Simplify.cpp revision 534aa5b9460639a09b9dc30d29e77782e44b8fff
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// An Edge is a Segment generated from a Span
21
22// FIXME: remove once debugging is complete
23#ifdef SK_DEBUG
24int gDebugMaxWindSum = SK_MaxS32;
25int gDebugMaxWindValue = SK_MaxS32;
26#endif
27
28#define DEBUG_UNUSED 0 // set to expose unused functions
29
30#if 01 // set to 1 for multiple thread -- no debugging
31
32const bool gRunTestsInOneThread = false;
33
34#define DEBUG_ACTIVE_SPANS 0
35#define DEBUG_ADD_INTERSECTING_TS 0
36#define DEBUG_ADD_T_PAIR 0
37#define DEBUG_CONCIDENT 0
38#define DEBUG_CROSS 0
39#define DEBUG_DUMP 0
40#define DEBUG_MARK_DONE 0
41#define DEBUG_PATH_CONSTRUCTION 0
42#define DEBUG_SORT 0
43#define DEBUG_WIND_BUMP 0
44#define DEBUG_WINDING 0
45
46#else
47
48const bool gRunTestsInOneThread = true;
49
50#define DEBUG_ACTIVE_SPANS 1
51#define DEBUG_ADD_INTERSECTING_TS 0
52#define DEBUG_ADD_T_PAIR 0
53#define DEBUG_CONCIDENT 0
54#define DEBUG_CROSS 0
55#define DEBUG_DUMP 1
56#define DEBUG_MARK_DONE 1
57#define DEBUG_PATH_CONSTRUCTION 1
58#define DEBUG_SORT 1
59#define DEBUG_WIND_BUMP 0
60#define DEBUG_WINDING 1
61
62#endif
63
64#if (DEBUG_ACTIVE_SPANS || DEBUG_CONCIDENT || DEBUG_SORT) && !DEBUG_DUMP
65#undef DEBUG_DUMP
66#define DEBUG_DUMP 1
67#endif
68
69#if DEBUG_DUMP
70static const char* kLVerbStr[] = {"", "line", "quad", "cubic"};
71// static const char* kUVerbStr[] = {"", "Line", "Quad", "Cubic"};
72static int gContourID;
73static int gSegmentID;
74#endif
75
76#ifndef DEBUG_TEST
77#define DEBUG_TEST 0
78#endif
79
80static int LineIntersect(const SkPoint a[2], const SkPoint b[2],
81        Intersections& intersections) {
82    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
83    const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
84    return intersect(aLine, bLine, intersections.fT[0], intersections.fT[1]);
85}
86
87static int QuadLineIntersect(const SkPoint a[3], const SkPoint b[2],
88        Intersections& intersections) {
89    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
90    const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
91    intersect(aQuad, bLine, intersections);
92    return intersections.fUsed;
93}
94
95static int CubicLineIntersect(const SkPoint a[2], const SkPoint b[3],
96        Intersections& intersections) {
97    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
98            {a[3].fX, a[3].fY}};
99    const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
100    return intersect(aCubic, bLine, intersections.fT[0], intersections.fT[1]);
101}
102
103static int QuadIntersect(const SkPoint a[3], const SkPoint b[3],
104        Intersections& intersections) {
105    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
106    const Quadratic bQuad = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}, {b[2].fX, b[2].fY}};
107    intersect(aQuad, bQuad, intersections);
108    return intersections.fUsed;
109}
110
111static int CubicIntersect(const SkPoint a[4], const SkPoint b[4],
112        Intersections& intersections) {
113    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
114            {a[3].fX, a[3].fY}};
115    const Cubic bCubic = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}, {b[2].fX, b[2].fY},
116            {b[3].fX, b[3].fY}};
117    intersect(aCubic, bCubic, intersections);
118    return intersections.fUsed;
119}
120
121static int HLineIntersect(const SkPoint a[2], SkScalar left, SkScalar right,
122        SkScalar y, bool flipped, Intersections& intersections) {
123    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
124    return horizontalIntersect(aLine, left, right, y, flipped, intersections);
125}
126
127static int HQuadIntersect(const SkPoint a[3], SkScalar left, SkScalar right,
128        SkScalar y, bool flipped, Intersections& intersections) {
129    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
130    return horizontalIntersect(aQuad, left, right, y, flipped, intersections);
131}
132
133static int HCubicIntersect(const SkPoint a[4], SkScalar left, SkScalar right,
134        SkScalar y, bool flipped, Intersections& intersections) {
135    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
136            {a[3].fX, a[3].fY}};
137    return horizontalIntersect(aCubic, left, right, y, flipped, intersections);
138}
139
140static int VLineIntersect(const SkPoint a[2], SkScalar top, SkScalar bottom,
141        SkScalar x, bool flipped, Intersections& intersections) {
142    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
143    return verticalIntersect(aLine, top, bottom, x, flipped, intersections);
144}
145
146static int VQuadIntersect(const SkPoint a[3], SkScalar top, SkScalar bottom,
147        SkScalar x, bool flipped, Intersections& intersections) {
148    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
149    return verticalIntersect(aQuad, top, bottom, x, flipped, intersections);
150}
151
152static int VCubicIntersect(const SkPoint a[4], SkScalar top, SkScalar bottom,
153        SkScalar x, bool flipped, Intersections& intersections) {
154    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
155            {a[3].fX, a[3].fY}};
156    return verticalIntersect(aCubic, top, bottom, x, flipped, intersections);
157}
158
159static int (* const VSegmentIntersect[])(const SkPoint [], SkScalar ,
160        SkScalar , SkScalar , bool , Intersections& ) = {
161    NULL,
162    VLineIntersect,
163    VQuadIntersect,
164    VCubicIntersect
165};
166
167static void LineXYAtT(const SkPoint a[2], double t, SkPoint* out) {
168    const _Line line = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
169    double x, y;
170    xy_at_t(line, t, x, y);
171    out->fX = SkDoubleToScalar(x);
172    out->fY = SkDoubleToScalar(y);
173}
174
175static void QuadXYAtT(const SkPoint a[3], double t, SkPoint* out) {
176    const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
177    double x, y;
178    xy_at_t(quad, t, x, y);
179    out->fX = SkDoubleToScalar(x);
180    out->fY = SkDoubleToScalar(y);
181}
182
183static void CubicXYAtT(const SkPoint a[4], double t, SkPoint* out) {
184    const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
185            {a[3].fX, a[3].fY}};
186    double x, y;
187    xy_at_t(cubic, t, x, y);
188    out->fX = SkDoubleToScalar(x);
189    out->fY = SkDoubleToScalar(y);
190}
191
192static void (* const SegmentXYAtT[])(const SkPoint [], double , SkPoint* ) = {
193    NULL,
194    LineXYAtT,
195    QuadXYAtT,
196    CubicXYAtT
197};
198
199static SkScalar LineXAtT(const SkPoint a[2], double t) {
200    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
201    double x;
202    xy_at_t(aLine, t, x, *(double*) 0);
203    return SkDoubleToScalar(x);
204}
205
206static SkScalar QuadXAtT(const SkPoint a[3], double t) {
207    const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
208    double x;
209    xy_at_t(quad, t, x, *(double*) 0);
210    return SkDoubleToScalar(x);
211}
212
213static SkScalar CubicXAtT(const SkPoint a[4], double t) {
214    const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
215            {a[3].fX, a[3].fY}};
216    double x;
217    xy_at_t(cubic, t, x, *(double*) 0);
218    return SkDoubleToScalar(x);
219}
220
221static SkScalar (* const SegmentXAtT[])(const SkPoint [], double ) = {
222    NULL,
223    LineXAtT,
224    QuadXAtT,
225    CubicXAtT
226};
227
228static SkScalar LineYAtT(const SkPoint a[2], double t) {
229    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
230    double y;
231    xy_at_t(aLine, t, *(double*) 0, y);
232    return SkDoubleToScalar(y);
233}
234
235static SkScalar QuadYAtT(const SkPoint a[3], double t) {
236    const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
237    double y;
238    xy_at_t(quad, t, *(double*) 0, y);
239    return SkDoubleToScalar(y);
240}
241
242static SkScalar CubicYAtT(const SkPoint a[4], double t) {
243    const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
244            {a[3].fX, a[3].fY}};
245    double y;
246    xy_at_t(cubic, t, *(double*) 0, y);
247    return SkDoubleToScalar(y);
248}
249
250static SkScalar (* const SegmentYAtT[])(const SkPoint [], double ) = {
251    NULL,
252    LineYAtT,
253    QuadYAtT,
254    CubicYAtT
255};
256
257static SkScalar LineDXAtT(const SkPoint a[2], double ) {
258    return a[1].fX - a[0].fX;
259}
260
261static SkScalar QuadDXAtT(const SkPoint a[3], double t) {
262    const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
263    double x;
264    dxdy_at_t(quad, t, x, *(double*) 0);
265    return SkDoubleToScalar(x);
266}
267
268static SkScalar CubicDXAtT(const SkPoint a[4], double t) {
269    const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
270            {a[3].fX, a[3].fY}};
271    double x;
272    dxdy_at_t(cubic, t, x, *(double*) 0);
273    return SkDoubleToScalar(x);
274}
275
276static SkScalar (* const SegmentDXAtT[])(const SkPoint [], double ) = {
277    NULL,
278    LineDXAtT,
279    QuadDXAtT,
280    CubicDXAtT
281};
282
283static void LineSubDivide(const SkPoint a[2], double startT, double endT,
284        SkPoint sub[2]) {
285    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
286    _Line dst;
287    sub_divide(aLine, 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}
293
294static void QuadSubDivide(const SkPoint a[3], double startT, double endT,
295        SkPoint sub[3]) {
296    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
297            {a[2].fX, a[2].fY}};
298    Quadratic dst;
299    sub_divide(aQuad, startT, endT, dst);
300    sub[0].fX = SkDoubleToScalar(dst[0].x);
301    sub[0].fY = SkDoubleToScalar(dst[0].y);
302    sub[1].fX = SkDoubleToScalar(dst[1].x);
303    sub[1].fY = SkDoubleToScalar(dst[1].y);
304    sub[2].fX = SkDoubleToScalar(dst[2].x);
305    sub[2].fY = SkDoubleToScalar(dst[2].y);
306}
307
308static void CubicSubDivide(const SkPoint a[4], double startT, double endT,
309        SkPoint sub[4]) {
310    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
311            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
312    Cubic dst;
313    sub_divide(aCubic, startT, endT, dst);
314    sub[0].fX = SkDoubleToScalar(dst[0].x);
315    sub[0].fY = SkDoubleToScalar(dst[0].y);
316    sub[1].fX = SkDoubleToScalar(dst[1].x);
317    sub[1].fY = SkDoubleToScalar(dst[1].y);
318    sub[2].fX = SkDoubleToScalar(dst[2].x);
319    sub[2].fY = SkDoubleToScalar(dst[2].y);
320    sub[3].fX = SkDoubleToScalar(dst[3].x);
321    sub[3].fY = SkDoubleToScalar(dst[3].y);
322}
323
324static void (* const SegmentSubDivide[])(const SkPoint [], double , double ,
325        SkPoint []) = {
326    NULL,
327    LineSubDivide,
328    QuadSubDivide,
329    CubicSubDivide
330};
331
332#if DEBUG_UNUSED
333static void QuadSubBounds(const SkPoint a[3], double startT, double endT,
334        SkRect& bounds) {
335    SkPoint dst[3];
336    QuadSubDivide(a, startT, endT, dst);
337    bounds.fLeft = bounds.fRight = dst[0].fX;
338    bounds.fTop = bounds.fBottom = dst[0].fY;
339    for (int index = 1; index < 3; ++index) {
340        bounds.growToInclude(dst[index].fX, dst[index].fY);
341    }
342}
343
344static void CubicSubBounds(const SkPoint a[4], double startT, double endT,
345        SkRect& bounds) {
346    SkPoint dst[4];
347    CubicSubDivide(a, startT, endT, dst);
348    bounds.fLeft = bounds.fRight = dst[0].fX;
349    bounds.fTop = bounds.fBottom = dst[0].fY;
350    for (int index = 1; index < 4; ++index) {
351        bounds.growToInclude(dst[index].fX, dst[index].fY);
352    }
353}
354#endif
355
356static SkPath::Verb QuadReduceOrder(const SkPoint a[3],
357        SkTDArray<SkPoint>& reducePts) {
358    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
359            {a[2].fX, a[2].fY}};
360    Quadratic dst;
361    int order = reduceOrder(aQuad, dst);
362    if (order == 3) {
363        return SkPath::kQuad_Verb;
364    }
365    for (int index = 0; index < order; ++index) {
366        SkPoint* pt = reducePts.append();
367        pt->fX = SkDoubleToScalar(dst[index].x);
368        pt->fY = SkDoubleToScalar(dst[index].y);
369    }
370    return (SkPath::Verb) (order - 1);
371}
372
373static SkPath::Verb CubicReduceOrder(const SkPoint a[4],
374        SkTDArray<SkPoint>& reducePts) {
375    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
376            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
377    Cubic dst;
378    int order = reduceOrder(aCubic, dst, kReduceOrder_QuadraticsAllowed);
379    if (order == 4) {
380        return SkPath::kCubic_Verb;
381    }
382    for (int index = 0; index < order; ++index) {
383        SkPoint* pt = reducePts.append();
384        pt->fX = SkDoubleToScalar(dst[index].x);
385        pt->fY = SkDoubleToScalar(dst[index].y);
386    }
387    return (SkPath::Verb) (order - 1);
388}
389
390static bool QuadIsLinear(const SkPoint a[3]) {
391    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
392            {a[2].fX, a[2].fY}};
393    return isLinear(aQuad, 0, 2);
394}
395
396static bool CubicIsLinear(const SkPoint a[4]) {
397    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
398            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
399    return isLinear(aCubic, 0, 3);
400}
401
402static SkScalar LineLeftMost(const SkPoint a[2], double startT, double endT) {
403    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
404    double x[2];
405    xy_at_t(aLine, startT, x[0], *(double*) 0);
406    xy_at_t(aLine, endT, x[1], *(double*) 0);
407    return SkMinScalar((float) x[0], (float) x[1]);
408}
409
410static SkScalar QuadLeftMost(const SkPoint a[3], double startT, double endT) {
411    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
412            {a[2].fX, a[2].fY}};
413    return (float) leftMostT(aQuad, startT, endT);
414}
415
416static SkScalar CubicLeftMost(const SkPoint a[4], double startT, double endT) {
417    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
418            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
419    return (float) leftMostT(aCubic, startT, endT);
420}
421
422static SkScalar (* const SegmentLeftMost[])(const SkPoint [], double , double) = {
423    NULL,
424    LineLeftMost,
425    QuadLeftMost,
426    CubicLeftMost
427};
428
429#if DEBUG_UNUSED
430static bool IsCoincident(const SkPoint a[2], const SkPoint& above,
431        const SkPoint& below) {
432    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
433    const _Line bLine = {{above.fX, above.fY}, {below.fX, below.fY}};
434    return implicit_matches_ulps(aLine, bLine, 32);
435}
436#endif
437
438class Segment;
439
440// sorting angles
441// given angles of {dx dy ddx ddy dddx dddy} sort them
442class Angle {
443public:
444    // FIXME: this is bogus for quads and cubics
445    // if the quads and cubics' line from end pt to ctrl pt are coincident,
446    // there's no obvious way to determine the curve ordering from the
447    // derivatives alone. In particular, if one quadratic's coincident tangent
448    // is longer than the other curve, the final control point can place the
449    // longer curve on either side of the shorter one.
450    // Using Bezier curve focus http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf
451    // may provide some help, but nothing has been figured out yet.
