT, thisOne, endT);
2023                }
2024                thisOne.addTCoincident(startT, endT, other, oStartT, oEndT);
2025            }
2026        }
2027    }
2028
2029    const SkTArray<Segment>& segments() {
2030        return fSegments;
2031    }
2032
2033    void setWinding(int winding) {
2034        SkASSERT(fWindingSum < 0);
2035        fWindingSum = winding;
2036    }
2037
2038    // OPTIMIZATION: feel pretty uneasy about this. It seems like once again
2039    // we need to sort and walk edges in y, but that on the surface opens the
2040    // same can of worms as before. But then, this is a rough sort based on
2041    // segments' top, and not a true sort, so it could be ameniable to regular
2042    // sorting instead of linear searching. Still feel like I'm missing something
2043    Segment* topSegment(SkScalar& bestY) {
2044        int segmentCount = fSegments.count();
2045        SkASSERT(segmentCount > 0);
2046        int best = -1;
2047        Segment* bestSegment = NULL;
2048        while (++best < segmentCount) {
2049            Segment* testSegment = &fSegments[best];
2050            if (testSegment->done()) {
2051                continue;
2052            }
2053            bestSegment = testSegment;
2054            break;
2055        }
2056        if (!bestSegment) {
2057            return NULL;
2058        }
2059        SkScalar bestTop = bestSegment->activeTop();
2060        for (int test = best + 1; test < segmentCount; ++test) {
2061            Segment* testSegment = &fSegments[test];
2062            if (testSegment->done()) {
2063                continue;
2064            }
2065            if (testSegment->bounds().fTop > bestTop) {
2066                continue;
2067            }
2068            SkScalar testTop = testSegment->activeTop();
2069            if (bestTop > testTop) {
2070                bestTop = testTop;
2071                bestSegment = testSegment;
2072            }
2073        }
2074        bestY = bestTop;
2075        return bestSegment;
2076    }
2077
2078    int updateSegment(int index, const SkPoint* pts) {
2079        Segment& segment = fSegments[index];
2080        segment.updatePts(pts);
2081        return segment.verb() + 1;
2082    }
2083
2084    int windSum() {
2085        if (fWindingSum >= 0) {
2086            return fWindingSum;
2087        }
2088        // check peers
2089        int count = fCrosses.count();
2090        for (int index = 0; index < count; ++index) {
2091            const Contour* crosser = fCrosses[index];
2092            if (0 <= crosser->fWindingSum) {
2093                fWindingSum = crosser->fWindingSum;
2094                break;
2095            }
2096        }
2097        return fWindingSum;
2098    }
2099
2100#if DEBUG_TEST
2101    SkTArray<Segment>& debugSegments() {
2102        return fSegments;
2103    }
2104#endif
2105
2106#if DEBUG_DUMP
2107    void dump() {
2108        int i;
2109        const char className[] = "Contour";
2110        const int tab = 4;
2111        SkDebugf("%s %p (contour=%d)\n", className, this, fID);
2112        for (i = 0; i < fSegments.count(); ++i) {
2113            SkDebugf("%*s.fSegments[%d]:\n", tab + sizeof(className),
2114                    className, i);
2115            fSegments[i].dump();
2116        }
2117        SkDebugf("%*s.fBounds=(l:%1.9g, t:%1.9g r:%1.9g, b:%1.9g)\n",
2118                tab + sizeof(className), className,
2119                fBounds.fLeft, fBounds.fTop,
2120                fBounds.fRight, fBounds.fBottom);
2121        SkDebugf("%*s.fContainsIntercepts=%d\n", tab + sizeof(className),
2122                className, fContainsIntercepts);
2123        SkDebugf("%*s.fContainsCurves=%d\n", tab + sizeof(className),
2124                className, fContainsCurves);
2125    }
2126#endif
2127
2128#if DEBUG_ACTIVE_SPANS
2129    void debugShowActiveSpans() {
2130        for (int index = 0; index < fSegments.count(); ++index) {
2131            fSegments[index].debugShowActiveSpans(fID, index);
2132        }
2133    }
2134#endif
2135
2136protected:
2137    void setBounds() {
2138        int count = fSegments.count();
2139        if (count == 0) {
2140            SkDebugf("%s empty contour\n", __FUNCTION__);
2141            SkASSERT(0);
2142            // FIXME: delete empty contour?
