Simplify.cpp revision fcd4f3e5bf55d8cd1d97c8f620fabd41eb6a754b
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 "CurveIntersection.h"
8#include "Intersections.h"
9#include "LineIntersection.h"
10#include "SkPath.h"
11#include "SkRect.h"
12#include "SkTArray.h"
13#include "SkTDArray.h"
14#include "ShapeOps.h"
15#include "TSearch.h"
16#include <algorithm> // used for std::min
17
18#undef SkASSERT
19#define SkASSERT(cond) while (!(cond)) { sk_throw(); }
20
21// Terminology:
22// A Path contains one of more Contours
23// A Contour is made up of Segment array
24// A Segment is described by a Verb and a Point array
25// A Verb is one of Line, Quad(ratic), and Cubic
26// A Segment contains a Span array
27// A Span is describes a portion of a Segment using starting and ending T
28// T values range from 0 to 1, where 0 is the first Point in the Segment
29
30// FIXME: remove once debugging is complete
31#if 0 // set to 1 for no debugging whatsoever
32
33//const bool gxRunTestsInOneThread = false;
34
35#define DEBUG_ADD_INTERSECTING_TS 0
36#define DEBUG_BRIDGE 0
37#define DEBUG_DUMP 0
38
39#else
40
41//const bool gRunTestsInOneThread = true;
42
43#define DEBUG_ADD_INTERSECTING_TS 1
44#define DEBUG_BRIDGE 1
45#define DEBUG_DUMP 1
46
47#endif
48
49#if DEBUG_DUMP
50static const char* kLVerbStr[] = {"", "line", "quad", "cubic"};
51static const char* kUVerbStr[] = {"", "Line", "Quad", "Cubic"};
52static int gContourID;
53static int gSegmentID;
54#endif
55
56static int LineIntersect(const SkPoint a[2], const SkPoint b[2],
57        Intersections& intersections) {
58    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
59    const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
60    return intersect(aLine, bLine, intersections.fT[0], intersections.fT[1]);
61}
62
63static int QuadLineIntersect(const SkPoint a[3], const SkPoint b[2],
64        Intersections& intersections) {
65    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
66    const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
67    intersect(aQuad, bLine, intersections);
68    return intersections.fUsed;
69}
70
71static int CubicLineIntersect(const SkPoint a[2], const SkPoint b[3],
72        Intersections& intersections) {
73    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
74            {a[3].fX, a[3].fY}};
75    const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
76    return intersect(aCubic, bLine, intersections.fT[0], intersections.fT[1]);
77}
78
79static int QuadIntersect(const SkPoint a[3], const SkPoint b[3],
80        Intersections& intersections) {
81    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
82    const Quadratic bQuad = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}, {b[2].fX, b[2].fY}};
83    intersect(aQuad, bQuad, intersections);
84    return intersections.fUsed;
85}
86
87static int CubicIntersect(const SkPoint a[4], const SkPoint b[4],
88        Intersections& intersections) {
89    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
90            {a[3].fX, a[3].fY}};
91    const Cubic bCubic = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}, {b[2].fX, b[2].fY},
92            {b[3].fX, b[3].fY}};
93    intersect(aCubic, bCubic, intersections);
94    return intersections.fUsed;
95}
96
97static int HLineIntersect(const SkPoint a[2], SkScalar left, SkScalar right,
98        SkScalar y, bool flipped, Intersections& intersections) {
99    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
100    return horizontalIntersect(aLine, left, right, y, flipped, intersections);
101}
102
103static int VLineIntersect(const SkPoint a[2], SkScalar left, SkScalar right,
104        SkScalar y, bool flipped, Intersections& intersections) {
105    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
106    return verticalIntersect(aLine, left, right, y, flipped, intersections);
107}
108
109static int HQuadIntersect(const SkPoint a[3], SkScalar left, SkScalar right,