452    bool operator<(const Angle& rh) const {
453        if ((fDy < 0) ^ (rh.fDy < 0)) {
454            return fDy < 0;
455        }
456        if (fDy == 0 && rh.fDy == 0 && fDx != rh.fDx) {
457            return fDx < rh.fDx;
458        }
459        SkScalar cmp = fDx * rh.fDy - rh.fDx * fDy;
460        if (cmp) {
461            return cmp < 0;
462        }
463        if ((fDDy < 0) ^ (rh.fDDy < 0)) {
464            return fDDy < 0;
465        }
466        if (fDDy == 0 && rh.fDDy == 0 && fDDx != rh.fDDx) {
467            return fDDx < rh.fDDx;
468        }
469        cmp = fDDx * rh.fDDy - rh.fDDx * fDDy;
470        if (cmp) {
471            return cmp < 0;
472        }
473        if ((fDDDy < 0) ^ (rh.fDDDy < 0)) {
474            return fDDDy < 0;
475        }
476        if (fDDDy == 0 && rh.fDDDy == 0) {
477            return fDDDx < rh.fDDDx;
478        }
479        return fDDDx * rh.fDDDy < rh.fDDDx * fDDDy;
480    }
481
482    double dx() const {
483        return fDx;
484    }
485
486    double dy() const {
487        return fDy;
488    }
489
490    int end() const {
491        return fEnd;
492    }
493
494    bool firstBump(int sumWinding) const {
495        SkDebugf("%s sign=%d sumWinding=%d\n", __FUNCTION__, sign(), sumWinding);
496        return sign() * sumWinding > 0;
497    }
498
499    bool isHorizontal() const {
500        return fDy == 0 && fDDy == 0 && fDDDy == 0;
501    }
502
503    // since all angles share a point, this needs to know which point
504    // is the common origin, i.e., whether the center is at pts[0] or pts[verb]
505    // practically, this should only be called by addAngle
506    void set(const SkPoint* pts, SkPath::Verb verb, const Segment* segment,
507            int start, int end) {
508        SkASSERT(start != end);
509        fSegment = segment;
510        fStart = start;
511        fEnd = end;
512        fDx = pts[1].fX - pts[0].fX; // b - a
513        fDy = pts[1].fY - pts[0].fY;
514        if (verb == SkPath::kLine_Verb) {
515            fDDx = fDDy = fDDDx = fDDDy = 0;
516            return;
517        }
518        fDDx = pts[2].fX - pts[1].fX - fDx; // a - 2b + c
519        fDDy = pts[2].fY - pts[1].fY - fDy;
520        if (verb == SkPath::kQuad_Verb) {
521            fDDDx = fDDDy = 0;
522            return;
523        }
524        fDDDx = pts[3].fX + 3 * (pts[1].fX - pts[2].fX) - pts[0].fX;
525        fDDDy = pts[3].fY + 3 * (pts[1].fY - pts[2].fY) - pts[0].fY;
526    }
527
528    // noncoincident quads/cubics may have the same initial angle
529    // as lines, so must sort by derivatives as well
530    // if flatness turns out to be a reasonable way to sort, use the below:
531    void setFlat(const SkPoint* pts, SkPath::Verb verb, Segment* segment,
532            int start, int end) {
533        fSegment = segment;
534        fStart = start;
535        fEnd = end;
536        fDx = pts[1].fX - pts[0].fX; // b - a
537        fDy = pts[1].fY - pts[0].fY;
538        if (verb == SkPath::kLine_Verb) {
539            fDDx = fDDy = fDDDx = fDDDy = 0;
540            return;
541        }
542        if (verb == SkPath::kQuad_Verb) {
543            int uplsX = FloatAsInt(pts[2].fX - pts[1].fY - fDx);
544            int uplsY = FloatAsInt(pts[2].fY - pts[1].fY - fDy);
545            int larger = std::max(abs(uplsX), abs(uplsY));
546            int shift = 0;
547            double flatT;
548            SkPoint ddPt; // FIXME: get rid of copy (change fDD_ to point)
549            LineParameters implicitLine;
550            _Line tangent = {{pts[0].fX, pts[0].fY}, {pts[1].fX, pts[1].fY}};
551            implicitLine.lineEndPoints(tangent);
552            implicitLine.normalize();
553            while (larger > UlpsEpsilon * 1024) {
554                larger >>= 2;
555                ++shift;
556                flatT = 0.5 / (1 << shift);
557                QuadXYAtT(pts, flatT, &ddPt);
558                _Point _pt = {ddPt.fX, ddPt.fY};
559                double distance = implicitLine.pointDistance(_pt);
560                if (approximately_zero(distance)) {
561                    SkDebugf("%s ulps too small %1.9g\n", __FUNCTION__, distance);
562                    break;
563                }
564            }
565            flatT = 0.5 / (1 << shift);
566            QuadXYAtT(pts, flatT, &ddPt);
567            fDDx = ddPt.fX - pts[0].fX;
568            fDDy = ddPt.fY - pts[0].fY;
569            SkASSERT(fDDx != 0 || fDDy != 0);
570            fDDDx = fDDDy = 0;
571            return;
572        }
573        SkASSERT(0); // FIXME: add cubic case
574    }
575
576    Segment* segment() const {
577        return const_cast<Segment*>(fSegment);
578    }
579
580    int sign() const {
581        return SkSign32(fStart - fEnd);
582    }
583
584    int start() const {
585        return fStart;
586    }
587
588private:
589    SkScalar fDx;
590    SkScalar fDy;
591    SkScalar fDDx;
592    SkScalar fDDy;
593    SkScalar fDDDx;
594    SkScalar fDDDy;
595    const Segment* fSegment;
596    int fStart;
597    int fEnd;
598};
599
600static void sortAngles(SkTDArray<Angle>& angles, SkTDArray<Angle*>& angleList) {
601    int angleCount = angles.count();
602    int angleIndex;
603    angleList.setReserve(angleCount);
604    for (angleIndex = 0; angleIndex < angleCount; ++angleIndex) {
605        *angleList.append() = &angles[angleIndex];
606    }
607    QSort<Angle>(angleList.begin(), angleList.end() - 1);
608}
609
610// Bounds, unlike Rect, does not consider a line to be empty.
611struct Bounds : public SkRect {
612    static bool Intersects(const Bounds& a, const Bounds& b) {
613        return a.fLeft <= b.fRight && b.fLeft <= a.fRight &&
614                a.fTop <= b.fBottom && b.fTop <= a.fBottom;
615    }
616
617    void add(SkScalar left, SkScalar top, SkScalar right, SkScalar bottom) {
618        if (left < fLeft) {
619            fLeft = left;
620        }
621        if (top < fTop) {
622            fTop = top;
623        }
624        if (right > fRight) {
625            fRight = right;
626        }
627        if (bottom > fBottom) {
628            fBottom = bottom;
629        }
630    }
631
632    void add(const Bounds& toAdd) {
633        add(toAdd.fLeft, toAdd.fTop, toAdd.fRight, toAdd.fBottom);
634    }
635
636    bool isEmpty() {
637        return fLeft > fRight || fTop > fBottom
638                || fLeft == fRight && fTop == fBottom
639                || isnan(fLeft) || isnan(fRight)
640                || isnan(fTop) || isnan(fBottom);
641    }
642
643    void setCubicBounds(const SkPoint a[4]) {
644        _Rect dRect;
645        Cubic cubic  = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
646            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
647        dRect.setBounds(cubic);
648        set((float) dRect.left, (float) dRect.top, (float) dRect.right,
649                (float) dRect.bottom);
650    }
651
652    void setQuadBounds(const SkPoint a[3]) {
653        const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
654                {a[2].fX, a[2].fY}};
655        _Rect dRect;
656        dRect.setBounds(quad);
657        set((float) dRect.left, (float) dRect.top, (float) dRect.right,
658                (float) dRect.bottom);
659    }
660};
661
662struct Span {
663    Segment* fOther;
664    mutable SkPoint fPt; // lazily computed as needed
665    double fT;
666    double fOtherT; // value at fOther[fOtherIndex].fT
667    int fOtherIndex;  // can't be used during intersection
668    int fWindSum; // accumulated from contours surrounding this one
669    int fWindValue; // 0 == canceled; 1 == normal; >1 == coincident
670    bool fDone; // if set, this span to next higher T has been processed
671};
672
673class Segment {
674public:
675    Segment() {
676#if DEBUG_DUMP
677        fID = ++gSegmentID;
678#endif
679    }
680
681    bool activeAngle(int index, int& done, SkTDArray<Angle>& angles) const {
682        if (activeAngleInner(index, done, angles)) {
683            return true;
684        }
685        double referenceT = fTs[index].fT;
686        int lesser = index;
687        while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
688            if (activeAngleOther(lesser, done, angles)) {
689                return true;
690            }
691        }
692        do {
693            if (activeAngleOther(index, done, angles)) {
694                return true;
695            }
696        } while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
697        return false;
698    }
699
700    bool activeAngleOther(int index, int& done, SkTDArray<Angle>& angles) const {
701        Span* span = &fTs[index];
702        Segment* other = span->fOther;
703        int oIndex = span->fOtherIndex;
704        return other->activeAngleInner(oIndex, done, angles);
705    }
706
707    bool activeAngleInner(int index, int& done, SkTDArray<Angle>& angles) const {
708        int next = nextSpan(index, 1);
709        if (next > 0) {
710            const Span& upSpan = fTs[index];
711            if (upSpan.fWindValue) {
712                addAngle(angles, index, next);
713                if (upSpan.fDone) {
714                    done++;
715                } else if (upSpan.fWindSum != SK_MinS32) {
716                    return true;
717                }
718            }
719        }
720        int prev = nextSpan(index, -1);
721        // edge leading into junction
722        if (prev >= 0) {
723            const Span& downSpan = fTs[prev];
724            if (downSpan.fWindValue) {
725                addAngle(angles, index, prev);
726                if (downSpan.fDone) {
727                    done++;
728                 } else if (downSpan.fWindSum != SK_MinS32) {
729                    return true;
730                }
731            }
732        }
733        return false;
734    }
735
736    SkScalar activeTop() const {
737        SkASSERT(!done());
738        int count = fTs.count();
739        SkScalar result = SK_ScalarMax;
740        bool lastDone = true;
741        for (int index = 0; index < count; ++index) {
742            bool done = fTs[index].fDone;
743            if (!done || !lastDone) {
744                SkScalar y = yAtT(index);
745                if (result > y) {
746                    result = y;
747                }
748            }
749            lastDone = done;
750        }
751        SkASSERT(result < SK_ScalarMax);
752        return result;
753    }
754
755    void addAngle(SkTDArray<Angle>& angles, int start, int end) const {
756        SkASSERT(start != end);
757        SkPoint edge[4];
758        (*SegmentSubDivide[fVerb])(fPts, fTs[start].fT, fTs[end].fT, edge);
759        Angle* angle = angles.append();
760        angle->set(edge, fVerb, this, start, end);
761    }
762
763    void addCancelOutsides(const SkTDArray<double>& outsideTs, Segment& other,
764            double oEnd) {
765        int tIndex = -1;
766        int tCount = fTs.count();
767        int oIndex = -1;
768        int oCount = other.fTs.count();
769        double tStart = outsideTs[0];
770        double oStart = outsideTs[1];
771        do {
772            ++tIndex;
773        } while (tStart - fTs[tIndex].fT >= FLT_EPSILON && tIndex < tCount);
774        int tIndexStart = tIndex;
775        do {
776            ++oIndex;
777        } while (oStart - other.fTs[oIndex].fT >= FLT_EPSILON && oIndex < oCount);
778        int oIndexStart = oIndex;
779        double nextT;
780        do {
781            nextT = fTs[++tIndex].fT;
782        } while (nextT < 1 && nextT - tStart < FLT_EPSILON);
783        double oNextT;
784        do {
785            oNextT = other.fTs[++oIndex].fT;
786        } while (oNextT < 1 && oNextT - oStart < FLT_EPSILON);
787        // at this point, spans before and after are at:
788        //  fTs[tIndexStart - 1], fTs[tIndexStart], fTs[tIndex]
789        // if tIndexStart == 0, no prior span
790        // if nextT == 1, no following span
791
792        // advance the span with zero winding
793        // if the following span exists (not past the end, non-zero winding)
794        // connect the two edges
795        if (!fTs[tIndexStart].fWindValue) {
796            if (tIndexStart > 0 && fTs[tIndexStart - 1].fWindValue) {
797    #if DEBUG_CONCIDENT
798                SkDebugf("%s 1 this=%d other=%d t [%d] %1.9g (%1.9g,%1.9g)\n",
799                        __FUNCTION__, fID, other.fID, tIndexStart - 1,
800                        fTs[tIndexStart].fT, xyAtT(tIndexStart).fX,
801                        xyAtT(tIndexStart).fY);
802    #endif
803                addTPair(fTs[tIndexStart].fT, other, other.fTs[oIndex].fT);
804            }
805            if (nextT < 1 && fTs[tIndex].fWindValue) {
806    #if DEBUG_CONCIDENT
807                SkDebugf("%s 2 this=%d other=%d t [%d] %1.9g (%1.9g,%1.9g)\n",
808                        __FUNCTION__, fID, other.fID, tIndex,
809                        fTs[tIndex].fT, xyAtT(tIndex).fX,
810                        xyAtT(tIndex).fY);
811    #endif
812                addTPair(fTs[tIndex].fT, other, other.fTs[oIndexStart].fT);
813            }
814        } else {
815            SkASSERT(!other.fTs[oIndexStart].fWindValue);
816            if (oIndexStart > 0 && other.fTs[oIndexStart - 1].fWindValue) {
817    #if DEBUG_CONCIDENT
818                SkDebugf("%s 3 this=%d other=%d t [%d] %1.9g (%1.9g,%1.9g)\n",
819                        __FUNCTION__, fID, other.fID, oIndexStart - 1,
820                        other.fTs[oIndexStart].fT, other.xyAtT(oIndexStart).fX,
821                        other.xyAtT(oIndexStart).fY);
822                other.debugAddTPair(other.fTs[oIndexStart].fT, *this, fTs[tIndex].fT);
823    #endif
824            }
825            if (oNextT < 1 && other.fTs[oIndex].fWindValue) {
826    #if DEBUG_CONCIDENT
827                SkDebugf("%s 4 this=%d other=%d t [%d] %1.9g (%1.9g,%1.9g)\n",
828                        __FUNCTION__, fID, other.fID, oIndex,
829                        other.fTs[oIndex].fT, other.xyAtT(oIndex).fX,
830                        other.xyAtT(oIndex).fY);
831                other.debugAddTPair(other.fTs[oIndex].fT, *this, fTs[tIndexStart].fT);
832    #endif
833            }
834        }
835    }
836
837    void addCoinOutsides(const SkTDArray<double>& outsideTs, Segment& other,
838            double oEnd) {
839        // walk this to outsideTs[0]
840        // walk other to outsideTs[1]
841        // if either is > 0, add a pointer to the other, copying adjacent winding
842        int tIndex = -1;
843        int oIndex = -1;
844        double tStart = outsideTs[0];
845        double oStart = outsideTs[1];
846        do {
847            ++tIndex;
848        } while (tStart - fTs[tIndex].fT >= FLT_EPSILON);
849        do {
850            ++oIndex;
851        } while (oStart - other.fTs[oIndex].fT >= FLT_EPSILON);
852        if (tIndex > 0 || oIndex > 0) {
853            addTPair(tStart, other, oStart);
854        }
855        tStart = fTs[tIndex].fT;
856        oStart = other.fTs[oIndex].fT;
857        do {
858            double nextT;
859            do {
860                nextT = fTs[++tIndex].fT;
861            } while (nextT - tStart < FLT_EPSILON);
862            tStart = nextT;
863            do {
864                nextT = other.fTs[++oIndex].fT;
865            } while (nextT - oStart < FLT_EPSILON);
866            oStart = nextT;
867            if (tStart == 1 && oStart == 1) {
868                break;
869            }
870            addTPair(tStart, other, oStart);
871        } while (tStart < 1 && oStart < 1 && oEnd - oStart >= FLT_EPSILON);
872    }
873
874    void addCubic(const SkPoint pts[4]) {
875        init(pts, SkPath::kCubic_Verb);
876        fBounds.setCubicBounds(pts);
877    }
878
879    // FIXME: this needs to defer add for aligned consecutive line segments
880    SkPoint addCurveTo(int start, int end, SkPath& path, bool active) {
881        SkPoint edge[4];
882        // OPTIMIZE? if not active, skip remainder and return xy_at_t(end)
883        (*SegmentSubDivide[fVerb])(fPts, fTs[start].fT, fTs[end].fT, edge);
884        if (active) {
885    #if DEBUG_PATH_CONSTRUCTION
886            SkDebugf("%s %s (%1.9g,%1.9g)", __FUNCTION__,
887                    kLVerbStr[fVerb], edge[1].fX, edge[1].fY);
888            if (fVerb > 1) {
889                SkDebugf(" (%1.9g,%1.9g)", edge[2].fX, edge[2].fY);
890            }
891            if (fVerb > 2) {
892                SkDebugf(" (%1.9g,%1.9g)", edge[3].fX, edge[3].fY);
893            }
894            SkDebugf("\n");
895    #endif
896            switch (fVerb) {
897                case SkPath::kLine_Verb:
898                    path.lineTo(edge[1].fX, edge[1].fY);
899                    break;
900                case SkPath::kQuad_Verb:
901                    path.quadTo(edge[1].fX, edge[1].fY, edge[2].fX, edge[2].fY);
902                    break;
903                case SkPath::kCubic_Verb:
904                    path.cubicTo(edge[1].fX, edge[1].fY, edge[2].fX, edge[2].fY,
905                            edge[3].fX, edge[3].fY);
906                    break;
907            }
908        }
909        return edge[fVerb];
910    }
911
912    void addLine(const SkPoint pts[2]) {
913        init(pts, SkPath::kLine_Verb);
914        fBounds.set(pts, 2);
915    }
916
917    const SkPoint& addMoveTo(int tIndex, SkPath& path, bool active) {
918        const SkPoint& pt = xyAtT(tIndex);
919        if (active) {
920    #if DEBUG_PATH_CONSTRUCTION
921            SkDebugf("%s (%1.9g,%1.9g)\n", __FUNCTION__, pt.fX, pt.fY);
922    #endif
923            path.moveTo(pt.fX, pt.fY);
924        }
925        return pt;
926    }
927
928    // add 2 to edge or out of range values to get T extremes
929    void addOtherT(int index, double otherT, int otherIndex) {
930        Span& span = fTs[index];
931        span.fOtherT = otherT;
932        span.fOtherIndex = otherIndex;
933    }
934
935    void addQuad(const SkPoint pts[3]) {
936        init(pts, SkPath::kQuad_Verb);
937        fBounds.setQuadBounds(pts);
938    }
939
940    // Defer all coincident edge processing until
941    // after normal intersections have been computed
942
943// no need to be tricky; insert in normal T order
944// resolve overlapping ts when considering coincidence later
945
946    // add non-coincident intersection. Resulting edges are sorted in T.