2143            return;
2144        }
2145        fBounds = fSegments.front().bounds();
2146        for (int index = 1; index < count; ++index) {
2147            fBounds.add(fSegments[index].bounds());
2148        }
2149    }
2150
2151private:
2152    SkTArray<Segment> fSegments;
2153    SkTDArray<Coincidence> fCoincidences;
2154    SkTDArray<const Contour*> fCrosses;
2155    Bounds fBounds;
2156    bool fContainsIntercepts;
2157    bool fContainsCurves;
2158    int fWindingSum; // initial winding number outside
2159#if DEBUG_DUMP
2160    int fID;
2161#endif
2162};
2163
2164class EdgeBuilder {
2165public:
2166
2167EdgeBuilder(const SkPath& path, SkTArray<Contour>& contours)
2168    : fPath(path)
2169    , fCurrentContour(NULL)
2170    , fContours(contours)
2171{
2172#if DEBUG_DUMP
2173    gContourID = 0;
2174    gSegmentID = 0;
2175#endif
2176    walk();
2177}
2178
2179protected:
2180
2181void complete() {
2182    if (fCurrentContour && fCurrentContour->segments().count()) {
2183        fCurrentContour->complete();
2184        fCurrentContour = NULL;
2185    }
2186}
2187
2188void walk() {
2189    // FIXME:remove once we can access path pts directly
2190    SkPath::RawIter iter(fPath); // FIXME: access path directly when allowed
2191    SkPoint pts[4];
2192    SkPath::Verb verb;
2193    do {
2194        verb = iter.next(pts);
2195        *fPathVerbs.append() = verb;
2196        if (verb == SkPath::kMove_Verb) {
2197            *fPathPts.append() = pts[0];
2198        } else if (verb >= SkPath::kLine_Verb && verb <= SkPath::kCubic_Verb) {
2199            fPathPts.append(verb, &pts[1]);
2200        }
2201    } while (verb != SkPath::kDone_Verb);
2202    // FIXME: end of section to remove once path pts are accessed directly
2203
2204    SkPath::Verb reducedVerb;
2205    uint8_t* verbPtr = fPathVerbs.begin();
2206    const SkPoint* pointsPtr = fPathPts.begin();
2207    const SkPoint* finalCurveStart = NULL;
2208    const SkPoint* finalCurveEnd = NULL;
2209    while ((verb = (SkPath::Verb) *verbPtr++) != SkPath::kDone_Verb) {
2210        switch (verb) {
2211            case SkPath::kMove_Verb:
2212                complete();
2213                if (!fCurrentContour) {
2214                    fCurrentContour = fContours.push_back_n(1);
2215                    finalCurveEnd = pointsPtr++;
2216                    *fExtra.append() = -1; // start new contour
2217                }
2218                continue;
2219            case SkPath::kLine_Verb:
2220                // skip degenerate points
2221                if (pointsPtr[-1].fX != pointsPtr[0].fX
2222                        || pointsPtr[-1].fY != pointsPtr[0].fY) {
2223                    fCurrentContour->addLine(&pointsPtr[-1]);
2224                }
2225                break;
2226            case SkPath::kQuad_Verb:
2227
2228                reducedVerb = QuadReduceOrder(&pointsPtr[-1], fReducePts);
2229                if (reducedVerb == 0) {
2230                    break; // skip degenerate points
2231                }
2232                if (reducedVerb == 1) {
2233                    *fExtra.append() =
2234                            fCurrentContour->addLine(fReducePts.end() - 2);
2235                    break;
2236                }
2237                fCurrentContour->addQuad(&pointsPtr[-1]);
2238                break;
2239            case SkPath::kCubic_Verb:
2240                reducedVerb = CubicReduceOrder(&pointsPtr[-1], fReducePts);
2241                if (reducedVerb == 0) {
2242                    break; // skip degenerate points
2243                }
2244                if (reducedVerb == 1) {
2245                    *fExtra.append() =
2246                            fCurrentContour->addLine(fReducePts.end() - 2);
2247                    break;
2248                }
2249                if (reducedVerb == 2) {
2250                    *fExtra.append() =
2251                            fCurrentContour->addQuad(fReducePts.end() - 3);
2252                    break;
2253                }
2254                fCurrentContour->addCubic(&pointsPtr[-1]);
2255                break;
2256            case SkPath::kClose_Verb:
2257                SkASSERT(fCurrentContour);
2258                if (finalCurveStart && finalCurveEnd
2259                        && *finalCurveStart != *finalCurveEnd) {
2260                    *fReducePts.append() = *finalCurveStart;
2261                    *fReducePts.append() = *finalCurveEnd;
2262                    *fExtra.append() =
2263                            fCurrentContour->addLine(fReducePts.end() - 2);
2264                }
2265                complete();
2266                continue;
2267            default:
2268                SkDEBUGFAIL("bad verb");
2269                return;
2270        }
2271        finalCurveStart = &pointsPtr[verb - 1];
2272        pointsPtr += verb;
2273        SkASSERT(fCurrentContour);
2274    }
2275    complete();
2276    if (fCurrentContour && !fCurrentContour->segments().count()) {
2277        fContours.pop_back();
2278    }
2279    // correct pointers in contours since fReducePts may have moved as it grew
2280    int cIndex = 0;
2281    int extraCount = fExtra.count();
2282    SkASSERT(extraCount == 0 || fExtra[0] == -1);
2283    int eIndex = 0;
2284    int rIndex = 0;
2285    while (++eIndex < extraCount) {
2286        int offset = fExtra[eIndex];
2287        if (offset < 0) {
2288            ++cIndex;
2289            continue;
2290        }
2291        fCurrentContour = &fContours[cIndex];
2292        rIndex += fCurrentContour->updateSegment(offset - 1,
2293                &fReducePts[rIndex]);
2294    }
2295    fExtra.reset(); // we're done with this
2296}
2297
2298private:
2299    const SkPath& fPath;
2300    SkTDArray<SkPoint> fPathPts; // FIXME: point directly to path pts instead
2301    SkTDArray<uint8_t> fPathVerbs; // FIXME: remove
2302    Contour* fCurrentContour;
2303    SkTArray<Contour>& fContours;
2304    SkTDArray<SkPoint> fReducePts; // segments created on the fly
2305    SkTDArray<int> fExtra; // -1 marks new contour, > 0 offsets into contour
2306};
2307
2308class Work {
2309public:
2310    enum SegmentType {
2311        kHorizontalLine_Segment = -1,
2312        kVerticalLine_Segment = 0,
2313        kLine_Segment = SkPath::kLine_Verb,
2314        kQuad_Segment = SkPath::kQuad_Verb,
2315        kCubic_Segment = SkPath::kCubic_Verb,
2316    };
2317
2318    void addCoincident(Work& other, const Intersections& ts, bool swap) {
2319        fContour->addCoincident(fIndex, other.fContour, other.fIndex, ts, swap);
2320    }
2321
2322    // FIXME: does it make sense to write otherIndex now if we're going to
2323    // fix it up later?
2324    void addOtherT(int index, double otherT, int otherIndex) {
2325        fContour->addOtherT(fIndex, index, otherT, otherIndex);
2326    }
2327
2328    // Avoid collapsing t values that are close to the same since
2329    // we walk ts to describe consecutive intersections. Since a pair of ts can
2330    // be nearly equal, any problems caused by this should be taken care
2331    // of later.
2332    // On the edge or out of range values are negative; add 2 to get end
2333    int addT(double newT, const Work& other) {
2334        return fContour->addT(fIndex, newT, other.fContour, other.fIndex);
2335    }
2336
2337    bool advance() {
2338        return ++fIndex < fLast;
2339    }
2340
2341    SkScalar bottom() const {
2342        return bounds().fBottom;
2343    }
2344
2345    const Bounds& bounds() const {
2346        return fContour->segments()[fIndex].bounds();
2347    }
2348
2349    const SkPoint* cubic() const {
2350        return fCubic;
2351    }
2352
2353    void init(Contour* contour) {
2354        fContour = contour;
2355        fIndex = 0;
2356        fLast = contour->segments().count();
2357    }
2358
2359    bool isAdjacent(const Work& next) {
2360        return fContour == next.fContour && fIndex + 1 == next.fIndex;
2361    }
2362
2363    bool isFirstLast(const Work& next) {
2364        return fContour == next.fContour && fIndex == 0
2365                && next.fIndex == fLast - 1;
2366    }
2367
2368    SkScalar left() const {
2369        return bounds().fLeft;
2370    }
2371
2372    void promoteToCubic() {
2373        fCubic[0] = pts()[0];
2374        fCubic[2] = pts()[1];
2375        fCubic[3] = pts()[2];
2376        fCubic[1].fX = (fCubic[0].fX + fCubic[2].fX * 2) / 3;
2377        fCubic[1].fY = (fCubic[0].fY + fCubic[2].fY * 2) / 3;
2378        fCubic[2].fX = (fCubic[3].fX + fCubic[2].fX * 2) / 3;
2379        fCubic[2].fY = (fCubic[3].fY + fCubic[2].fY * 2) / 3;
2380    }
2381
2382    const SkPoint* pts() const {
2383        return fContour->segments()[fIndex].pts();
2384    }
2385
2386    SkScalar right() const {
2387        return bounds().fRight;
2388    }
2389
2390    ptrdiff_t segmentIndex() const {
2391        return fIndex;
2392    }
2393
2394    SegmentType segmentType() const {
2395        const Segment& segment = fContour->segments()[fIndex];
2396        SegmentType type = (SegmentType) segment.verb();
2397        if (type != kLine_Segment) {
2398            return type;
2399        }
2400        if (segment.isHorizontal()) {
2401            return kHorizontalLine_Segment;
2402        }
2403        if (segment.isVertical()) {
2404            return kVerticalLine_Segment;
2405        }
2406        return kLine_Segment;
2407    }
2408
2409    bool startAfter(const Work& after) {
2410        fIndex = after.fIndex;
2411        return advance();
2412    }
2413
2414    SkScalar top() const {
2415        return bounds().fTop;
2416    }
2417
2418    SkPath::Verb verb() const {
2419        return fContour->segments()[fIndex].verb();
2420    }
2421
2422    SkScalar x() const {
2423        return bounds().fLeft;
2424    }
2425
2426    bool xFlipped() const {
2427        return x() != pts()[0].fX;
2428    }
2429
2430    SkScalar y() const {
2431        return bounds().fTop;
2432    }
2433
2434    bool yFlipped() const {
2435        return y() != pts()[0].fY;
2436    }
2437
2438protected:
2439    Contour* fContour;
2440    SkPoint fCubic[4];
2441    int fIndex;
2442    int fLast;
2443};
2444
2445#if DEBUG_ADD_INTERSECTING_TS
2446static void debugShowLineIntersection(int pts, const Work& wt,
2447        const Work& wn, const double wtTs[2], const double wnTs[2]) {
2448    if (!pts) {
2449        SkDebugf("%s no intersect (%1.9g,%1.9g %1.9g,%1.9g) (%1.9g,%1.9g %1.9g,%1.9g)\n",
2450                __FUNCTION__, wt.pts()[0].fX, wt.pts()[0].fY,
2451                wt.pts()[1].fX, wt.pts()[1].fY, wn.pts()[0].fX, wn.pts()[0].fY,
2452                wn.pts()[1].fX, wn.pts()[1].fY);
2453        return;
2454    }
2455    SkPoint wtOutPt, wnOutPt;
2456    LineXYAtT(wt.pts(), wtTs[0], &wtOutPt);
2457    LineXYAtT(wn.pts(), wnTs[0], &wnOutPt);
2458    SkDebugf("%s wtTs[0]=%g (%g,%g, %g,%g) (%g,%g)",
2459            __FUNCTION__,
2460            wtTs[0], wt.pts()[0].fX, wt.pts()[0].fY,
2461            wt.pts()[1].fX, wt.pts()[1].fY, wtOutPt.fX, wtOutPt.fY);
2462    if (pts == 2) {
2463        SkDebugf(" wtTs[1]=%g", wtTs[1]);
2464    }
2465    SkDebugf(" wnTs[0]=%g (%g,%g, %g,%g) (%g,%g)",
2466            wnTs[0], wn.pts()[0].fX, wn.pts()[0].fY,
2467            wn.pts()[1].fX, wn.pts()[1].fY, wnOutPt.fX, wnOutPt.fY);
2468    if (pts == 2) {
2469        SkDebugf(" wnTs[1]=%g", wnTs[1]);
2470    }
2471    SkDebugf("\n");
2472}
2473#else
2474static void debugShowLineIntersection(int , const Work& ,
2475        const Work& , const double [2], const double [2]) {
2476}
2477#endif
2478
2479static bool addIntersectTs(Contour* test, Contour* next) {
2480
2481    if (test != next) {
2482        if (test->bounds().fBottom < next->bounds().fTop) {
2483            return false;