947    int addT(double newT, Segment* other) {
948        // FIXME: in the pathological case where there is a ton of intercepts,
949        //  binary search?
950        int insertedAt = -1;
951        size_t tCount = fTs.count();
952        for (size_t index = 0; index < tCount; ++index) {
953            // OPTIMIZATION: if there are three or more identical Ts, then
954            // the fourth and following could be further insertion-sorted so
955            // that all the edges are clockwise or counterclockwise.
956            // This could later limit segment tests to the two adjacent
957            // neighbors, although it doesn't help with determining which
958            // circular direction to go in.
959            if (newT < fTs[index].fT) {
960                insertedAt = index;
961                break;
962            }
963        }
964        Span* span;
965        if (insertedAt >= 0) {
966            span = fTs.insert(insertedAt);
967        } else {
968            insertedAt = tCount;
969            span = fTs.append();
970        }
971        span->fT = newT;
972        span->fOther = other;
973        span->fPt.fX = SK_ScalarNaN;
974        span->fWindSum = SK_MinS32;
975        span->fWindValue = 1;
976        if ((span->fDone = newT == 1)) {
977            ++fDoneSpans;
978        }
979        return insertedAt;
980    }
981
982    // set spans from start to end to decrement by one
983    // note this walks other backwards
984    // FIMXE: there's probably an edge case that can be constructed where
985    // two span in one segment are separated by float epsilon on one span but
986    // not the other, if one segment is very small. For this
987    // case the counts asserted below may or may not be enough to separate the
988    // spans. Even if the counts work out, what if the spanw aren't correctly
989    // sorted? It feels better in such a case to match the span's other span
990    // pointer since both coincident segments must contain the same spans.
991    void addTCancel(double startT, double endT, Segment& other,
992            double oStartT, double oEndT) {
993        SkASSERT(endT - startT >= FLT_EPSILON);
994        SkASSERT(oEndT - oStartT >= FLT_EPSILON);
995        int index = 0;
996        while (startT - fTs[index].fT >= FLT_EPSILON) {
997            ++index;
998        }
999        int oIndex = other.fTs.count();
1000        while (other.fTs[--oIndex].fT - oEndT > -FLT_EPSILON)
1001            ;
1002        Span* test = &fTs[index];
1003        Span* oTest = &other.fTs[oIndex];
1004        SkTDArray<double> outsideTs;
1005        SkTDArray<double> oOutsideTs;
1006        do {
1007            bool decrement = test->fWindValue && oTest->fWindValue;
1008            bool track = test->fWindValue || oTest->fWindValue;
1009            Span* end = test;
1010            double startT = end->fT;
1011            double oStartT = oTest->fT;
1012            do {
1013                if (decrement) {
1014                    decrementSpan(end);
1015                } else if (track && end->fT < 1 && oStartT < 1) {
1016                    TrackOutside(outsideTs, end->fT, oStartT);
1017                }
1018                end = &fTs[++index];
1019            } while (end->fT - test->fT < FLT_EPSILON);
1020            Span* oTestStart = oTest;
1021            do {
1022                if (decrement) {
1023                    other.decrementSpan(oTestStart);
1024                } else if (track && oTestStart->fT < 1 && startT < 1) {
1025                    TrackOutside(oOutsideTs, oTestStart->fT, startT);
1026                }
1027                if (!oIndex) {
1028                    break;
1029                }
1030                oTestStart = &other.fTs[--oIndex];
1031            } while (oTest->fT - oTestStart->fT < FLT_EPSILON);
1032            test = end;
1033            oTest = oTestStart;
1034        } while (test->fT < endT - FLT_EPSILON);
1035        SkASSERT(!oIndex || oTest->fT <= oStartT - FLT_EPSILON);
1036        // FIXME: determine if canceled edges need outside ts added
1037        if (!done() && outsideTs.count()) {
1038            addCancelOutsides(outsideTs, other, oEndT);
1039        }
1040        if (!other.done() && oOutsideTs.count()) {
1041            other.addCancelOutsides(oOutsideTs, *this, endT);
1042        }
1043    }
1044
1045    // set spans from start to end to increment the greater by one and decrement
1046    // the lesser
1047    void addTCoincident(double startT, double endT, Segment& other,
1048            double oStartT, double oEndT) {
1049        SkASSERT(endT - startT >= FLT_EPSILON);
1050        SkASSERT(oEndT - oStartT >= FLT_EPSILON);
1051        int index = 0;
1052        while (startT - fTs[index].fT >= FLT_EPSILON) {
1053            ++index;
1054        }
1055        int oIndex = 0;
1056        while (oStartT - other.fTs[oIndex].fT >= FLT_EPSILON) {
1057            ++oIndex;
1058        }
1059        Span* test = &fTs[index];
1060        Span* oTest = &other.fTs[oIndex];
1061        SkTDArray<double> outsideTs;
1062        SkTDArray<double> xOutsideTs;
1063        SkTDArray<double> oOutsideTs;
1064        SkTDArray<double> oxOutsideTs;
1065        do {
1066            bool transfer = test->fWindValue && oTest->fWindValue;
1067            bool decrementOther = test->fWindValue >= oTest->fWindValue;
1068            Span* end = test;
1069            double startT = end->fT;
1070            int startIndex = index;
1071            double oStartT = oTest->fT;
1072            int oStartIndex = oIndex;
1073            do {
1074                if (transfer) {
1075                    if (decrementOther) {
1076                        SkASSERT(abs(end->fWindValue) <= gDebugMaxWindValue);
1077                        ++(end->fWindValue);
1078                    } else if (decrementSpan(end)) {
1079                        TrackOutside(outsideTs, end->fT, oStartT);
1080                    }
1081                } else if (oTest->fWindValue) {
1082                    SkASSERT(!decrementOther);
1083                    if (startIndex > 0 && fTs[startIndex - 1].fWindValue) {
1084                        TrackOutside(xOutsideTs, end->fT, oStartT);
1085                    }
1086                }
1087                end = &fTs[++index];
1088            } while (end->fT - test->fT < FLT_EPSILON);
1089            Span* oEnd = oTest;
1090            do {
1091                if (transfer) {
1092                    if (!decrementOther) {
1093                        SkASSERT(abs(oEnd->fWindValue) <= gDebugMaxWindValue);
1094                        ++(oEnd->fWindValue);
1095                    } else if (other.decrementSpan(oEnd)) {
1096                        TrackOutside(oOutsideTs, oEnd->fT, startT);
1097                    }
1098                } else if (test->fWindValue) {
1099                    SkASSERT(!decrementOther);
1100                    if (oStartIndex > 0 && other.fTs[oStartIndex - 1].fWindValue) {
1101                        SkASSERT(0); // track for later?
1102                    }
1103                }
1104                oEnd = &other.fTs[++oIndex];
1105            } while (oEnd->fT - oTest->fT < FLT_EPSILON);
1106            test = end;
1107            oTest = oEnd;
1108        } while (test->fT < endT - FLT_EPSILON);
1109        SkASSERT(oTest->fT < oEndT + FLT_EPSILON);
1110        SkASSERT(oTest->fT > oEndT - FLT_EPSILON);
1111        if (!done()) {
1112            if (outsideTs.count()) {
1113                addCoinOutsides(outsideTs, other, oEndT);
1114            }
1115            if (xOutsideTs.count()) {
1116                addCoinOutsides(xOutsideTs, other, oEndT);
1117            }
1118        }
1119        if (!other.done() && oOutsideTs.count()) {
1120            other.addCoinOutsides(oOutsideTs, *this, endT);
1121        }
1122    }
1123
1124    // FIXME: this doesn't prevent the same span from being added twice
1125    // fix in caller, assert here?
1126    void addTPair(double t, Segment& other, double otherT) {
1127        int tCount = fTs.count();
1128        for (int tIndex = 0; tIndex < tCount; ++tIndex) {
1129            const Span& span = fTs[tIndex];
1130            if (span.fT > t) {
1131                break;
1132            }
1133            if (span.fT == t && span.fOther == &other && span.fOtherT == otherT) {
1134#if DEBUG_ADD_T_PAIR
1135                SkDebugf("%s addTPair duplicate this=%d %1.9g other=%d %1.9g\n",
1136                        __FUNCTION__, fID, t, other.fID, otherT);
1137#endif
1138                return;
1139            }
1140        }
1141#if DEBUG_ADD_T_PAIR
1142        SkDebugf("%s addTPair this=%d %1.9g other=%d %1.9g\n",
1143                __FUNCTION__, fID, t, other.fID, otherT);
1144#endif
1145        int insertedAt = addT(t, &other);
1146        int otherInsertedAt = other.addT(otherT, this);
1147        addOtherT(insertedAt, otherT, otherInsertedAt);
1148        other.addOtherT(otherInsertedAt, t, insertedAt);
1149        Span& newSpan = fTs[insertedAt];
1150        if (insertedAt > 0) {
1151            const Span& lastSpan = fTs[insertedAt - 1];
1152            if (t - lastSpan.fT < FLT_EPSILON) {
1153                int tWind = lastSpan.fWindValue;
1154                newSpan.fWindValue = tWind;
1155                if (!tWind) {
1156                    newSpan.fDone = true;
1157                    ++fDoneSpans;
1158                }
1159            }
1160        }
1161        int oIndex = newSpan.fOtherIndex;
1162        if (oIndex > 0) {
1163            const Span& lastOther = other.fTs[oIndex - 1];
1164            if (otherT - lastOther.fT < FLT_EPSILON) {
1165                int oWind = lastOther.fWindValue;
1166                Span& otherSpan = other.fTs[oIndex];
1167                otherSpan.fWindValue = oWind;
1168                if (!oWind) {
1169                    otherSpan.fDone = true;
1170                    ++(other.fDoneSpans);
1171                }
1172            }
1173        }
1174    }
1175
1176    void addTwoAngles(int start, int end, SkTDArray<Angle>& angles) const {
1177        // add edge leading into junction
1178        if (fTs[SkMin32(end, start)].fWindValue > 0) {
1179            addAngle(angles, end, start);
1180        }
1181        // add edge leading away from junction
1182        int step = SkSign32(end - start);
1183        int tIndex = nextSpan(end, step);
1184        if (tIndex >= 0 && fTs[SkMin32(end, tIndex)].fWindValue > 0) {
1185            addAngle(angles, end, tIndex);
1186        }
1187    }
1188
1189    const Bounds& bounds() const {
1190        return fBounds;
1191    }
1192
1193    void buildAngles(int index, SkTDArray<Angle>& angles) const {
1194        double referenceT = fTs[index].fT;
1195        int lesser = index;
1196        while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
1197            buildAnglesInner(lesser, angles);
1198        }
1199        do {
1200            buildAnglesInner(index, angles);
1201        } while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
1202    }
1203
1204    void buildAnglesInner(int index, SkTDArray<Angle>& angles) const {
1205        Span* span = &fTs[index];
1206        Segment* other = span->fOther;
1207    // if there is only one live crossing, and no coincidence, continue
1208    // in the same direction
1209    // if there is coincidence, the only choice may be to reverse direction
1210        // find edge on either side of intersection
1211        int oIndex = span->fOtherIndex;
1212        // if done == -1, prior span has already been processed
1213        int step = 1;
1214        int next = other->nextSpan(oIndex, step);
1215        if (next < 0) {
1216            step = -step;
1217            next = other->nextSpan(oIndex, step);
1218        }
1219        // add candidate into and away from junction
1220        other->addTwoAngles(next, oIndex, angles);
1221    }
1222
1223    bool cancels(const Segment& other) const {
1224        SkASSERT(fVerb == SkPath::kLine_Verb);
1225        SkASSERT(other.fVerb == SkPath::kLine_Verb);
1226        SkPoint dxy = fPts[0] - fPts[1];
1227        SkPoint odxy = other.fPts[0] - other.fPts[1];
1228        return dxy.fX * odxy.fX < 0 || dxy.fY * odxy.fY < 0;
1229    }
1230
1231    // figure out if the segment's ascending T goes clockwise or not
1232    // not enough context to write this as shown
1233    // instead, add all segments meeting at the top
1234    // sort them using buildAngleList
1235    // find the first in the sort
1236    // see if ascendingT goes to top
1237    bool clockwise(int /* tIndex */) const {
1238        SkASSERT(0); // incomplete
1239        return false;
1240    }
1241
1242    int computeSum(int startIndex, int endIndex) {
1243        SkTDArray<Angle> angles;
1244        addTwoAngles(startIndex, endIndex, angles);
1245        buildAngles(endIndex, angles);
1246        SkTDArray<Angle*> sorted;
1247        sortAngles(angles, sorted);
1248        int angleCount = angles.count();
1249        const Angle* angle;
1250        const Segment* base;
1251        int winding;
1252        int firstIndex = 0;
1253        do {
1254            angle = sorted[firstIndex];
1255            base = angle->segment();
1256            winding = base->windSum(angle);
1257            if (winding != SK_MinS32) {
1258                break;
1259            }
1260            if (++firstIndex == angleCount) {
1261                return SK_MinS32;
1262            }
1263        } while (true);
1264        // turn winding into contourWinding
1265        int spanWinding = base->spanSign(angle->start(), angle->end());
1266        if (spanWinding * winding < 0) {
1267            winding += spanWinding;
1268        }
1269    #if DEBUG_SORT
1270        base->debugShowSort(sorted, firstIndex, winding);
1271    #endif
1272        int nextIndex = firstIndex + 1;
1273        int lastIndex = firstIndex != 0 ? firstIndex : angleCount;
1274        winding -= base->windBump(angle);
1275        do {
1276            if (nextIndex == angleCount) {
1277                nextIndex = 0;
1278            }
1279            angle = sorted[nextIndex];
1280            Segment* segment = angle->segment();
1281            int maxWinding = winding;
1282            winding -= segment->windBump(angle);
1283            if (segment->windSum(nextIndex) == SK_MinS32) {
1284                if (abs(maxWinding) < abs(winding) || maxWinding * winding < 0) {
1285                    maxWinding = winding;
1286                }
1287                segment->markAndChaseWinding(angle, maxWinding);
1288            }
1289        } while (++nextIndex != lastIndex);
1290        return windSum(SkMin32(startIndex, endIndex));
1291    }
1292
1293    int crossedSpan(const SkPoint& basePt, SkScalar& bestY, double& hitT) const {
1294        int bestT = -1;
1295        SkScalar top = bounds().fTop;
1296        SkScalar bottom = bounds().fBottom;
1297        int end = 0;
1298        do {
1299            int start = end;
1300            end = nextSpan(start, 1);
1301            if (fTs[start].fWindValue == 0) {
1302                continue;
1303            }
1304            SkPoint edge[4];
1305            // OPTIMIZE: wrap this so that if start==0 end==fTCount-1 we can
1306            // work with the original data directly
1307            (*SegmentSubDivide[fVerb])(fPts, fTs[start].fT, fTs[end].fT, edge);
1308            // intersect ray starting at basePt with edge
1309            Intersections intersections;
1310            int pts = (*VSegmentIntersect[fVerb])(edge, top, bottom, basePt.fX,
1311                    false, intersections);
1312            if (pts == 0) {
1313                continue;
1314            }
1315            if (pts > 1 && fVerb == SkPath::kLine_Verb) {
1316            // if the intersection is edge on, wait for another one
1317                continue;
1318            }
1319            SkASSERT(pts == 1); // FIXME: more code required to disambiguate
1320            SkPoint pt;
1321            double foundT = intersections.fT[0][0];
1322            (*SegmentXYAtT[fVerb])(fPts, foundT, &pt);
1323            if (bestY < pt.fY) {
1324                bestY = pt.fY;
1325                bestT = foundT < 1 ? start : end;
1326                hitT = fTs[start].fT + (fTs[end].fT - fTs[start].fT) * foundT;
1327            }
1328        } while (fTs[end].fT != 1);
1329        return bestT;
1330    }
1331
1332    bool crossedSpanHalves(const SkPoint& basePt, bool leftHalf, bool rightHalf) {
1333        // if a segment is connected to this one, consider it crossing
1334        int tIndex;
1335        if (fPts[0].fX == basePt.fX) {
1336            tIndex = 0;
1337            do {
1338                const Span& sSpan = fTs[tIndex];
1339                const Segment* sOther = sSpan.fOther;
1340                if (!sOther->fTs[sSpan.fOtherIndex].fWindValue) {
1341                    continue;
1342                }
1343                if (leftHalf ? sOther->fBounds.fLeft < basePt.fX
1344                        : sOther->fBounds.fRight > basePt.fX) {
1345                    return true;
1346                }
1347            } while (fTs[++tIndex].fT == 0);
1348        }
1349        if (fPts[fVerb].fX == basePt.fX) {
1350            tIndex = fTs.count() - 1;
1351            do {
1352                const Span& eSpan = fTs[tIndex];
1353                const Segment* eOther = eSpan.fOther;
1354                if (!eOther->fTs[eSpan.fOtherIndex].fWindValue) {
1355                    continue;
1356                }
1357                if (leftHalf ? eOther->fBounds.fLeft < basePt.fX
1358                        : eOther->fBounds.fRight > basePt.fX) {
1359                    return true;
1360                }
1361            } while (fTs[--tIndex].fT == 1);
1362        }
1363        return false;
1364    }
1365
1366    bool decrementSpan(Span* span) {
1367        SkASSERT(span->fWindValue > 0);
1368        if (--(span->fWindValue) == 0) {
1369            span->fDone = true;
1370            ++fDoneSpans;
1371            return true;
1372        }
1373        return false;
1374    }
1375
1376    bool done() const {
1377        SkASSERT(fDoneSpans <= fTs.count());
1378        return fDoneSpans == fTs.count();
1379    }
1380
1381    bool done(const Angle& angle) const {
1382        int start = angle.start();
1383        int end = angle.end();
1384        const Span& mSpan = fTs[SkMin32(start, end)];
1385        return mSpan.fDone;
1386    }
1387
1388    // so the span needs to contain the pairing info found here
1389    // this should include the winding computed for the edge, and
1390    //  what edge it connects to, and whether it is discarded
1391    //  (maybe discarded == abs(winding) > 1) ?
1392    // only need derivatives for duration of sorting, add a new struct
1393    // for pairings, remove extra spans that have zero length and
1394    //  reference an unused other
1395    // for coincident, the last span on the other may be marked done
1396    //  (always?)
1397
1398    // if loop is exhausted, contour may be closed.
1399    // FIXME: pass in close point so we can check for closure
1400
1401    // given a segment, and a sense of where 'inside' is, return the next
1402    // segment. If this segment has an intersection, or ends in multiple
1403    // segments, find the mate that continues the outside.
1404    // note that if there are multiples, but no coincidence, we can limit
1405    // choices to connections in the correct direction
1406
1407    // mark found segments as done
1408
1409    // start is the index of the beginning T of this edge
1410    // it is guaranteed to have an end which describes a non-zero length (?)
1411    // winding -1 means ccw, 1 means cw
1412    // firstFind allows coincident edges to be treated differently
1413    Segment* findNext(SkTDArray<Span*>& chase, bool firstFind, bool active,
1414            const int startIndex, const int endIndex, int& nextStart,
1415            int& nextEnd, int& winding, int& spanWinding) {
1416        int outerWinding = winding;
1417        int innerWinding = winding + spanWinding;
1418    #if DEBUG_WINDING
1419        SkDebugf("%s winding=%d spanWinding=%d outerWinding=%d innerWinding=%d\n",
1420                __FUNCTION__, winding, spanWinding, outerWinding, innerWinding);
1421    #endif
1422        if (abs(outerWinding) < abs(innerWinding)
1423                || outerWinding * innerWinding < 0) {
1424            outerWinding = innerWinding;
1425        }
1426        SkASSERT(startIndex != endIndex);
1427        int count = fTs.count();
1428        SkASSERT(startIndex < endIndex ? startIndex < count - 1
1429                : startIndex > 0);
1430        int step = SkSign32(endIndex - startIndex);
1431        int end = nextSpan(startIndex, step);
1432        SkASSERT(end >= 0);
1433        Span* endSpan = &fTs[end];
1434        Segment* other;
1435        if (isSimple(end)) {
1436        // mark the smaller of startIndex, endIndex done, and all adjacent
1437        // spans with the same T value (but not 'other' spans)
1438    #if DEBUG_WINDING
1439            SkDebugf("%s simple\n", __FUNCTION__);
1440    #endif
1441            markDone(SkMin32(startIndex, endIndex), outerWinding);
1442            other = endSpan->fOther;
1443            nextStart = endSpan->fOtherIndex;
1444            double startT = other->fTs[nextStart].fT;
1445            nextEnd = nextStart;
1446            do {
1447                nextEnd += step;
1448            } while (fabs(startT - other->fTs[nextEnd].fT) < FLT_EPSILON);
1449            SkASSERT(step < 0 ? nextEnd >= 0 : nextEnd < other->fTs.count());
1450            return other;
1451        }
1452        // more than one viable candidate -- measure angles to find best
1453        SkTDArray<Angle> angles;
1454        SkASSERT(startIndex - endIndex != 0);
1455        SkASSERT((startIndex - endIndex < 0) ^ (step < 0));
1456        addTwoAngles(startIndex, end, angles);
1457        buildAngles(end, angles);
1458        SkTDArray<Angle*> sorted;
1459        sortAngles(angles, sorted);
1460        int angleCount = angles.count();
1461        int firstIndex = findStartingEdge(sorted, startIndex, end);
1462        SkASSERT(firstIndex >= 0);
1463    #if DEBUG_SORT
1464        debugShowSort(sorted, firstIndex, winding);
1465    #endif
1466        SkASSERT(sorted[firstIndex]->segment() == this);
1467    #if DEBUG_WINDING
1468        SkDebugf("%s sign=%d\n", __FUNCTION__, sorted[firstIndex]->sign());
1469    #endif
1470        int sumWinding = winding - windBump(sorted[firstIndex]);
1471        int nextIndex = firstIndex + 1;
1472        int lastIndex = firstIndex != 0 ? firstIndex : angleCount;
1473        const Angle* foundAngle = NULL;
1474        bool foundDone = false;
1475        // iterate through the angle, and compute everyone's winding
1476        int toggleWinding = SK_MinS32;
1477        bool flipFound = false;
1478        int flipped = 1;
1479        Segment* nextSegment;
1480        do {
1481            if (nextIndex == angleCount) {
1482                nextIndex = 0;
1483            }
1484            const Angle* nextAngle = sorted[nextIndex];
1485            int maxWinding = sumWinding;
1486            nextSegment = nextAngle->segment();
1487            sumWinding -= nextSegment->windBump(nextAngle);
1488            SkASSERT(abs(sumWinding) <= gDebugMaxWindSum);
1489    #if DEBUG_WINDING
1490            SkDebugf("%s maxWinding=%d sumWinding=%d sign=%d\n", __FUNCTION__,
1491                    maxWinding, sumWinding, nextAngle->sign());
1492    #endif
1493            if (maxWinding * sumWinding < 0) {
1494                flipFound ^= true;
1495    #if DEBUG_WINDING
1496                SkDebugf("%s flipFound=%d maxWinding=%d sumWinding=%d\n",
1497                        __FUNCTION__, flipFound, maxWinding, sumWinding);
1498    #endif
1499            }
1500            if (!sumWinding) {
1501                if (!active) {
1502                    markDone(SkMin32(startIndex, endIndex), outerWinding);
1503                    nextSegment->markWinding(SkMin32(nextAngle->start(),
1504                                nextAngle->end()), maxWinding);
1505    #if DEBUG_WINDING
1506                    SkDebugf("%s inactive\n", __FUNCTION__);
1507    #endif
1508                    return NULL;
1509                }
1510                if (!foundAngle || foundDone) {
1511                    foundAngle = nextAngle;
1512                    foundDone = nextSegment->done(*nextAngle);
1513                    if (flipFound || (maxWinding * outerWinding < 0)) {
1514                        flipped = -flipped;
1515            #if DEBUG_WINDING
1516                        SkDebugf("%s flipped=%d flipFound=%d maxWinding=%d"
1517                                " outerWinding=%d\n", __FUNCTION__, flipped,
1518                                flipFound, maxWinding, outerWinding);
1519            #endif
1520                    }
1521                }
1522                continue;
1523            }
1524            if (!maxWinding && !foundAngle) {
1525        #if DEBUG_WINDING
1526                if (flipped > 0) {
1527                    SkDebugf("%s sumWinding=%d * outerWinding=%d < 0 (%s)\n",
1528                            __FUNCTION__, sumWinding, outerWinding,
1529                            sumWinding * outerWinding < 0 ? "true" : "false");
1530                }
1531        #endif
1532                if (sumWinding * outerWinding < 0 && flipped > 0) {
1533        #if DEBUG_WINDING
1534                    SkDebugf("%s toggleWinding=%d\n", __FUNCTION__, sumWinding);
1535        #endif
1536                    toggleWinding = sumWinding;
1537                } else if (outerWinding != sumWinding) {
1538        #if DEBUG_WINDING
1539                    SkDebugf("%s outerWinding=%d != sumWinding=%d winding=%d\n",
1540                            __FUNCTION__, outerWinding, sumWinding, winding);
1541        #endif
1542                    winding = sumWinding;
1543                }
1544                foundAngle = nextAngle;
1545                if (flipFound) {
1546                    flipped = -flipped;
1547        #if DEBUG_WINDING
1548                    SkDebugf("%s flipped flipFound=%d\n", __FUNCTION__, flipFound);
1549        #endif
1550                }
1551            }
1552            if (nextSegment->done()) {
1553                continue;
1554            }
1555            // if the winding is non-zero, nextAngle does not connect to
1556            // current chain. If we haven't done so already, mark the angle
1557            // as done, record the winding value, and mark connected unambiguous
1558            // segments as well.
1559            if (nextSegment->windSum(nextAngle) == SK_MinS32) {
1560                if (abs(maxWinding) < abs(sumWinding)
1561                        || maxWinding * sumWinding < 0) {
1562                    maxWinding = sumWinding;
1563                }
1564                Span* last;
1565                if (foundAngle) {
1566                    last = nextSegment->markAndChaseWinding(nextAngle, maxWinding);
1567                } else {
1568                    last = nextSegment->markAndChaseDone(nextAngle, maxWinding);
1569                }
1570                if (last) {
1571                    *chase.append() = last;
1572                }
1573            }
1574        } while (++nextIndex != lastIndex);
1575        SkASSERT(sorted[firstIndex]->segment() == this);
1576        markDone(SkMin32(startIndex, endIndex), outerWinding);
1577        if (!foundAngle) {
1578            return NULL;
1579        }
1580        nextStart = foundAngle->start();
1581        nextEnd = foundAngle->end();
1582        nextSegment = foundAngle->segment();
1583        spanWinding = SkSign32(spanWinding) * flipped * nextSegment->windValue(
1584                SkMin32(nextStart, nextEnd));
1585        if (toggleWinding != SK_MinS32) {
1586            winding = toggleWinding;
1587            spanWinding = -spanWinding;
1588        }
1589    #if DEBUG_WINDING
1590        SkDebugf("%s spanWinding=%d\n", __FUNCTION__, spanWinding);
1591    #endif
1592        return nextSegment;
1593    }
1594
1595    int findStartingEdge(SkTDArray<Angle*>& sorted, int start, int end) {
1596        int angleCount = sorted.count();
1597        int firstIndex = -1;
1598        for (int angleIndex = 0; angleIndex < angleCount; ++angleIndex) {
1599            const Angle* angle = sorted[angleIndex];
1600            if (angle->segment() == this && angle->start() == end &&
1601                    angle->end() == start) {
1602                firstIndex = angleIndex;
1603                break;
1604            }
1605        }
1606        return firstIndex;
1607    }
1608
1609    // FIXME: this is tricky code; needs its own unit test
1610    void findTooCloseToCall(int /* winding */ ) { // FIXME: winding should be considered
1611        int count = fTs.count();
1612        if (count < 3) { // require t=0, x, 1 at minimum
1613            return;
1614        }
1615        int matchIndex = 0;
1616        int moCount;
1617        Span* match;
1618        Segment* mOther;
1619        do {
1620            match = &fTs[matchIndex];
1621            mOther = match->fOther;
1622            moCount = mOther->fTs.count();
1623            if (moCount >= 3) {
1624                break;
1625            }
1626            if (++matchIndex >= count) {
1627                return;
1628            }
1629        } while (true); // require t=0, x, 1 at minimum
1630        // OPTIMIZATION: defer matchPt until qualifying toCount is found?
1631        const SkPoint* matchPt = &xyAtT(match);
1632        // look for a pair of nearby T values that map to the same (x,y) value
1633        // if found, see if the pair of other segments share a common point. If
1634        // so, the span from here to there is coincident.
1635        for (int index = matchIndex + 1; index < count; ++index) {
1636            Span* test = &fTs[index];
1637            if (test->fDone) {
1638                continue;
1639            }
1640            Segment* tOther = test->fOther;
1641            int toCount = tOther->fTs.count();
1642            if (toCount < 3) { // require t=0, x, 1 at minimum
1643                continue;
1644            }
1645            const SkPoint* testPt = &xyAtT(test);
1646            if (*matchPt != *testPt) {
1647                matchIndex = index;
1648                moCount = toCount;
1649                match = test;
1650                mOther = tOther;
1651                matchPt = testPt;
1652                continue;
1653            }
1654            int moStart = -1;
1655            int moEnd = -1;
1656            double moStartT, moEndT;
1657            for (int moIndex = 0; moIndex < moCount; ++moIndex) {
1658                Span& moSpan = mOther->fTs[moIndex];
1659                if (moSpan.fDone) {
1660                    continue;
1661                }
1662                if (moSpan.fOther == this) {
1663                    if (moSpan.fOtherT == match->fT) {
1664                        moStart = moIndex;
1665                        moStartT = moSpan.fT;
1666                    }
1667                    continue;
1668                }
1669                if (moSpan.fOther == tOther) {
1670                    SkASSERT(moEnd == -1);
1671                    moEnd = moIndex;
1672                    moEndT = moSpan.fT;
1673                }
1674            }
1675            if (moStart < 0 || moEnd < 0) {
1676                continue;
1677            }
1678            // FIXME: if moStartT, moEndT are initialized to NaN, can skip this test
1679            if (moStartT == moEndT) {
1680                continue;
1681            }
1682            int toStart = -1;
1683            int toEnd = -1;
1684            double toStartT, toEndT;
1685            for (int toIndex = 0; toIndex < toCount; ++toIndex) {
1686                Span& toSpan = tOther->fTs[toIndex];
1687                if (toSpan.fOther == this) {
1688                    if (toSpan.fOtherT == test->fT) {
1689                        toStart = toIndex;
1690                        toStartT = toSpan.fT;
1691                    }
1692                    continue;
1693                }
1694                if (toSpan.fOther == mOther && toSpan.fOtherT == moEndT) {
1695                    SkASSERT(toEnd == -1);
1696                    toEnd = toIndex;
1697                    toEndT = toSpan.fT;
1698                }
1699            }
1700            // FIXME: if toStartT, toEndT are initialized to NaN, can skip this test
1701            if (toStart <= 0 || toEnd <= 0) {
1702                continue;
1703            }
1704            if (toStartT == toEndT) {
1705                continue;
1706            }
1707            // test to see if the segment between there and here is linear
1708            if (!mOther->isLinear(moStart, moEnd)
1709                    || !tOther->isLinear(toStart, toEnd)) {
1710                continue;
1711            }
1712            // FIXME: defer implementation until the rest works
1713            // this may share code with regular coincident detection
1714            SkASSERT(0);
1715        #if 0
1716            if (flipped) {
1717                mOther->addTCancel(moStart, moEnd, tOther, tStart, tEnd);
1718            } else {
1719                mOther->addTCoincident(moStart, moEnd, tOther, tStart, tEnd);
1720            }
1721        #endif
1722        }
1723    }
1724
1725    // OPTIMIZATION : for a pair of lines, can we compute points at T (cached)
1726    // and use more concise logic like the old edge walker code?
1727    // FIXME: this needs to deal with coincident edges
1728    Segment* findTop(int& tIndex, int& endIndex) {
1729        // iterate through T intersections and return topmost
1730        // topmost tangent from y-min to first pt is closer to horizontal
1731        SkASSERT(!done());
1732        int firstT;
1733        int lastT;
1734        SkPoint topPt;
1735        topPt.fY = SK_ScalarMax;
1736        int count = fTs.count();
1737        // see if either end is not done since we want smaller Y of the pair
1738        bool lastDone = true;
1739        for (int index = 0; index < count; ++index) {
1740            const Span& span = fTs[index];
1741            if (!span.fDone || !lastDone) {
1742                const SkPoint& intercept = xyAtT(&span);
1743                if (topPt.fY > intercept.fY || (topPt.fY == intercept.fY
1744                        && topPt.fX > intercept.fX)) {
1745                    topPt = intercept;
1746                    firstT = lastT = index;
1747                } else if (topPt == intercept) {
1748                    lastT = index;
1749                }
1750            }
1751            lastDone = span.fDone;
1752        }
1753        // sort the edges to find the leftmost
1754        int step = 1;
1755        int end = nextSpan(firstT, step);
1756        if (end == -1) {
1757            step = -1;
1758            end = nextSpan(firstT, step);
1759            SkASSERT(end != -1);
1760        }
1761        // if the topmost T is not on end, or is three-way or more, find left
1762        // look for left-ness from tLeft to firstT (matching y of other)
1763        SkTDArray<Angle> angles;
1764        SkASSERT(firstT - end != 0);
1765        addTwoAngles(end, firstT, angles);
1766        buildAngles(firstT, angles);
1767        SkTDArray<Angle*> sorted;
1768        sortAngles(angles, sorted);
1769        // skip edges that have already been processed
1770        firstT = -1;
1771        Segment* leftSegment;
1772        do {
1773            const Angle* angle = sorted[++firstT];
1774            leftSegment = angle->segment();
1775            tIndex = angle->end();
1776            endIndex = angle->start();
1777        } while (leftSegment->fTs[SkMin32(tIndex, endIndex)].fDone);
1778        return leftSegment;
1779    }
1780
1781    bool firstBump(const Angle* angle, int sumWinding) const {
1782        int winding = spanSign(angle->start(), angle->end());
1783        sumWinding -= winding;
1784        if (sumWinding == 0) {
1785            sumWinding = winding;
1786        }
1787        bool result = angle->sign() * sumWinding > 0;
1788        SkASSERT(result == angle->firstBump(sumWinding));
1789        return result;
1790    }
1791
1792    // FIXME: not crazy about this
1793    // when the intersections are performed, the other index is into an
1794    // incomplete array. as the array grows, the indices become incorrect
1795    // while the following fixes the indices up again, it isn't smart about
1796    // skipping segments whose indices are already correct
1797    // assuming we leave the code that wrote the index in the first place
1798    void fixOtherTIndex() {
1799        int iCount = fTs.count();
1800        for (int i = 0; i < iCount; ++i) {
1801            Span& iSpan = fTs[i];
1802            double oT = iSpan.fOtherT;
1803            Segment* other = iSpan.fOther;
1804            int oCount = other->fTs.count();
1805            for (int o = 0; o < oCount; ++o) {
1806                Span& oSpan = other->fTs[o];
1807                if (oT == oSpan.fT && this == oSpan.fOther) {
1808                    iSpan.fOtherIndex = o;
1809                    break;
1810                }
1811            }
1812        }
1813    }
1814
1815    // OPTIMIZATION: uses tail recursion. Unwise?