2484        }
2485        if (!Bounds::Intersects(test->bounds(), next->bounds())) {
2486            return true;
2487        }
2488    }
2489    Work wt;
2490    wt.init(test);
2491    bool foundCommonContour = test == next;
2492    do {
2493        Work wn;
2494        wn.init(next);
2495        if (test == next && !wn.startAfter(wt)) {
2496            continue;
2497        }
2498        do {
2499            if (!Bounds::Intersects(wt.bounds(), wn.bounds())) {
2500                continue;
2501            }
2502            int pts;
2503            Intersections ts;
2504            bool swap = false;
2505            switch (wt.segmentType()) {
2506                case Work::kHorizontalLine_Segment:
2507                    swap = true;
2508                    switch (wn.segmentType()) {
2509                        case Work::kHorizontalLine_Segment:
2510                        case Work::kVerticalLine_Segment:
2511                        case Work::kLine_Segment: {
2512                            pts = HLineIntersect(wn.pts(), wt.left(),
2513                                    wt.right(), wt.y(), wt.xFlipped(), ts);
2514                            debugShowLineIntersection(pts, wt, wn,
2515                                    ts.fT[1], ts.fT[0]);
2516                            break;
2517                        }
2518                        case Work::kQuad_Segment: {
2519                            pts = HQuadIntersect(wn.pts(), wt.left(),
2520                                    wt.right(), wt.y(), wt.xFlipped(), ts);
2521                            break;
2522                        }
2523                        case Work::kCubic_Segment: {
2524                            pts = HCubicIntersect(wn.pts(), wt.left(),
2525                                    wt.right(), wt.y(), wt.xFlipped(), ts);
2526                            break;
2527                        }
2528                        default:
2529                            SkASSERT(0);
2530                    }
2531                    break;
2532                case Work::kVerticalLine_Segment:
2533                    swap = true;
2534                    switch (wn.segmentType()) {
2535                        case Work::kHorizontalLine_Segment:
2536                        case Work::kVerticalLine_Segment:
2537                        case Work::kLine_Segment: {
2538                            pts = VLineIntersect(wn.pts(), wt.top(),
2539                                    wt.bottom(), wt.x(), wt.yFlipped(), ts);
2540                            debugShowLineIntersection(pts, wt, wn,
2541                                    ts.fT[1], ts.fT[0]);
2542                            break;
2543                        }
2544                        case Work::kQuad_Segment: {
2545                            pts = VQuadIntersect(wn.pts(), wt.top(),
2546                                    wt.bottom(), wt.x(), wt.yFlipped(), ts);
2547                            break;
2548                        }
2549                        case Work::kCubic_Segment: {
2550                            pts = VCubicIntersect(wn.pts(), wt.top(),
2551                                    wt.bottom(), wt.x(), wt.yFlipped(), ts);
2552                            break;
2553                        }
2554                        default:
2555                            SkASSERT(0);
2556                    }
2557                    break;
2558                case Work::kLine_Segment:
2559                    switch (wn.segmentType()) {
2560                        case Work::kHorizontalLine_Segment:
2561                            pts = HLineIntersect(wt.pts(), wn.left(),
2562                                    wn.right(), wn.y(), wn.xFlipped(), ts);
2563                            debugShowLineIntersection(pts, wt, wn,
2564                                    ts.fT[1], ts.fT[0]);
2565                            break;
2566                        case Work::kVerticalLine_Segment:
2567                            pts = VLineIntersect(wt.pts(), wn.top(),
2568                                    wn.bottom(), wn.x(), wn.yFlipped(), ts);
2569                            debugShowLineIntersection(pts, wt, wn,
2570                                    ts.fT[1], ts.fT[0]);
2571                            break;
2572                        case Work::kLine_Segment: {
2573                            pts = LineIntersect(wt.pts(), wn.pts(), ts);
2574                            debugShowLineIntersection(pts, wt, wn,
2575                                    ts.fT[1], ts.fT[0]);
2576                            break;
2577                        }
2578                        case Work::kQuad_Segment: {
2579                            swap = true;
2580                            pts = QuadLineIntersect(wn.pts(), wt.pts(), ts);
2581                            break;
2582                        }
2583                        case Work::kCubic_Segment: {
2584                            swap = true;
2585                            pts = CubicLineIntersect(wn.pts(), wt.pts(), ts);
2586                            break;