1816    Span* innerChaseDone(int index, int step, int winding) {
1817        int end = nextSpan(index, step);
1818        SkASSERT(end >= 0);
1819        if (multipleSpans(end)) {
1820            return &fTs[end];
1821        }
1822        const Span& endSpan = fTs[end];
1823        Segment* other = endSpan.fOther;
1824        index = endSpan.fOtherIndex;
1825        int otherEnd = other->nextSpan(index, step);
1826        Span* last = other->innerChaseDone(index, step, winding);
1827        other->markDone(SkMin32(index, otherEnd), winding);
1828        return last;
1829    }
1830
1831    Span* innerChaseWinding(int index, int step, int winding) {
1832        int end = nextSpan(index, step);
1833        SkASSERT(end >= 0);
1834        if (multipleSpans(end)) {
1835            return &fTs[end];
1836        }
1837        const Span& endSpan = fTs[end];
1838        Segment* other = endSpan.fOther;
1839        index = endSpan.fOtherIndex;
1840        int otherEnd = other->nextSpan(index, step);
1841        int min = SkMin32(index, otherEnd);
1842        if (other->fTs[min].fWindSum != SK_MinS32) {
1843            SkASSERT(other->fTs[min].fWindSum == winding);
1844            return NULL;
1845        }
1846        Span* last = other->innerChaseWinding(index, step, winding);
1847        other->markWinding(min, winding);
1848        return last;
1849    }
1850
1851    void init(const SkPoint pts[], SkPath::Verb verb) {
1852        fPts = pts;
1853        fVerb = verb;
1854        fDoneSpans = 0;
1855    }
1856
1857    bool intersected() const {
1858        return fTs.count() > 0;
1859    }
1860
1861    bool isConnected(int startIndex, int endIndex) const {
1862        return fTs[startIndex].fWindSum != SK_MinS32
1863                || fTs[endIndex].fWindSum != SK_MinS32;
1864    }
1865
1866    bool isLinear(int start, int end) const {
1867        if (fVerb == SkPath::kLine_Verb) {
1868            return true;
1869        }
1870        if (fVerb == SkPath::kQuad_Verb) {
1871            SkPoint qPart[3];
1872            QuadSubDivide(fPts, fTs[start].fT, fTs[end].fT, qPart);
1873            return QuadIsLinear(qPart);
1874        } else {
1875            SkASSERT(fVerb == SkPath::kCubic_Verb);
1876            SkPoint cPart[4];
1877            CubicSubDivide(fPts, fTs[start].fT, fTs[end].fT, cPart);
1878            return CubicIsLinear(cPart);
1879        }
1880    }
1881
1882    // OPTIMIZE: successive calls could start were the last leaves off
1883    // or calls could specialize to walk forwards or backwards
1884    bool isMissing(double startT) const {
1885        size_t tCount = fTs.count();
1886        for (size_t index = 0; index < tCount; ++index) {
1887            if (fabs(startT - fTs[index].fT) < FLT_EPSILON) {
1888                return false;
1889            }
1890        }
1891        return true;
1892    }
1893
1894    bool isSimple(int end) const {
1895        int count = fTs.count();
1896        if (count == 2) {
1897            return true;
1898        }
1899        double t = fTs[end].fT;
1900        if (t < FLT_EPSILON) {
1901            return fTs[1].fT >= FLT_EPSILON;
1902        }
1903        if (t > 1 - FLT_EPSILON) {
1904            return fTs[count - 2].fT <= 1 - FLT_EPSILON;
1905        }
1906        return false;
1907    }
1908
1909    bool isHorizontal() const {
1910        return fBounds.fTop == fBounds.fBottom;
1911    }
1912
1913    bool isVertical() const {
1914        return fBounds.fLeft == fBounds.fRight;
1915    }
1916
1917    SkScalar leftMost(int start, int end) const {
1918        return (*SegmentLeftMost[fVerb])(fPts, fTs[start].fT, fTs[end].fT);
1919    }
1920
1921    // this span is excluded by the winding rule -- chase the ends
1922    // as long as they are unambiguous to mark connections as done
1923    // and give them the same winding value
1924    Span* markAndChaseDone(const Angle* angle, int winding) {
1925        int index = angle->start();
1926        int endIndex = angle->end();
1927        int step = SkSign32(endIndex - index);
1928        Span* last = innerChaseDone(index, step, winding);
1929        markDone(SkMin32(index, endIndex), winding);
1930        return last;
1931    }
1932
1933    Span* markAndChaseWinding(const Angle* angle, int winding) {
1934        int index = angle->start();
1935        int endIndex = angle->end();
1936        int min = SkMin32(index, endIndex);
1937        int step = SkSign32(endIndex - index);
1938        Span* last = innerChaseWinding(index, step, winding);
1939        markWinding(min, winding);
1940        return last;
1941    }
1942
1943    // FIXME: this should also mark spans with equal (x,y)
1944    // This may be called when the segment is already marked done. While this
1945    // wastes time, it shouldn't do any more than spin through the T spans.
1946    // OPTIMIZATION: abort on first done found (assuming that this code is
1947    // always called to mark segments done).
1948    void markDone(int index, int winding) {
1949      //  SkASSERT(!done());
1950        double referenceT = fTs[index].fT;
1951        int lesser = index;
1952        while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
1953            Span& span = fTs[lesser];
1954            if (span.fDone) {
1955                continue;
1956            }
1957        #if DEBUG_MARK_DONE
1958            const SkPoint& pt = xyAtT(&span);
1959            SkDebugf("%s id=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
1960                    __FUNCTION__, fID, lesser, span.fT, pt.fX, pt.fY, winding);
1961        #endif
1962            span.fDone = true;
1963            SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
1964            SkASSERT(abs(winding) <= gDebugMaxWindSum);
1965            span.fWindSum = winding;
1966            fDoneSpans++;
1967        }
1968        do {
1969            Span& span = fTs[index];
1970     //       SkASSERT(!span.fDone);
1971            if (span.fDone) {
1972                continue;
1973            }
1974        #if DEBUG_MARK_DONE
1975            const SkPoint& pt = xyAtT(&span);
1976            SkDebugf("%s id=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
1977                    __FUNCTION__, fID, index, span.fT, pt.fX, pt.fY, winding);
1978        #endif
1979            span.fDone = true;
1980            SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
1981            SkASSERT(abs(winding) <= gDebugMaxWindSum);
1982            span.fWindSum = winding;
1983            fDoneSpans++;
1984        } while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
1985    }
1986
1987    void markWinding(int index, int winding) {
1988    //    SkASSERT(!done());
1989        double referenceT = fTs[index].fT;
1990        int lesser = index;
1991        while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
1992            Span& span = fTs[lesser];
1993            if (span.fDone) {
1994                continue;
1995            }
1996      //      SkASSERT(span.fWindValue == 1 || winding == 0);
1997            SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
1998        #if DEBUG_MARK_DONE
1999            const SkPoint& pt = xyAtT(&span);
2000            SkDebugf("%s id=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
2001                    __FUNCTION__, fID, lesser, span.fT, pt.fX, pt.fY, winding);
2002        #endif
2003            SkASSERT(abs(winding) <= gDebugMaxWindSum);
2004            span.fWindSum = winding;
2005        }
2006        do {
2007            Span& span = fTs[index];
2008     //       SkASSERT(!span.fDone || span.fCoincident);
2009            if (span.fDone) {
2010                continue;
2011            }
2012     //       SkASSERT(span.fWindValue == 1 || winding == 0);
2013            SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
2014        #if DEBUG_MARK_DONE
2015            const SkPoint& pt = xyAtT(&span);
2016            SkDebugf("%s id=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
2017                    __FUNCTION__, fID, index, span.fT, pt.fX, pt.fY, winding);
2018        #endif
2019            SkASSERT(abs(winding) <= gDebugMaxWindSum);
2020            span.fWindSum = winding;
2021        } while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
2022    }
2023
2024    // return span if when chasing, two or more radiating spans are not done
2025    // OPTIMIZATION: ? multiple spans is detected when there is only one valid
2026    // candidate and the remaining spans have windValue == 0 (canceled by
2027    // coincidence). The coincident edges could either be removed altogether,
2028    // or this code could be more complicated in detecting this case. Worth it?
2029    bool multipleSpans(int end) const {
2030        return end > 0 && end < fTs.count() - 1;
2031    }
2032
2033    // This has callers for two different situations: one establishes the end
2034    // of the current span, and one establishes the beginning of the next span
2035    // (thus the name). When this is looking for the end of the current span,
2036    // coincidence is found when the beginning Ts contain -step and the end
2037    // contains step. When it is looking for the beginning of the next, the
2038    // first Ts found can be ignored and the last Ts should contain -step.
2039    // OPTIMIZATION: probably should split into two functions
2040    int nextSpan(int from, int step) const {
2041        const Span& fromSpan = fTs[from];
2042        int count = fTs.count();
2043        int to = from;
2044        while (step > 0 ? ++to < count : --to >= 0) {
2045            const Span& span = fTs[to];
2046            if ((step > 0 ? span.fT - fromSpan.fT : fromSpan.fT - span.fT) < FLT_EPSILON) {
2047                continue;
2048            }
2049            return to;
2050        }
2051        return -1;
2052    }
2053
2054    const SkPoint* pts() const {
2055        return fPts;
2056    }
2057
2058    void reset() {
2059        init(NULL, (SkPath::Verb) -1);
2060        fBounds.set(SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, SK_ScalarMax);
2061        fTs.reset();
2062    }
2063
2064    // OPTIMIZATION: mark as debugging only if used solely by tests
2065    const Span& span(int tIndex) const {
2066        return fTs[tIndex];
2067    }
2068
2069    int spanSign(int startIndex, int endIndex) const {
2070        return startIndex < endIndex ? -fTs[startIndex].fWindValue :
2071                fTs[endIndex].fWindValue;
2072    }
2073
2074    // OPTIMIZATION: mark as debugging only if used solely by tests
2075    double t(int tIndex) const {
2076        return fTs[tIndex].fT;
2077    }
2078
2079    static void TrackOutside(SkTDArray<double>& outsideTs, double end,
2080            double start) {
2081        int outCount = outsideTs.count();
2082        if (outCount == 0 || end - outsideTs[outCount - 2] >= FLT_EPSILON) {
2083            *outsideTs.append() = end;
2084            *outsideTs.append() = start;
2085        }
2086    }
2087
2088    void updatePts(const SkPoint pts[]) {
2089        fPts = pts;
2090    }
2091
2092    SkPath::Verb verb() const {
2093        return fVerb;
2094    }
2095
2096    int windBump(const Angle* angle) const {
2097        SkASSERT(angle->segment() == this);
2098        const Span& span = fTs[SkMin32(angle->start(), angle->end())];
2099        int result = angle->sign() * span.fWindValue;
2100#if DEBUG_WIND_BUMP
2101        SkDebugf("%s bump=%d\n", __FUNCTION__, result);
2102#endif
2103        return result;
2104    }
2105
2106    int windSum(int tIndex) const {
2107        return fTs[tIndex].fWindSum;
2108    }
2109
2110    int windSum(const Angle* angle) const {
2111        int start = angle->start();
2112        int end = angle->end();
2113        int index = SkMin32(start, end);
2114        return windSum(index);
2115    }
2116
2117    int windValue(int tIndex) const {
2118        return fTs[tIndex].fWindValue;
2119    }
2120
2121    int windValue(const Angle* angle) const {
2122        int start = angle->start();
2123        int end = angle->end();
2124        int index = SkMin32(start, end);
2125        return windValue(index);
2126    }
2127
2128    SkScalar xAtT(const Span* span) const {
2129        return xyAtT(span).fX;
2130    }
2131
2132    const SkPoint& xyAtT(int index) const {
2133        return xyAtT(&fTs[index]);
2134    }
2135
2136    const SkPoint& xyAtT(const Span* span) const {
2137        if (SkScalarIsNaN(span->fPt.fX)) {
2138            if (span->fT == 0) {
2139                span->fPt = fPts[0];
2140            } else if (span->fT == 1) {
2141                span->fPt = fPts[fVerb];
2142            } else {
2143                (*SegmentXYAtT[fVerb])(fPts, span->fT, &span->fPt);
2144            }
2145        }
2146        return span->fPt;
2147    }
2148
2149    SkScalar yAtT(int index) const {
2150        return yAtT(&fTs[index]);
2151    }
2152
2153    SkScalar yAtT(const Span* span) const {
2154        return xyAtT(span).fY;
2155    }
2156
2157#if DEBUG_DUMP
2158    void dump() const {
2159        const char className[] = "Segment";
2160        const int tab = 4;
2161        for (int i = 0; i < fTs.count(); ++i) {
2162            SkPoint out;
2163            (*SegmentXYAtT[fVerb])(fPts, t(i), &out);
2164            SkDebugf("%*s [%d] %s.fTs[%d]=%1.9g (%1.9g,%1.9g) other=%d"
2165                    " otherT=%1.9g windSum=%d\n",
2166                    tab + sizeof(className), className, fID,
2167                    kLVerbStr[fVerb], i, fTs[i].fT, out.fX, out.fY,
2168                    fTs[i].fOther->fID, fTs[i].fOtherT, fTs[i].fWindSum);
2169        }
2170        SkDebugf("%*s [%d] fBounds=(l:%1.9g, t:%1.9g r:%1.9g, b:%1.9g)",
2171                tab + sizeof(className), className, fID,
2172                fBounds.fLeft, fBounds.fTop, fBounds.fRight, fBounds.fBottom);
2173    }
2174#endif
2175
2176#if DEBUG_CONCIDENT
2177    // assert if pair has not already been added
2178     void debugAddTPair(double t, const Segment& other, double otherT) const {
2179        for (int i = 0; i < fTs.count(); ++i) {
2180            if (fTs[i].fT == t && fTs[i].fOther == &other && fTs[i].fOtherT == otherT) {
2181                return;
2182            }
2183        }
2184        SkASSERT(0);
2185     }
2186#endif
2187
2188#if DEBUG_DUMP
2189    int debugID() const {
2190        return fID;
2191    }
2192#endif
2193
2194#if DEBUG_CONCIDENT
2195    void debugShowTs() const {
2196        SkDebugf("%s %d", __FUNCTION__, fID);
2197        for (int i = 0; i < fTs.count(); ++i) {
2198            SkDebugf(" [o=%d %1.9g (%1.9g,%1.9g) w=%d]", fTs[i].fOther->fID,
2199                    fTs[i].fT, xAtT(&fTs[i]), yAtT(&fTs[i]), fTs[i].fWindValue);
2200        }
2201        SkDebugf("\n");
2202    }
2203#endif
2204
2205#if DEBUG_ACTIVE_SPANS
2206    void debugShowActiveSpans() const {
2207        if (done()) {
2208            return;
2209        }
2210        for (int i = 0; i < fTs.count(); ++i) {
2211            if (fTs[i].fDone) {
2212                continue;
2213            }
2214            SkDebugf("%s id=%d", __FUNCTION__, fID);
2215            SkDebugf(" (%1.9g,%1.9g", fPts[0].fX, fPts[0].fY);
2216            for (int vIndex = 1; vIndex <= fVerb; ++vIndex) {
2217                SkDebugf(" %1.9g,%1.9g", fPts[vIndex].fX, fPts[vIndex].fY);
2218            }
2219            const Span* span = &fTs[i];
2220            SkDebugf(") fT=%d (%1.9g) (%1.9g,%1.9g)", i, fTs[i].fT,
2221                     xAtT(span), yAtT(i));
2222            const Segment* other = fTs[i].fOther;
2223            SkDebugf(" other=%d otherT=%1.9g otherIndex=%d windSum=",
2224                    other->fID, fTs[i].fOtherT, fTs[i].fOtherIndex);
2225            if (fTs[i].fWindSum == SK_MinS32) {
2226                SkDebugf("?");
2227            } else {
2228                SkDebugf("%d", fTs[i].fWindSum);
2229            }
2230            SkDebugf(" windValue=%d\n", fTs[i].fWindValue);
2231        }
2232    }
2233#endif
2234
2235#if DEBUG_SORT
2236    void debugShowSort(const SkTDArray<Angle*>& angles, int first,
2237            const int contourWinding) const {
2238        SkASSERT(angles[first]->segment() == this);
2239        int lastSum = contourWinding;
2240        int windSum = lastSum - windBump(angles[first]);
2241        SkDebugf("%s contourWinding=%d bump=%d\n", __FUNCTION__,
2242                contourWinding, windBump(angles[first]));
2243        int index = first;
2244        bool firstTime = true;
2245        do {
2246            const Angle& angle = *angles[index];
2247            const Segment& segment = *angle.segment();
2248            int start = angle.start();
2249            int end = angle.end();
2250            const Span& sSpan = segment.fTs[start];
2251            const Span& eSpan = segment.fTs[end];
2252            const Span& mSpan = segment.fTs[SkMin32(start, end)];
2253            if (!firstTime) {
2254                lastSum = windSum;
2255                windSum -= segment.windBump(&angle);
2256            }
2257            SkDebugf("%s [%d] id=%d start=%d (%1.9g,%,1.9g) end=%d (%1.9g,%,1.9g)"
2258                     " sign=%d windValue=%d winding: %d->%d (max=%d) done=%d\n",
2259                     __FUNCTION__, index, segment.fID, start, segment.xAtT(&sSpan),
2260                     segment.yAtT(&sSpan), end, segment.xAtT(&eSpan),
2261                     segment.yAtT(&eSpan), angle.sign(), mSpan.fWindValue,
2262                     lastSum, windSum, abs(lastSum) > abs(windSum) ? lastSum :
2263                     windSum, mSpan.fDone);
2264            ++index;
2265            if (index == angles.count()) {
2266                index = 0;
2267            }
2268            if (firstTime) {
2269                firstTime = false;
2270            }
2271        } while (index != first);
2272    }
2273#endif
2274
2275#if DEBUG_WINDING
2276    bool debugVerifyWinding(int start, int end, int winding) const {
2277        const Span& span = fTs[SkMin32(start, end)];
2278        int spanWinding = span.fWindSum;
2279        if (spanWinding == SK_MinS32) {
2280            return true;
2281        }
2282        int spanSign = SkSign32(start - end);