2587                        }
2588                        default:
2589                            SkASSERT(0);
2590                    }
2591                    break;
2592                case Work::kQuad_Segment:
2593                    switch (wn.segmentType()) {
2594                        case Work::kHorizontalLine_Segment:
2595                            pts = HQuadIntersect(wt.pts(), wn.left(),
2596                                    wn.right(), wn.y(), wn.xFlipped(), ts);
2597                            break;
2598                        case Work::kVerticalLine_Segment:
2599                            pts = VQuadIntersect(wt.pts(), wn.top(),
2600                                    wn.bottom(), wn.x(), wn.yFlipped(), ts);
2601                            break;
2602                        case Work::kLine_Segment: {
2603                            pts = QuadLineIntersect(wt.pts(), wn.pts(), ts);
2604                            break;
2605                        }
2606                        case Work::kQuad_Segment: {
2607                            pts = QuadIntersect(wt.pts(), wn.pts(), ts);
2608                            break;
2609                        }
2610                        case Work::kCubic_Segment: {
2611                            wt.promoteToCubic();
2612                            pts = CubicIntersect(wt.cubic(), wn.pts(), ts);
2613                            break;
2614                        }
2615                        default:
2616                            SkASSERT(0);
2617                    }
2618                    break;
2619                case Work::kCubic_Segment:
2620                    switch (wn.segmentType()) {
2621                        case Work::kHorizontalLine_Segment:
2622                            pts = HCubicIntersect(wt.pts(), wn.left(),
2623                                    wn.right(), wn.y(), wn.xFlipped(), ts);
2624                            break;
2625                        case Work::kVerticalLine_Segment:
2626                            pts = VCubicIntersect(wt.pts(), wn.top(),
2627                                    wn.bottom(), wn.x(), wn.yFlipped(), ts);
2628                            break;
2629                        case Work::kLine_Segment: {
2630                            pts = CubicLineIntersect(wt.pts(), wn.pts(), ts);
2631                            break;
2632                        }
2633                        case Work::kQuad_Segment: {
2634                            wn.promoteToCubic();
2635                            pts = CubicIntersect(wt.pts(), wn.cubic(), ts);
2636                            break;
2637                        }
2638                        case Work::kCubic_Segment: {
2639                            pts = CubicIntersect(wt.pts(), wn.pts(), ts);
2640                            break;
2641                        }
2642                        default:
2643                            SkASSERT(0);
2644                    }
2645                    break;
2646                default:
2647                    SkASSERT(0);
2648            }
2649            if (!foundCommonContour && pts > 0) {
2650                test->addCross(next);
2651                next->addCross(test);
2652                foundCommonContour = true;
2653            }
2654            // in addition to recording T values, record matching segment
2655            if (pts == 2 && wn.segmentType() <= Work::kLine_Segment
2656                    && wt.segmentType() <= Work::kLine_Segment) {
2657                wt.addCoincident(wn, ts, swap);
2658                continue;
2659            }
2660            for (int pt = 0; pt < pts; ++pt) {
2661                SkASSERT(ts.fT[0][pt] >= 0 && ts.fT[0][pt] <= 1);
2662                SkASSERT(ts.fT[1][pt] >= 0 && ts.fT[1][pt] <= 1);
2663                int testTAt = wt.addT(ts.fT[swap][pt], wn);
2664                int nextTAt = wn.addT(ts.fT[!swap][pt], wt);
2665                wt.addOtherT(testTAt, ts.fT[!swap][pt], nextTAt);
2666                wn.addOtherT(nextTAt, ts.fT[swap][pt], testTAt);
2667            }
2668        } while (wn.advance());
2669    } while (wt.advance());
2670    return true;
2671}
2672
2673// resolve any coincident pairs found while intersecting, and
2674// see if coincidence is formed by clipping non-concident segments
2675static void coincidenceCheck(SkTDArray<Contour*>& contourList, int winding) {
2676    int contourCount = contourList.count();
2677    for (int cIndex = 0; cIndex < contourCount; ++cIndex) {
2678        Contour* contour = contourList[cIndex];
2679        contour->findTooCloseToCall(winding);
2680    }
2681    for (int cIndex = 0; cIndex < contourCount; ++cIndex) {
2682        Contour* contour = contourList[cIndex];
2683        contour->resolveCoincidence(winding);
2684    }
2685}
2686
2687// project a ray from the top of the contour up and see if it hits anything
2688// note: when we compute line intersections, we keep track of whether
2689// two contours touch, so we need only look at contours not touching this one.
2690// OPTIMIZATION: sort contourList vertically to avoid linear walk
2691static int innerContourCheck(SkTDArray<Contour*>& contourList,
2692        Contour* baseContour, const SkPoint& basePt) {
2693    int contourCount = contourList.count();
2694    int winding = 0;
2695    SkScalar bestY = SK_ScalarMin;
2696    for (int cTest = 0; cTest < contourCount; ++cTest) {
2697        Contour* contour = contourList[cTest];
2698        if (basePt.fY < contour->bounds().fTop) {
2699            continue;
2700        }
2701        if (bestY > contour->bounds().fBottom) {
2702            continue;
2703        }
2704        if (baseContour->crosses(contour)) {
2705           continue;
2706        }
2707        int tIndex;
2708        double tHit;
2709        const Segment* test = contour->crossedSegment(basePt, bestY, tIndex,
2710            tHit);
2711        if (!test) {
2712            continue;
2713        }
2714        // If the ray hit the end of a span, we need to construct the wheel of
2715        // angles to find the span closest to the ray -- even if there are just
2716        // two spokes on the wheel.
2717        if (tHit == test->t(tIndex)) {
2718            SkTDArray<Angle> angles;
2719            int end = test->nextSpan(tIndex, 1);
2720            if (end < 0) {
2721                end = test->nextSpan(tIndex, -1);
2722            }
2723            test->addTwoAngles(tIndex, end, angles);
2724     //       test->buildAnglesInner(tIndex, angles);
2725            test->buildAngles(tIndex, angles);
2726            SkTDArray<Angle*> sorted;
2727            sortAngles(angles, sorted);
2728            const Angle* angle = sorted[0];
2729            test = angle->segment();
2730            SkScalar testDx = (*SegmentDXAtT[test->verb()])(test->pts(), tHit);
2731            if (testDx == 0) {
2732                angle = *(sorted.end() - 1);
2733                test = angle->segment();
2734                SkASSERT((*SegmentDXAtT[test->verb()])(test->pts(), tHit) != 0);
2735            }
2736            tIndex = angle->start(); // lesser Y
2737            winding = test->windSum(SkMin32(tIndex, angle->end()));
2738    #if DEBUG_WINDING
2739           SkDebugf("%s 1 winding=%d\n", __FUNCTION__, winding);
2740    #endif
2741        } else {
2742            winding = test->windSum(tIndex);
2743    #if DEBUG_WINDING
2744            SkDebugf("%s 2 winding=%d\n", __FUNCTION__, winding);
2745    #endif
2746        }
2747        // see if a + change in T results in a +/- change in X (compute x'(T))
2748        SkScalar dx = (*SegmentDXAtT[test->verb()])(test->pts(), tHit);
2749    #if DEBUG_WINDING
2750        SkDebugf("%s dx=%1.9g\n", __FUNCTION__, dx);
2751    #endif
2752        SkASSERT(dx != 0);
2753        if (winding * dx > 0) { // if same signs, result is negative
2754            winding += dx > 0 ? -1 : 1;
2755    #if DEBUG_WINDING
2756            SkDebugf("%s 3 winding=%d\n", __FUNCTION__, winding);
2757    #endif
2758        }
2759    }
2760    baseContour->setWinding(winding);
2761    return winding;
2762}
2763
2764// OPTIMIZATION: not crazy about linear search here to find top active y.
2765// seems like we should break down and do the sort, or maybe sort each
2766// contours' segments?