2283        int signedVal = spanSign * span.fWindValue;
2284        if (signedVal < 0) {
2285            spanWinding -= signedVal;
2286        }
2287        return span.fWindSum == winding;
2288    }
2289#endif
2290
2291private:
2292    const SkPoint* fPts;
2293    SkPath::Verb fVerb;
2294    Bounds fBounds;
2295    SkTDArray<Span> fTs; // two or more (always includes t=0 t=1)
2296    int fDoneSpans; // used for quick check that segment is finished
2297#if DEBUG_DUMP
2298    int fID;
2299#endif
2300};
2301
2302class Contour;
2303
2304struct Coincidence {
2305    Contour* fContours[2];
2306    int fSegments[2];
2307    double fTs[2][2];
2308};
2309
2310class Contour {
2311public:
2312    Contour() {
2313        reset();
2314#if DEBUG_DUMP
2315        fID = ++gContourID;
2316#endif
2317    }
2318
2319    bool operator<(const Contour& rh) const {
2320        return fBounds.fTop == rh.fBounds.fTop
2321                ? fBounds.fLeft < rh.fBounds.fLeft
2322                : fBounds.fTop < rh.fBounds.fTop;
2323    }
2324
2325    void addCoincident(int index, Contour* other, int otherIndex,
2326            const Intersections& ts, bool swap) {
2327        Coincidence& coincidence = *fCoincidences.append();
2328        coincidence.fContours[0] = this;
2329        coincidence.fContours[1] = other;
2330        coincidence.fSegments[0] = index;
2331        coincidence.fSegments[1] = otherIndex;
2332        coincidence.fTs[swap][0] = ts.fT[0][0];
2333        coincidence.fTs[swap][1] = ts.fT[0][1];
2334        coincidence.fTs[!swap][0] = ts.fT[1][0];
2335        coincidence.fTs[!swap][1] = ts.fT[1][1];
2336    }
2337
2338    void addCross(const Contour* crosser) {
2339#ifdef DEBUG_CROSS
2340        for (int index = 0; index < fCrosses.count(); ++index) {
2341            SkASSERT(fCrosses[index] != crosser);
2342        }
2343#endif
2344        *fCrosses.append() = crosser;
2345    }
2346
2347    void addCubic(const SkPoint pts[4]) {
2348        fSegments.push_back().addCubic(pts);
2349        fContainsCurves = true;
2350    }
2351
2352    int addLine(const SkPoint pts[2]) {
2353        fSegments.push_back().addLine(pts);
2354        return fSegments.count();
2355    }
2356
2357    void addOtherT(int segIndex, int tIndex, double otherT, int otherIndex) {
2358        fSegments[segIndex].addOtherT(tIndex, otherT, otherIndex);
2359    }
2360
2361    int addQuad(const SkPoint pts[3]) {
2362        fSegments.push_back().addQuad(pts);
2363        fContainsCurves = true;
2364        return fSegments.count();
2365    }
2366
2367    int addT(int segIndex, double newT, Contour* other, int otherIndex) {
2368        containsIntercepts();
2369        return fSegments[segIndex].addT(newT, &other->fSegments[otherIndex]);
2370    }
2371
2372    const Bounds& bounds() const {
2373        return fBounds;
2374    }
2375
2376    void complete() {
2377        setBounds();
2378        fContainsIntercepts = false;
2379    }
2380
2381    void containsIntercepts() {
2382        fContainsIntercepts = true;
2383    }
2384
2385    const Segment* crossedSegment(const SkPoint& basePt, SkScalar& bestY,
2386            int &tIndex, double& hitT) {
2387        int segmentCount = fSegments.count();
2388        const Segment* bestSegment = NULL;
2389        for (int test = 0; test < segmentCount; ++test) {
2390            Segment* testSegment = &fSegments[test];
2391            const SkRect& bounds = testSegment->bounds();
2392            if (bounds.fBottom <= bestY) {
2393                continue;
2394            }
2395            if (bounds.fTop >= basePt.fY) {
2396                continue;
2397            }
2398            if (bounds.fLeft > basePt.fX) {
2399                continue;
2400            }
2401            if (bounds.fRight < basePt.fX) {
2402                continue;
2403            }
2404            if (bounds.fLeft == bounds.fRight) {
2405                continue;
2406            }
2407     #if 0
2408            bool leftHalf = bounds.fLeft == basePt.fX;
2409            bool rightHalf = bounds.fRight == basePt.fX;
2410            if ((leftHalf || rightHalf) && !testSegment->crossedSpanHalves(
2411                    basePt, leftHalf, rightHalf)) {
2412                continue;
2413            }
2414     #endif
2415            double testHitT;
2416            int testT = testSegment->crossedSpan(basePt, bestY, testHitT);
2417            if (testT >= 0) {
2418                bestSegment = testSegment;
2419                tIndex = testT;
2420                hitT = testHitT;
2421            }
2422        }
2423        return bestSegment;
2424    }
2425
2426    bool crosses(const Contour* crosser) const {
2427        for (int index = 0; index < fCrosses.count(); ++index) {
2428            if (fCrosses[index] == crosser) {
2429                return true;
2430            }
2431        }
2432        return false;
2433    }
2434
2435    void findTooCloseToCall(int winding) {
2436        int segmentCount = fSegments.count();
2437        for (int sIndex = 0; sIndex < segmentCount; ++sIndex) {
2438            fSegments[sIndex].findTooCloseToCall(winding);
2439        }
2440    }
2441
2442    void fixOtherTIndex() {
2443        int segmentCount = fSegments.count();
2444        for (int sIndex = 0; sIndex < segmentCount; ++sIndex) {
2445            fSegments[sIndex].fixOtherTIndex();
2446        }
2447    }
2448
2449    void reset() {
2450        fSegments.reset();
2451        fBounds.set(SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, SK_ScalarMax);
2452        fContainsCurves = fContainsIntercepts = false;
2453    }
2454
2455    void resolveCoincidence(int winding) {
2456        int count = fCoincidences.count();
2457        for (int index = 0; index < count; ++index) {
2458            Coincidence& coincidence = fCoincidences[index];
2459            Contour* thisContour = coincidence.fContours[0];
2460            Contour* otherContour = coincidence.fContours[1];
2461            int thisIndex = coincidence.fSegments[0];
2462            int otherIndex = coincidence.fSegments[1];
2463            Segment& thisOne = thisContour->fSegments[thisIndex];
2464            Segment& other = otherContour->fSegments[otherIndex];
2465        #if DEBUG_CONCIDENT
2466            thisOne.debugShowTs();
2467            other.debugShowTs();
2468        #endif
2469            double startT = coincidence.fTs[0][0];
2470            double endT = coincidence.fTs[0][1];
2471            if (startT > endT) {
2472                SkTSwap<double>(startT, endT);
2473            }
2474            SkASSERT(endT - startT >= FLT_EPSILON);
2475            double oStartT = coincidence.fTs[1][0];
2476            double oEndT = coincidence.fTs[1][1];
2477            if (oStartT > oEndT) {
2478                SkTSwap<double>(oStartT, oEndT);
2479            }
2480            SkASSERT(oEndT - oStartT >= FLT_EPSILON);
2481            if (winding > 0 || thisOne.cancels(other)) {
2482                        // make sure startT and endT have t entries
2483                if (thisOne.isMissing(startT) || other.isMissing(oEndT)) {
2484                    thisOne.addTPair(startT, other, oEndT);
2485                }
2486                if (thisOne.isMissing(endT) || other.isMissing(oStartT)) {
2487                    other.addTPair(oStartT, thisOne, endT);
2488                }
2489                thisOne.addTCancel(startT, endT, other, oStartT, oEndT);
2490            } else {
2491                if (thisOne.isMissing(startT) || other.isMissing(oStartT)) {
2492                    thisOne.addTPair(startT, other, oStartT);
2493                }
2494                if (thisOne.isMissing(endT) || other.isMissing(oEndT)) {
2495                    other.addTPair(oEndT, thisOne, endT);
2496                }
2497                thisOne.addTCoincident(startT, endT, other, oStartT, oEndT);
2498            }
2499        #if DEBUG_CONCIDENT
2500            thisOne.debugShowTs();
2501            other.debugShowTs();
2502        #endif
2503        }
2504    }
2505
2506    const SkTArray<Segment>& segments() {
2507        return fSegments;
2508    }
2509
2510    // OPTIMIZATION: feel pretty uneasy about this. It seems like once again
2511    // we need to sort and walk edges in y, but that on the surface opens the
2512    // same can of worms as before. But then, this is a rough sort based on
2513    // segments' top, and not a true sort, so it could be ameniable to regular
2514    // sorting instead of linear searching. Still feel like I'm missing something
2515    Segment* topSegment(SkScalar& bestY) {
2516        int segmentCount = fSegments.count();
2517        SkASSERT(segmentCount > 0);
2518        int best = -1;
2519        Segment* bestSegment = NULL;
2520        while (++best < segmentCount) {
2521            Segment* testSegment = &fSegments[best];
2522            if (testSegment->done()) {
2523                continue;
2524            }
2525            bestSegment = testSegment;
2526            break;
2527        }
2528        if (!bestSegment) {
2529            return NULL;
2530        }
2531        SkScalar bestTop = bestSegment->activeTop();
2532        for (int test = best + 1; test < segmentCount; ++test) {
2533            Segment* testSegment = &fSegments[test];
2534            if (testSegment->done()) {
2535                continue;
2536            }
2537            if (testSegment->bounds().fTop > bestTop) {
2538                continue;
2539            }
2540            SkScalar testTop = testSegment->activeTop();
2541            if (bestTop > testTop) {
2542                bestTop = testTop;
2543                bestSegment = testSegment;
2544            }
2545        }
2546        bestY = bestTop;
2547        return bestSegment;
2548    }
2549
2550    int updateSegment(int index, const SkPoint* pts) {
2551        Segment& segment = fSegments[index];
2552        segment.updatePts(pts);
2553        return segment.verb() + 1;
2554    }
2555
2556#if DEBUG_TEST
2557    SkTArray<Segment>& debugSegments() {
2558        return fSegments;
2559    }
2560#endif
2561
2562#if DEBUG_DUMP
2563    void dump() {
2564        int i;
2565        const char className[] = "Contour";
2566        const int tab = 4;
2567        SkDebugf("%s %p (contour=%d)\n", className, this, fID);
2568        for (i = 0; i < fSegments.count(); ++i) {
2569            SkDebugf("%*s.fSegments[%d]:\n", tab + sizeof(className),
2570                    className, i);
2571            fSegments[i].dump();
2572        }
2573        SkDebugf("%*s.fBounds=(l:%1.9g, t:%1.9g r:%1.9g, b:%1.9g)\n",
2574                tab + sizeof(className), className,
2575                fBounds.fLeft, fBounds.fTop,
2576                fBounds.fRight, fBounds.fBottom);
2577        SkDebugf("%*s.fContainsIntercepts=%d\n", tab + sizeof(className),
2578                className, fContainsIntercepts);
2579        SkDebugf("%*s.fContainsCurves=%d\n", tab + sizeof(className),
2580                className, fContainsCurves);
2581    }
2582#endif
2583
2584#if DEBUG_ACTIVE_SPANS
2585    void debugShowActiveSpans() {
2586        for (int index = 0; index < fSegments.count(); ++index) {
2587            fSegments[index].debugShowActiveSpans();
2588        }
2589    }
2590#endif
2591
2592protected:
2593    void setBounds() {
2594        int count = fSegments.count();
2595        if (count == 0) {
2596            SkDebugf("%s empty contour\n", __FUNCTION__);
2597            SkASSERT(0);
2598            // FIXME: delete empty contour?
2599            return;
2600        }
2601        fBounds = fSegments.front().bounds();
2602        for (int index = 1; index < count; ++index) {
2603            fBounds.add(fSegments[index].bounds());
2604        }
2605    }
2606
2607private:
2608    SkTArray<Segment> fSegments;
2609    SkTDArray<Coincidence> fCoincidences;
2610    SkTDArray<const Contour*> fCrosses;
2611    Bounds fBounds;
2612    bool fContainsIntercepts;
2613    bool fContainsCurves;
2614#if DEBUG_DUMP
2615    int fID;
2616#endif
2617};
2618
2619class EdgeBuilder {
2620public:
2621
2622EdgeBuilder(const SkPath& path, SkTArray<Contour>& contours)
2623    : fPath(path)
2624    , fCurrentContour(NULL)
2625    , fContours(contours)
2626{
2627#if DEBUG_DUMP
2628    gContourID = 0;
2629    gSegmentID = 0;
2630#endif
2631    walk();
2632}
2633
2634protected:
2635
2636void complete() {
2637    if (fCurrentContour && fCurrentContour->segments().count()) {
2638        fCurrentContour->complete();
2639        fCurrentContour = NULL;
2640    }
2641}
2642
2643void walk() {
2644    // FIXME:remove once we can access path pts directly
2645    SkPath::RawIter iter(fPath); // FIXME: access path directly when allowed
2646    SkPoint pts[4];
2647    SkPath::Verb verb;
2648    do {
2649        verb = iter.next(pts);
2650        *fPathVerbs.append() = verb;
2651        if (verb == SkPath::kMove_Verb) {
2652            *fPathPts.append() = pts[0];
2653        } else if (verb >= SkPath::kLine_Verb && verb <= SkPath::kCubic_Verb) {
2654            fPathPts.append(verb, &pts[1]);
2655        }
2656    } while (verb != SkPath::kDone_Verb);
2657    // FIXME: end of section to remove once path pts are accessed directly
2658
2659    SkPath::Verb reducedVerb;
2660    uint8_t* verbPtr = fPathVerbs.begin();
2661    const SkPoint* pointsPtr = fPathPts.begin();
2662    const SkPoint* finalCurveStart = NULL;
2663    const SkPoint* finalCurveEnd = NULL;
2664    while ((verb = (SkPath::Verb) *verbPtr++) != SkPath::kDone_Verb) {
2665        switch (verb) {
2666            case SkPath::kMove_Verb:
2667                complete();
2668                if (!fCurrentContour) {
2669                    fCurrentContour = fContours.push_back_n(1);
2670                    finalCurveEnd = pointsPtr++;
2671                    *fExtra.append() = -1; // start new contour
2672                }
2673                continue;
2674            case SkPath::kLine_Verb:
2675                // skip degenerate points
2676                if (pointsPtr[-1].fX != pointsPtr[0].fX
2677                        || pointsPtr[-1].fY != pointsPtr[0].fY) {
2678                    fCurrentContour->addLine(&pointsPtr[-1]);
2679                }
2680                break;
2681            case SkPath::kQuad_Verb:
2682
2683                reducedVerb = QuadReduceOrder(&pointsPtr[-1], fReducePts);
2684                if (reducedVerb == 0) {
2685                    break; // skip degenerate points
2686                }
2687                if (reducedVerb == 1) {
2688                    *fExtra.append() =
2689                            fCurrentContour->addLine(fReducePts.end() - 2);
2690                    break;
2691                }
2692                fCurrentContour->addQuad(&pointsPtr[-1]);
2693                break;
2694            case SkPath::kCubic_Verb:
2695                reducedVerb = CubicReduceOrder(&pointsPtr[-1], fReducePts);
2696                if (reducedVerb == 0) {
2697                    break; // skip degenerate points
2698                }
2699                if (reducedVerb == 1) {
2700                    *fExtra.append() =
2701                            fCurrentContour->addLine(fReducePts.end() - 2);
2702                    break;
2703                }
2704                if (reducedVerb == 2) {
2705                    *fExtra.append() =
2706                            fCurrentContour->addQuad(fReducePts.end() - 3);
2707                    break;
2708                }
2709                fCurrentContour->addCubic(&pointsPtr[-1]);
2710                break;
2711            case SkPath::kClose_Verb:
2712                SkASSERT(fCurrentContour);
2713                if (finalCurveStart && finalCurveEnd
2714                        && *finalCurveStart != *finalCurveEnd) {
2715                    *fReducePts.append() = *finalCurveStart;
2716                    *fReducePts.append() = *finalCurveEnd;
2717                    *fExtra.append() =
2718                            fCurrentContour->addLine(fReducePts.end() - 2);
2719                }
2720                complete();
2721                continue;
2722            default:
2723                SkDEBUGFAIL("bad verb");
2724                return;
2725        }
2726        finalCurveStart = &pointsPtr[verb - 1];
2727        pointsPtr += verb;
2728        SkASSERT(fCurrentContour);
2729    }
2730    complete();
2731    if (fCurrentContour && !fCurrentContour->segments().count()) {
2732        fContours.pop_back();
2733    }
2734    // correct pointers in contours since fReducePts may have moved as it grew
2735    int cIndex = 0;
2736    int extraCount = fExtra.count();
2737    SkASSERT(extraCount == 0 || fExtra[0] == -1);
2738    int eIndex = 0;
2739    int rIndex = 0;
2740    while (++eIndex < extraCount) {
2741        int offset = fExtra[eIndex];
2742        if (offset < 0) {
2743            ++cIndex;
2744            continue;
2745        }
2746        fCurrentContour = &fContours[cIndex];
2747        rIndex += fCurrentContour->updateSegment(offset - 1,
2748                &fReducePts[rIndex]);
2749    }
2750    fExtra.reset(); // we're done with this
2751}
2752
2753private:
2754    const SkPath& fPath;
2755    SkTDArray<SkPoint> fPathPts; // FIXME: point directly to path pts instead
2756    SkTDArray<uint8_t> fPathVerbs; // FIXME: remove
2757    Contour* fCurrentContour;
2758    SkTArray<Contour>& fContours;
2759    SkTDArray<SkPoint> fReducePts; // segments created on the fly
2760    SkTDArray<int> fExtra; // -1 marks new contour, > 0 offsets into contour
2761};
2762
2763class Work {
2764public:
2765    enum SegmentType {
2766        kHorizontalLine_Segment = -1,
2767        kVerticalLine_Segment = 0,
2768        kLine_Segment = SkPath::kLine_Verb,
2769        kQuad_Segment = SkPath::kQuad_Verb,
2770        kCubic_Segment = SkPath::kCubic_Verb,
2771    };
2772
2773    void addCoincident(Work& other, const Intersections& ts, bool swap) {
2774        fContour->addCoincident(fIndex, other.fContour, other.fIndex, ts, swap);
2775    }
2776
2777    // FIXME: does it make sense to write otherIndex now if we're going to
2778    // fix it up later?