2767// Once the segment array is built, there's no reason I can think of not to
2768// sort it in Y. hmmm
2769// FIXME: return the contour found to pass to inner contour check
2770static Segment* findTopContour(SkTDArray<Contour*>& contourList,
2771        Contour*& topContour) {
2772    int contourCount = contourList.count();
2773    int cIndex = 0;
2774    Segment* topStart;
2775    SkScalar bestY = SK_ScalarMax;
2776    Contour* contour;
2777    do {
2778        contour = contourList[cIndex];
2779        topStart = contour->topSegment(bestY);
2780    } while (!topStart && ++cIndex < contourCount);
2781    if (!topStart) {
2782        return NULL;
2783    }
2784    topContour = contour;
2785    while (++cIndex < contourCount) {
2786        contour = contourList[cIndex];
2787        if (bestY < contour->bounds().fTop) {
2788            continue;
2789        }
2790        SkScalar testY = SK_ScalarMax;
2791        Segment* test = contour->topSegment(testY);
2792        if (!test || bestY <= testY) {
2793            continue;
2794        }
2795        topContour = contour;
2796        topStart = test;
2797        bestY = testY;
2798    }
2799    return topStart;
2800}
2801
2802static Segment* findChase(SkTDArray<Span*>& chase, int& tIndex, int& endIndex) {
2803    while (chase.count()) {
2804        Span* span = chase[chase.count() - 1];
2805        const Span& backPtr = span->fOther->span(span->fOtherIndex);
2806        Segment* segment = backPtr.fOther;
2807        tIndex = backPtr.fOtherIndex;
2808        SkTDArray<Angle> angles;
2809        int done = 0;
2810        if (segment->activeAngle(tIndex, done, angles)) {
2811            Angle* last = angles.end() - 1;
2812            tIndex = last->start();
2813            endIndex = last->end();
2814            return last->segment();
2815        }
2816        if (done == angles.count()) {
2817            chase.pop(&span);
2818            continue;
2819        }
2820        SkTDArray<Angle*> sorted;
2821        sortAngles(angles, sorted);
2822        // find first angle, initialize winding to computed fWindSum
2823        int firstIndex = -1;
2824        const Angle* angle;
2825        int winding;
2826        do {
2827            angle = sorted[++firstIndex];
2828            winding = angle->segment()->windSum(angle);
2829        } while (winding == SK_MinS32);
2830        int firstSign = angle->sign();
2831        if (firstSign * winding > 0) {
2832            winding -= firstSign;
2833        }
2834        SkDebugf("%s firstSign=%d\n", __FUNCTION__, firstSign);
2835        // we care about first sign and whether wind sum indicates this
2836        // edge is inside or outside. Maybe need to pass span winding
2837        // or first winding or something into this function?
2838        // advance to first undone angle, then return it and winding
2839        // (to set whether edges are active or not)
2840        int nextIndex = firstIndex + 1;
2841        int angleCount = sorted.count();
2842        int lastIndex = firstIndex != 0 ? firstIndex : angleCount;
2843        do {
2844            SkASSERT(nextIndex != firstIndex);
2845            if (nextIndex == angleCount) {
2846                nextIndex = 0;
2847            }
2848            const Angle* angle = sorted[nextIndex];
2849            segment = angle->segment();
2850            int windValue = segment->windValue(angle);
2851            SkASSERT(windValue > 0);
2852            int maxWinding = winding;
2853            winding -= angle->sign() * windValue;
2854            if (maxWinding * winding < 0) {
2855                SkDebugf("%s flipped sign %d %d\n", __FUNCTION__, maxWinding, winding);
2856            }
2857            tIndex = angle->start();
2858            endIndex = angle->end();
2859            int lesser = SkMin32(tIndex, endIndex);
2860            const Span& nextSpan = segment->span(lesser);
2861            if (!nextSpan.fDone) {
2862            // FIXME: this be wrong. assign startWinding if edge is in
2863            // same direction. If the direction is opposite, winding to
2864            // assign is flipped sign or +/- 1?
2865                if (abs(maxWinding) < abs(winding)) {
2866                    maxWinding = winding;
2867                }
2868                segment->markWinding(lesser, maxWinding);
2869                break;
2870            }
2871        } while (++nextIndex != lastIndex);
2872        return segment;
2873    }
2874    return NULL;
2875}
2876
2877#if DEBUG_ACTIVE_SPANS
2878static void debugShowActiveSpans(SkTDArray<Contour*>& contourList) {
2879    for (int index = 0; index < contourList.count(); ++ index) {
2880        contourList[index]->debugShowActiveSpans();
2881    }
2882}
2883#endif
2884
2885// Each segment may have an inside or an outside. Segments contained within
2886// winding may have insides on either side, and form a contour that should be
2887// ignored. Segments that are coincident with opposing direction segments may
2888// have outsides on either side, and should also disappear.
2889// 'Normal' segments will have one inside and one outside. Subsequent connections
2890// when winding should follow the intersection direction. If more than one edge
2891// is an option, choose first edge that continues the inside.
2892    // since we start with leftmost top edge, we'll traverse through a
2893    // smaller angle counterclockwise to get to the next edge.
2894static void bridge(SkTDArray<Contour*>& contourList, SkPath& simple) {
2895    bool firstContour = true;
2896    do {
2897        Contour* topContour;
2898        Segment* topStart = findTopContour(contourList, topContour);
2899        if (!topStart) {
2900            break;
2901        }
2902        // Start at the top. Above the top is outside, below is inside.
2903        // follow edges to intersection by changing the index by direction.
2904        int index, endIndex;
2905        Segment* current = topStart->findTop(index, endIndex);
2906        int contourWinding;
2907        if (firstContour) {
2908            contourWinding = 0;
2909            firstContour = false;
2910        } else {
2911            const SkPoint& topPoint = current->xyAtT(endIndex);
2912            contourWinding = innerContourCheck(contourList, topContour, topPoint);
2913#if DEBUG_WINDING
2914            SkDebugf("%s contourWinding=%d\n", __FUNCTION__, contourWinding);
2915#endif
2916        }
2917        SkPoint lastPt;
2918        bool firstTime = true;
2919        int winding = contourWinding;
2920        int spanWinding = current->spanSign(index, endIndex);
2921     //   int firstWinding = contourWinding + spanWinding;
2922        // FIXME: needs work. While it works in limited situations, it does
2923        // not always compute winding correctly. Active should be removed and instead
2924        // the initial winding should be correctly passed in so that if the
2925        // inner contour is wound the same way, it never finds an accumulated
2926        // winding of zero. Inside 'find next', we need to look for transitions
2927        // other than zero when resolving sorted angles.
2928        SkTDArray<Span*> chaseArray;
2929        do {
2930            bool active = winding * spanWinding <= 0;
2931            const SkPoint* firstPt = NULL;
2932            do {
2933                SkASSERT(!current->done());
2934                int nextStart, nextEnd, flipped = 1;
2935                Segment* next = current->findNext(chaseArray,
2936                        winding + spanWinding, index,
2937                        endIndex, nextStart, nextEnd, flipped, firstTime);
2938                if (!next) {
2939                    break;
2940                }
2941                if (!firstPt) {
2942                    firstPt = &current->addMoveTo(index, simple, active);
2943                }
2944                lastPt = current->addCurveTo(index, endIndex, simple, active);
2945                current = next;
2946                index = nextStart;
2947                endIndex = nextEnd;
2948                spanWinding = SkSign32(spanWinding) * flipped * next->windValue(
2949                        SkMin32(nextStart, nextEnd));
2950        #if DEBUG_WINDING
2951                SkDebugf("%s spanWinding=%d\n", __FUNCTION__, spanWinding);
2952        #endif
2953                firstTime = false;
2954            } while (*firstPt != lastPt && (active || !current->done()));
2955            if (firstPt && active) {
2956        #if DEBUG_PATH_CONSTRUCTION
2957                SkDebugf("%s close\n", __FUNCTION__);
2958        #endif
2959                simple.close();
2960            }
2961            current = findChase(chaseArray, index, endIndex);
2962#if DEBUG_ACTIVE_SPANS
2963            debugShowActiveSpans(contourList);
2964#endif
2965            if (!current) {
2966                break;
2967            }
2968            int lesser = SkMin32(index, endIndex);
2969            spanWinding = current->windSum(lesser);
2970            int spanValue = current->windValue(lesser);
2971            SkASSERT(spanWinding != SK_MinS32);
2972            int spanSign = current->spanSign(index, endIndex);
2973        #if DEBUG_WINDING
2974            SkDebugf("%s spanWinding=%d spanSign=%d winding=%d spanValue=%d\n",
2975                    __FUNCTION__, spanWinding, spanSign, winding, spanValue);
2976        #endif
2977            if (spanWinding * spanSign < 0) {
2978        #if DEBUG_WINDING
2979                SkDebugf("%s spanWinding * spanSign < 0\n", __FUNCTION__);
2980        #endif
2981   //             SkTSwap<int>(index, endIndex);
2982            }
2983            if (abs(spanWinding) > spanValue) {
2984        #if DEBUG_WINDING
2985                SkDebugf("%s abs(spanWinding) > spanValue\n", __FUNCTION__);
2986        #endif
2987                winding = spanWinding;
2988                spanWinding = spanValue * SkSign32(spanWinding);
2989                winding -= spanWinding;
2990            }
2991        } while (true);
2992    } while (true);
2993}
2994
2995static void fixOtherTIndex(SkTDArray<Contour*>& contourList) {
2996    int contourCount = contourList.count();
2997    for (int cTest = 0; cTest < contourCount; ++cTest) {
2998        Contour* contour = contourList[cTest];
2999        contour->fixOtherTIndex();
3000    }
3001}
3002
3003static void makeContourList(SkTArray<Contour>& contours,
3004        SkTDArray<Contour*>& list) {
3005    int count = contours.count();
3006    if (count == 0) {
3007        return;
3008    }
3009    for (int index = 0; index < count; ++index) {
3010        *list.append() = &contours[index];
3011    }
3012    QSort<Contour>(list.begin(), list.end() - 1);
3013}
3014
3015void simplifyx(const SkPath& path, SkPath& simple) {
3016    // returns 1 for evenodd, -1 for winding, regardless of inverse-ness
3017    int winding = (path.getFillType() & 1) ? 1 : -1;
3018    simple.reset();
3019    simple.setFillType(SkPath::kEvenOdd_FillType);
3020
3021    // turn path into list of segments
3022    SkTArray<Contour> contours;
3023    // FIXME: add self-intersecting cubics' T values to segment
3024    EdgeBuilder builder(path, contours);
3025    SkTDArray<Contour*> contourList;
3026    makeContourList(contours, contourList);
3027    Contour** currentPtr = contourList.begin();
3028    if (!currentPtr) {
3029        return;
3030    }
3031    Contour** listEnd = contourList.end();
3032    // find all intersections between segments
3033    do {
3034        Contour** nextPtr = currentPtr;
3035        Contour* current = *currentPtr++;
3036        Contour* next;
3037        do {
3038            next = *nextPtr++;
3039        } while (addIntersectTs(current, next) && nextPtr != listEnd);
3040    } while (currentPtr != listEnd);
3041    // eat through coincident edges
3042    coincidenceCheck(contourList, winding);
3043    fixOtherTIndex(contourList);
3044    // construct closed contours
3045    bridge(contourList, simple);
3046}
3047
3048