2779    void addOtherT(int index, double otherT, int otherIndex) {
2780        fContour->addOtherT(fIndex, index, otherT, otherIndex);
2781    }
2782
2783    // Avoid collapsing t values that are close to the same since
2784    // we walk ts to describe consecutive intersections. Since a pair of ts can
2785    // be nearly equal, any problems caused by this should be taken care
2786    // of later.
2787    // On the edge or out of range values are negative; add 2 to get end
2788    int addT(double newT, const Work& other) {
2789        return fContour->addT(fIndex, newT, other.fContour, other.fIndex);
2790    }
2791
2792    bool advance() {
2793        return ++fIndex < fLast;
2794    }
2795
2796    SkScalar bottom() const {
2797        return bounds().fBottom;
2798    }
2799
2800    const Bounds& bounds() const {
2801        return fContour->segments()[fIndex].bounds();
2802    }
2803
2804    const SkPoint* cubic() const {
2805        return fCubic;
2806    }
2807
2808    void init(Contour* contour) {
2809        fContour = contour;
2810        fIndex = 0;
2811        fLast = contour->segments().count();
2812    }
2813
2814    bool isAdjacent(const Work& next) {
2815        return fContour == next.fContour && fIndex + 1 == next.fIndex;
2816    }
2817
2818    bool isFirstLast(const Work& next) {
2819        return fContour == next.fContour && fIndex == 0
2820                && next.fIndex == fLast - 1;
2821    }
2822
2823    SkScalar left() const {
2824        return bounds().fLeft;
2825    }
2826
2827    void promoteToCubic() {
2828        fCubic[0] = pts()[0];
2829        fCubic[2] = pts()[1];
2830        fCubic[3] = pts()[2];
2831        fCubic[1].fX = (fCubic[0].fX + fCubic[2].fX * 2) / 3;
2832        fCubic[1].fY = (fCubic[0].fY + fCubic[2].fY * 2) / 3;
2833        fCubic[2].fX = (fCubic[3].fX + fCubic[2].fX * 2) / 3;
2834        fCubic[2].fY = (fCubic[3].fY + fCubic[2].fY * 2) / 3;
2835    }
2836
2837    const SkPoint* pts() const {
2838        return fContour->segments()[fIndex].pts();
2839    }
2840
2841    SkScalar right() const {
2842        return bounds().fRight;
2843    }
2844
2845    ptrdiff_t segmentIndex() const {
2846        return fIndex;
2847    }
2848
2849    SegmentType segmentType() const {
2850        const Segment& segment = fContour->segments()[fIndex];
2851        SegmentType type = (SegmentType) segment.verb();
2852        if (type != kLine_Segment) {
2853            return type;
2854        }
2855        if (segment.isHorizontal()) {
2856            return kHorizontalLine_Segment;
2857        }
2858        if (segment.isVertical()) {
2859            return kVerticalLine_Segment;
2860        }
2861        return kLine_Segment;
2862    }
2863
2864    bool startAfter(const Work& after) {
2865        fIndex = after.fIndex;
2866        return advance();
2867    }
2868
2869    SkScalar top() const {
2870        return bounds().fTop;
2871    }
2872
2873    SkPath::Verb verb() const {
2874        return fContour->segments()[fIndex].verb();
2875    }
2876
2877    SkScalar x() const {
2878        return bounds().fLeft;
2879    }
2880
2881    bool xFlipped() const {
2882        return x() != pts()[0].fX;
2883    }
2884
2885    SkScalar y() const {
2886        return bounds().fTop;
2887    }
2888
2889    bool yFlipped() const {
2890        return y() != pts()[0].fY;
2891    }
2892
2893protected:
2894    Contour* fContour;
2895    SkPoint fCubic[4];
2896    int fIndex;
2897    int fLast;
2898};
2899
2900#if DEBUG_ADD_INTERSECTING_TS
2901static void debugShowLineIntersection(int pts, const Work& wt,
2902        const Work& wn, const double wtTs[2], const double wnTs[2]) {
2903    if (!pts) {
2904        SkDebugf("%s no intersect (%1.9g,%1.9g %1.9g,%1.9g) (%1.9g,%1.9g %1.9g,%1.9g)\n",
2905                __FUNCTION__, wt.pts()[0].fX, wt.pts()[0].fY,
2906                wt.pts()[1].fX, wt.pts()[1].fY, wn.pts()[0].fX, wn.pts()[0].fY,
2907                wn.pts()[1].fX, wn.pts()[1].fY);
2908        return;
2909    }
2910    SkPoint wtOutPt, wnOutPt;
2911    LineXYAtT(wt.pts(), wtTs[0], &wtOutPt);
2912    LineXYAtT(wn.pts(), wnTs[0], &wnOutPt);
2913    SkDebugf("%s wtTs[0]=%g (%g,%g, %g,%g) (%g,%g)",
2914            __FUNCTION__,
2915            wtTs[0], wt.pts()[0].fX, wt.pts()[0].fY,
2916            wt.pts()[1].fX, wt.pts()[1].fY, wtOutPt.fX, wtOutPt.fY);
2917    if (pts == 2) {
2918        SkDebugf(" wtTs[1]=%g", wtTs[1]);
2919    }
2920    SkDebugf(" wnTs[0]=%g (%g,%g, %g,%g) (%g,%g)",
2921            wnTs[0], wn.pts()[0].fX, wn.pts()[0].fY,
2922            wn.pts()[1].fX, wn.pts()[1].fY, wnOutPt.fX, wnOutPt.fY);
2923    if (pts == 2) {
2924        SkDebugf(" wnTs[1]=%g", wnTs[1]);
2925    }
2926    SkDebugf("\n");
2927}
2928#else
2929static void debugShowLineIntersection(int , const Work& ,
2930        const Work& , const double [2], const double [2]) {
2931}
2932#endif
2933
2934static bool addIntersectTs(Contour* test, Contour* next) {
2935
2936    if (test != next) {
2937        if (test->bounds().fBottom < next->bounds().fTop) {
2938            return false;
2939        }
2940        if (!Bounds::Intersects(test->bounds(), next->bounds())) {
2941            return true;
2942        }
2943    }
2944    Work wt;
2945    wt.init(test);
2946    bool foundCommonContour = test == next;
2947    do {
2948        Work wn;
2949        wn.init(next);
2950        if (test == next && !wn.startAfter(wt)) {
2951            continue;
2952        }
2953        do {
2954            if (!Bounds::Intersects(wt.bounds(), wn.bounds())) {
2955                continue;
2956            }
2957            int pts;
2958            Intersections ts;
2959            bool swap = false;
2960            switch (wt.segmentType()) {
2961                case Work::kHorizontalLine_Segment:
2962                    swap = true;
2963                    switch (wn.segmentType()) {
2964                        case Work::kHorizontalLine_Segment:
2965                        case Work::kVerticalLine_Segment:
2966                        case Work::kLine_Segment: {
2967                            pts = HLineIntersect(wn.pts(), wt.left(),
2968                                    wt.right(), wt.y(), wt.xFlipped(), ts);
2969                            debugShowLineIntersection(pts, wt, wn,
2970                                    ts.fT[1], ts.fT[0]);
2971                            break;
2972                        }
2973                        case Work::kQuad_Segment: {
2974                            pts = HQuadIntersect(wn.pts(), wt.left(),
2975                                    wt.right(), wt.y(), wt.xFlipped(), ts);
2976                            break;
2977                        }
2978                        case Work::kCubic_Segment: {
2979                            pts = HCubicIntersect(wn.pts(), wt.left(),
2980                                    wt.right(), wt.y(), wt.xFlipped(), ts);
2981                            break;
2982                        }
2983                        default:
2984                            SkASSERT(0);
2985                    }
2986                    break;
2987                case Work::kVerticalLine_Segment:
2988                    swap = true;
2989                    switch (wn.segmentType()) {
2990                        case Work::kHorizontalLine_Segment:
2991                        case Work::kVerticalLine_Segment:
2992                        case Work::kLine_Segment: {
2993                            pts = VLineIntersect(wn.pts(), wt.top(),
2994                                    wt.bottom(), wt.x(), wt.yFlipped(), ts);
2995                            debugShowLineIntersection(pts, wt, wn,
2996                                    ts.fT[1], ts.fT[0]);
2997                            break;
2998                        }
2999                        case Work::kQuad_Segment: {
3000                            pts = VQuadIntersect(wn.pts(), wt.top(),
3001                                    wt.bottom(), wt.x(), wt.yFlipped(), ts);
3002                            break;
3003                        }
3004                        case Work::kCubic_Segment: {
3005                            pts = VCubicIntersect(wn.pts(), wt.top(),
3006                                    wt.bottom(), wt.x(), wt.yFlipped(), ts);
3007                            break;
3008                        }
3009                        default:
3010                            SkASSERT(0);
3011                    }
3012                    break;
3013                case Work::kLine_Segment:
3014                    switch (wn.segmentType()) {
3015                        case Work::kHorizontalLine_Segment:
3016                            pts = HLineIntersect(wt.pts(), wn.left(),
3017                                    wn.right(), wn.y(), wn.xFlipped(), ts);
3018                            debugShowLineIntersection(pts, wt, wn,
3019                                    ts.fT[1], ts.fT[0]);
3020                            break;
3021                        case Work::kVerticalLine_Segment:
3022                            pts = VLineIntersect(wt.pts(), wn.top(),
3023                                    wn.bottom(), wn.x(), wn.yFlipped(), ts);
3024                            debugShowLineIntersection(pts, wt, wn,
3025                                    ts.fT[1], ts.fT[0]);
3026                            break;
3027                        case Work::kLine_Segment: {
3028                            pts = LineIntersect(wt.pts(), wn.pts(), ts);
3029                            debugShowLineIntersection(pts, wt, wn,
3030                                    ts.fT[1], ts.fT[0]);
3031                            break;
3032                        }
3033                        case Work::kQuad_Segment: {
3034                            swap = true;
3035                            pts = QuadLineIntersect(wn.pts(), wt.pts(), ts);
3036                            break;
3037                        }
3038                        case Work::kCubic_Segment: {
3039                            swap = true;
3040                            pts = CubicLineIntersect(wn.pts(), wt.pts(), ts);
3041                            break;
3042                        }
3043                        default:
3044                            SkASSERT(0);
3045                    }
3046                    break;
3047                case Work::kQuad_Segment:
3048                    switch (wn.segmentType()) {
3049                        case Work::kHorizontalLine_Segment:
3050                            pts = HQuadIntersect(wt.pts(), wn.left(),
3051                                    wn.right(), wn.y(), wn.xFlipped(), ts);
3052                            break;
3053                        case Work::kVerticalLine_Segment:
3054                            pts = VQuadIntersect(wt.pts(), wn.top(),
3055                                    wn.bottom(), wn.x(), wn.yFlipped(), ts);
3056                            break;
3057                        case Work::kLine_Segment: {
3058                            pts = QuadLineIntersect(wt.pts(), wn.pts(), ts);
3059                            break;
3060                        }
3061                        case Work::kQuad_Segment: {
3062                            pts = QuadIntersect(wt.pts(), wn.pts(), ts);
3063                            break;
3064                        }
3065                        case Work::kCubic_Segment: {
3066                            wt.promoteToCubic();
3067                            pts = CubicIntersect(wt.cubic(), wn.pts(), ts);
3068                            break;
3069                        }
3070                        default:
3071                            SkASSERT(0);
3072                    }
3073                    break;
3074                case Work::kCubic_Segment:
3075                    switch (wn.segmentType()) {
3076                        case Work::kHorizontalLine_Segment:
3077                            pts = HCubicIntersect(wt.pts(), wn.left(),
3078                                    wn.right(), wn.y(), wn.xFlipped(), ts);
3079                            break;
3080                        case Work::kVerticalLine_Segment:
3081                            pts = VCubicIntersect(wt.pts(), wn.top(),
3082                                    wn.bottom(), wn.x(), wn.yFlipped(), ts);
3083                            break;
3084                        case Work::kLine_Segment: {
3085                            pts = CubicLineIntersect(wt.pts(), wn.pts(), ts);
3086                            break;
3087                        }
3088                        case Work::kQuad_Segment: {
3089                            wn.promoteToCubic();
3090                            pts = CubicIntersect(wt.pts(), wn.cubic(), ts);
3091                            break;
3092                        }
3093                        case Work::kCubic_Segment: {
3094                            pts = CubicIntersect(wt.pts(), wn.pts(), ts);
3095                            break;
3096                        }
3097                        default:
3098                            SkASSERT(0);
3099                    }
3100                    break;
3101                default:
3102                    SkASSERT(0);
3103            }
3104            if (!foundCommonContour && pts > 0) {
3105                test->addCross(next);
3106                next->addCross(test);
3107                foundCommonContour = true;
3108            }
3109            // in addition to recording T values, record matching segment
3110            if (pts == 2 && wn.segmentType() <= Work::kLine_Segment
3111                    && wt.segmentType() <= Work::kLine_Segment) {
3112                wt.addCoincident(wn, ts, swap);
3113                continue;
3114            }
3115            for (int pt = 0; pt < pts; ++pt) {
3116                SkASSERT(ts.fT[0][pt] >= 0 && ts.fT[0][pt] <= 1);
3117                SkASSERT(ts.fT[1][pt] >= 0 && ts.fT[1][pt] <= 1);
3118                int testTAt = wt.addT(ts.fT[swap][pt], wn);
3119                int nextTAt = wn.addT(ts.fT[!swap][pt], wt);
3120                wt.addOtherT(testTAt, ts.fT[!swap][pt], nextTAt);
3121                wn.addOtherT(nextTAt, ts.fT[swap][pt], testTAt);
3122            }
3123        } while (wn.advance());
3124    } while (wt.advance());
3125    return true;
3126}
3127
3128// resolve any coincident pairs found while intersecting, and
3129// see if coincidence is formed by clipping non-concident segments
3130static void coincidenceCheck(SkTDArray<Contour*>& contourList, int winding) {
3131    int contourCount = contourList.count();
3132    for (int cIndex = 0; cIndex < contourCount; ++cIndex) {
3133        Contour* contour = contourList[cIndex];
3134        contour->findTooCloseToCall(winding);
3135    }
3136    for (int cIndex = 0; cIndex < contourCount; ++cIndex) {
3137        Contour* contour = contourList[cIndex];
3138        contour->resolveCoincidence(winding);
3139    }
3140}
3141
3142// project a ray from the top of the contour up and see if it hits anything
3143// note: when we compute line intersections, we keep track of whether
3144// two contours touch, so we need only look at contours not touching this one.
3145// OPTIMIZATION: sort contourList vertically to avoid linear walk
3146static int innerContourCheck(SkTDArray<Contour*>& contourList,
3147        const Segment* current, int index, int endIndex) {
3148    const SkPoint& basePt = current->xyAtT(endIndex);
3149    int contourCount = contourList.count();
3150    SkScalar bestY = SK_ScalarMin;
3151    const Segment* test = NULL;
3152    int tIndex;
3153    double tHit;
3154 //   bool checkCrosses = true;
3155    for (int cTest = 0; cTest < contourCount; ++cTest) {
3156        Contour* contour = contourList[cTest];
3157        if (basePt.fY < contour->bounds().fTop) {
3158            continue;
3159        }
3160        if (bestY > contour->bounds().fBottom) {
3161            continue;
3162        }
3163#if 0
3164        // even though the contours crossed, if spans cancel through concidence,
3165        // the contours may be not have any span links to chase, and the current
3166        // segment may be isolated. Detect this by seeing if current has
3167        // uninitialized wind sums. If so, project a ray instead of relying on
3168        // previously found intersections.
3169        if (baseContour == contour) {
3170            continue;
3171        }
3172        if (checkCrosses && baseContour->crosses(contour)) {
3173            if (current->isConnected(index, endIndex)) {
3174                continue;
3175            }
3176            checkCrosses = false;
3177        }
3178#endif
3179        const Segment* next = contour->crossedSegment(basePt, bestY, tIndex, tHit);
3180        if (next) {
3181            test = next;
3182        }
3183    }
3184    if (!test) {
3185        return 0;
3186    }
3187    int winding, windValue;
3188    // If the ray hit the end of a span, we need to construct the wheel of
3189    // angles to find the span closest to the ray -- even if there are just
3190    // two spokes on the wheel.
3191    const Angle* angle = NULL;
3192    if (fabs(tHit - test->t(tIndex)) < FLT_EPSILON) {
3193        SkTDArray<Angle> angles;
3194        int end = test->nextSpan(tIndex, 1);
3195        if (end < 0) {
3196            end = test->nextSpan(tIndex, -1);
3197        }
3198        test->addTwoAngles(end, tIndex, angles);
3199        test->buildAngles(tIndex, angles);
3200        SkTDArray<Angle*> sorted;
3201        // OPTIMIZATION: call a sort that, if base point is the leftmost,
3202        // returns the first counterclockwise hour before 6 o'clock,
3203        // or if the base point is rightmost, returns the first clockwise
3204        // hour after 6 o'clock
3205        sortAngles(angles, sorted);
3206#if DEBUG_SORT
3207        sorted[0]->segment()->debugShowSort(sorted, 0, 0);
3208#endif
3209        // walk the sorted angle fan to find the lowest angle
3210        // above the base point. Currently, the first angle in the sorted array
3211        // is 12 noon or an earlier hour (the next counterclockwise)
3212        int count = sorted.count();
3213        int left = -1;
3214        int mid = -1;
3215        int right = -1;
3216        bool baseMatches = test->yAtT(tIndex) == basePt.fY;
3217        for (int index = 0; index < count; ++index) {
3218            const Angle* angle = sorted[index];
3219            if (baseMatches && angle->isHorizontal()) {
3220                continue;
3221            }
3222            double indexDx = angle->dx();
3223            if (indexDx < 0) {
3224                left = index;
3225            } else if (indexDx > 0) {
3226                right = index;
3227                break;
3228            } else {
3229                mid = index;
3230            }
3231        }
3232        if (left < 0 && right < 0) {
3233            left = mid;
3234        }
3235        SkASSERT(left >= 0 || right >= 0);
3236        if (left < 0) {
3237            left = right;
3238        } else if (left >= 0 && mid >= 0 && right >= 0
3239                && sorted[mid]->sign() == sorted[right]->sign()) {
3240            left = right;
3241        }
3242        angle = sorted[left];
3243        test = angle->segment();
3244        winding = test->windSum(angle);
3245        SkASSERT(winding != SK_MinS32);
3246        windValue = test->windValue(angle);
3247#if DEBUG_WINDING
3248        SkDebugf("%s angle winding=%d windValue=%d sign=%d\n", __FUNCTION__, winding,
3249                windValue, angle->sign());
3250#endif
3251    } else {
3252        winding = test->windSum(tIndex);
3253        SkASSERT(winding != SK_MinS32);
3254        windValue = test->windValue(tIndex);
3255#if DEBUG_WINDING
3256        SkDebugf("%s single winding=%d windValue=%d\n", __FUNCTION__, winding,
3257                windValue);
3258#endif
3259    }
3260    // see if a + change in T results in a +/- change in X (compute x'(T))
3261    SkScalar dx = (*SegmentDXAtT[test->verb()])(test->pts(), tHit);
3262#if DEBUG_WINDING
3263    SkDebugf("%s dx=%1.9g\n", __FUNCTION__, dx);
3264#endif
3265    if (dx == 0) {
3266        SkASSERT(angle);
3267        if (test->firstBump(angle, winding)) {
3268            winding -= test->windBump(angle);
3269        }
3270    } else if (winding * dx > 0) { // if same signs, result is negative
3271        winding += dx > 0 ? -windValue : windValue;
3272#if DEBUG_WINDING
3273        SkDebugf("%s final winding=%d\n", __FUNCTION__, winding);
3274#endif
3275    }
3276 //   start here;
3277    // we're broken because we find a vertical span
3278    return winding;
3279}
3280
3281// OPTIMIZATION: not crazy about linear search here to find top active y.
3282// seems like we should break down and do the sort, or maybe sort each
3283// contours' segments?
3284// Once the segment array is built, there's no reason I can think of not to
3285// sort it in Y. hmmm
3286// FIXME: return the contour found to pass to inner contour check
3287static Segment* findTopContour(SkTDArray<Contour*>& contourList) {
3288    int contourCount = contourList.count();
3289    int cIndex = 0;
3290    Segment* topStart;
3291    SkScalar bestY = SK_ScalarMax;
3292    Contour* contour;
3293    do {
3294        contour = contourList[cIndex];
3295        topStart = contour->topSegment(bestY);
3296    } while (!topStart && ++cIndex < contourCount);
3297    if (!topStart) {
3298        return NULL;
3299    }
3300    while (++cIndex < contourCount) {
3301        contour = contourList[cIndex];
3302        if (bestY < contour->bounds().fTop) {
3303            continue;
3304        }
3305        SkScalar testY = SK_ScalarMax;
3306        Segment* test = contour->topSegment(testY);
3307        if (!test || bestY <= testY) {
3308            continue;
3309        }
3310        topStart = test;
3311        bestY = testY;
3312    }
3313    return topStart;
3314}
3315
3316static Segment* findChase(SkTDArray<Span*>& chase, int& tIndex, int& endIndex,
3317        int contourWinding) {
3318    while (chase.count()) {
3319        Span* span = chase[chase.count() - 1];
3320        const Span& backPtr = span->fOther->span(span->fOtherIndex);
3321        Segment* segment = backPtr.fOther;
3322        tIndex = backPtr.fOtherIndex;
3323        SkTDArray<Angle> angles;
3324        int done = 0;
3325        if (segment->activeAngle(tIndex, done, angles)) {
3326            Angle* last = angles.end() - 1;
3327            tIndex = last->start();
3328            endIndex = last->end();
3329            return last->segment();
3330        }
3331        if (done == angles.count()) {
3332            chase.pop(&span);
3333            continue;
3334        }
3335        SkTDArray<Angle*> sorted;
3336        sortAngles(angles, sorted);
3337        // find first angle, initialize winding to computed fWindSum
3338        int firstIndex = -1;
3339        const Angle* angle;
3340        int winding;
3341        do {
3342            angle = sorted[++firstIndex];
3343            segment = angle->segment();
3344            winding = segment->windSum(angle);
3345        } while (winding == SK_MinS32);
3346        int spanWinding = segment->spanSign(angle->start(), angle->end());
3347    #if DEBUG_WINDING
3348        SkDebugf("%s winding=%d spanWinding=%d contourWinding=%d\n",
3349                __FUNCTION__, winding, spanWinding, contourWinding);
3350    #endif
3351        // turn swinding into contourWinding
3352        if (spanWinding * winding < 0) {
3353            winding += spanWinding;
3354        }
3355    #if DEBUG_SORT
3356        segment->debugShowSort(sorted, firstIndex, winding);
3357    #endif
3358        // we care about first sign and whether wind sum indicates this
3359        // edge is inside or outside. Maybe need to pass span winding
3360        // or first winding or something into this function?
3361        // advance to first undone angle, then return it and winding
3362        // (to set whether edges are active or not)
3363        int nextIndex = firstIndex + 1;
3364        int angleCount = sorted.count();
3365        int lastIndex = firstIndex != 0 ? firstIndex : angleCount;
3366        angle = sorted[firstIndex];
3367        winding -= angle->segment()->windBump(angle);
3368        do {
3369            SkASSERT(nextIndex != firstIndex);
3370            if (nextIndex == angleCount) {
3371                nextIndex = 0;
3372            }
3373            angle = sorted[nextIndex];
3374            segment = angle->segment();
3375            int maxWinding = winding;
3376            winding -= segment->windBump(angle);
3377    #if DEBUG_SORT
3378            SkDebugf("%s id=%d maxWinding=%d winding=%d\n", __FUNCTION__,
3379                    segment->debugID(), maxWinding, winding);
3380    #endif
3381            tIndex = angle->start();
3382            endIndex = angle->end();
3383            int lesser = SkMin32(tIndex, endIndex);
3384            const Span& nextSpan = segment->span(lesser);
3385            if (!nextSpan.fDone) {
3386#if 1
3387            // FIXME: this be wrong. assign startWinding if edge is in
3388            // same direction. If the direction is opposite, winding to
3389            // assign is flipped sign or +/- 1?
3390                if (abs(maxWinding) < abs(winding)) {
3391                    maxWinding = winding;
3392                }
3393                segment->markWinding(lesser, maxWinding);
3394#endif
3395                break;
3396            }
3397        } while (++nextIndex != lastIndex);
3398        return segment;
3399    }
3400    return NULL;
3401}
3402
3403#if DEBUG_ACTIVE_SPANS
3404static void debugShowActiveSpans(SkTDArray<Contour*>& contourList) {
3405    for (int index = 0; index < contourList.count(); ++ index) {
3406        contourList[index]->debugShowActiveSpans();
3407    }
3408}
3409#endif
3410
3411static bool windingIsActive(int winding, int spanWinding) {
3412    return winding * spanWinding <= 0 && abs(winding) <= abs(spanWinding)
3413            && (!winding || !spanWinding || winding == -spanWinding);
3414}
3415
3416// Each segment may have an inside or an outside. Segments contained within
3417// winding may have insides on either side, and form a contour that should be
3418// ignored. Segments that are coincident with opposing direction segments may
3419// have outsides on either side, and should also disappear.
3420// 'Normal' segments will have one inside and one outside. Subsequent connections
3421// when winding should follow the intersection direction. If more than one edge
3422// is an option, choose first edge that continues the inside.
3423    // since we start with leftmost top edge, we'll traverse through a
3424    // smaller angle counterclockwise to get to the next edge.
3425static void bridge(SkTDArray<Contour*>& contourList, SkPath& simple) {
3426    bool firstContour = true;
3427    do {
3428        Segment* topStart = findTopContour(contourList);
3429        if (!topStart) {
3430            break;
3431        }
3432        // Start at the top. Above the top is outside, below is inside.
3433        // follow edges to intersection by changing the index by direction.
3434        int index, endIndex;
3435        Segment* current = topStart->findTop(index, endIndex);
3436        int contourWinding;
3437        if (firstContour) {
3438            contourWinding = 0;
3439            firstContour = false;
3440        } else {
3441            contourWinding = current->windSum(SkMin32(index, endIndex));
3442            // FIXME: don't I have to adjust windSum to get contourWinding?
3443            if (contourWinding == SK_MinS32) {
3444                contourWinding = current->computeSum(index, endIndex);
3445                if (contourWinding == SK_MinS32) {
3446                    contourWinding = innerContourCheck(contourList, current,
3447                            index, endIndex);
3448                }
3449            }
3450#if DEBUG_WINDING
3451         //   SkASSERT(current->debugVerifyWinding(index, endIndex, contourWinding));
3452            SkDebugf("%s contourWinding=%d\n", __FUNCTION__, contourWinding);
3453#endif
3454        }
3455        SkPoint lastPt;
3456        bool firstTime = true;
3457        int winding = contourWinding;
3458        int spanWinding = current->spanSign(index, endIndex);
3459        // FIXME: needs work. While it works in limited situations, it does
3460        // not always compute winding correctly. Active should be removed and instead
3461        // the initial winding should be correctly passed in so that if the
3462        // inner contour is wound the same way, it never finds an accumulated
3463        // winding of zero. Inside 'find next', we need to look for transitions
3464        // other than zero when resolving sorted angles.
3465        bool active = windingIsActive(winding, spanWinding);
3466        SkTDArray<Span*> chaseArray;
3467        do {
3468        #if DEBUG_WINDING
3469            SkDebugf("%s active=%s winding=%d spanWinding=%d\n",
3470                    __FUNCTION__, active ? "true" : "false",
3471                    winding, spanWinding);
3472        #endif
3473            const SkPoint* firstPt = NULL;
3474            do {
3475                SkASSERT(!current->done());
3476                int nextStart, nextEnd;
3477                Segment* next = current->findNext(chaseArray,
3478                        firstTime, active, index, endIndex,
3479                        nextStart, nextEnd, winding, spanWinding);
3480                if (!next) {
3481                    break;
3482                }
3483                if (!firstPt) {
3484                    firstPt = &current->addMoveTo(index, simple, active);
3485                }
3486                lastPt = current->addCurveTo(index, endIndex, simple, active);
3487                current = next;
3488                index = nextStart;
3489                endIndex = nextEnd;
3490                firstTime = false;
3491            } while (*firstPt != lastPt && (active || !current->done()));
3492            if (firstPt && active) {
3493        #if DEBUG_PATH_CONSTRUCTION
3494                SkDebugf("%s close\n", __FUNCTION__);
3495        #endif
3496                simple.close();
3497            }
3498            current = findChase(chaseArray, index, endIndex, contourWinding);
3499        #if DEBUG_ACTIVE_SPANS
3500            debugShowActiveSpans(contourList);
3501        #endif
3502            if (!current) {
3503                break;
3504            }
3505            int lesser = SkMin32(index, endIndex);
3506            spanWinding = current->spanSign(index, endIndex);
3507            winding = current->windSum(lesser);
3508            if (spanWinding * winding > 0) {
3509                winding -= spanWinding;
3510            }
3511            active = windingIsActive(winding, spanWinding);
3512        } while (true);
3513    } while (true);
3514}
3515
3516static void fixOtherTIndex(SkTDArray<Contour*>& contourList) {
3517    int contourCount = contourList.count();
3518    for (int cTest = 0; cTest < contourCount; ++cTest) {
3519        Contour* contour = contourList[cTest];
3520        contour->fixOtherTIndex();
3521    }
3522}
3523
3524static void makeContourList(SkTArray<Contour>& contours,
3525        SkTDArray<Contour*>& list) {
3526    int count = contours.count();
3527    if (count == 0) {
3528        return;
3529    }
3530    for (int index = 0; index < count; ++index) {
3531        *list.append() = &contours[index];
3532    }
3533    QSort<Contour>(list.begin(), list.end() - 1);
3534}
3535
3536void simplifyx(const SkPath& path, SkPath& simple) {
3537    // returns 1 for evenodd, -1 for winding, regardless of inverse-ness
3538    int winding = (path.getFillType() & 1) ? 1 : -1;
3539    simple.reset();
3540    simple.setFillType(SkPath::kEvenOdd_FillType);
3541
3542    // turn path into list of segments
3543    SkTArray<Contour> contours;
3544    // FIXME: add self-intersecting cubics' T values to segment
3545    EdgeBuilder builder(path, contours);
3546    SkTDArray<Contour*> contourList;
3547    makeContourList(contours, contourList);
3548    Contour** currentPtr = contourList.begin();
3549    if (!currentPtr) {
3550        return;
3551    }
3552    Contour** listEnd = contourList.end();
3553    // find all intersections between segments
3554    do {
3555        Contour** nextPtr = currentPtr;
3556        Contour* current = *currentPtr++;
3557        Contour* next;
3558        do {
3559            next = *nextPtr++;
3560        } while (addIntersectTs(current, next) && nextPtr != listEnd);
3561    } while (currentPtr != listEnd);
3562    // eat through coincident edges
3563    coincidenceCheck(contourList, winding);
3564    fixOtherTIndex(contourList);
3565    // construct closed contours
3566    bridge(contourList, simple);
3567}
3568
3569