110        SkScalar y, bool flipped, Intersections& intersections) {
111    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
112    return horizontalIntersect(aQuad, left, right, y, flipped, intersections);
113}
114
115static int VQuadIntersect(const SkPoint a[3], SkScalar left, SkScalar right,
116        SkScalar y, bool flipped, Intersections& intersections) {
117    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
118    return verticalIntersect(aQuad, left, right, y, flipped, intersections);
119}
120
121static int HCubicIntersect(const SkPoint a[4], SkScalar left, SkScalar right,
122        SkScalar y, bool flipped, Intersections& intersections) {
123    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
124            {a[3].fX, a[3].fY}};
125    return horizontalIntersect(aCubic, left, right, y, flipped, intersections);
126}
127
128static int VCubicIntersect(const SkPoint a[4], SkScalar left, SkScalar right,
129        SkScalar y, bool flipped, Intersections& intersections) {
130    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
131            {a[3].fX, a[3].fY}};
132    return verticalIntersect(aCubic, left, right, y, flipped, intersections);
133}
134
135static void LineXYAtT(const SkPoint a[2], double t, SkPoint* out) {
136    const _Line line = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
137    double x, y;
138    xy_at_t(line, t, x, y);
139    out->fX = SkDoubleToScalar(x);
140    out->fY = SkDoubleToScalar(y);
141}
142
143static void QuadXYAtT(const SkPoint a[3], double t, SkPoint* out) {
144    const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
145    double x, y;
146    xy_at_t(quad, t, x, y);
147    out->fX = SkDoubleToScalar(x);
148    out->fY = SkDoubleToScalar(y);
149}
150
151static void CubicXYAtT(const SkPoint a[4], double t, SkPoint* out) {
152    const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
153            {a[3].fX, a[3].fY}};
154    double x, y;
155    xy_at_t(cubic, t, x, y);
156    out->fX = SkDoubleToScalar(x);
157    out->fY = SkDoubleToScalar(y);
158}
159
160static void (* const SegmentXYAtT[])(const SkPoint [], double , SkPoint* ) = {
161    NULL,
162    LineXYAtT,
163    QuadXYAtT,
164    CubicXYAtT
165};
166
167static SkScalar LineXAtT(const SkPoint a[2], double t) {
168    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
169    double x;
170    xy_at_t(aLine, t, x, *(double*) 0);
171    return SkDoubleToScalar(x);
172}
173
174static SkScalar QuadXAtT(const SkPoint a[3], double t) {
175    const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
176    double x;
177    xy_at_t(quad, t, x, *(double*) 0);
178    return SkDoubleToScalar(x);
179}
180
181static SkScalar CubicXAtT(const SkPoint a[4], double t) {
182    const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
183            {a[3].fX, a[3].fY}};
184    double x;
185    xy_at_t(cubic, t, x, *(double*) 0);
186    return SkDoubleToScalar(x);
187}
188
189static SkScalar (* const SegmentXAtT[])(const SkPoint [], double ) = {
190    NULL,
191    LineXAtT,
192    QuadXAtT,
193    CubicXAtT
194};
195
196static SkScalar LineYAtT(const SkPoint a[2], double t) {
197    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
198    double y;
199    xy_at_t(aLine, t, *(double*) 0, y);
200    return SkDoubleToScalar(y);
201}
202
203static SkScalar QuadYAtT(const SkPoint a[3], double t) {
204    const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
205    double y;
206    xy_at_t(quad, t, *(double*) 0, y);
207    return SkDoubleToScalar(y);
208}
209
210static SkScalar CubicYAtT(const SkPoint a[4], double t) {
211    const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
212            {a[3].fX, a[3].fY}};
213    double y;
214    xy_at_t(cubic, t, *(double*) 0, y);
215    return SkDoubleToScalar(y);
216}
217
218static SkScalar (* const SegmentYAtT[])(const SkPoint [], double ) = {
219    NULL,
220    LineYAtT,
221    QuadYAtT,
222    CubicYAtT
223};
224
225static void LineSubDivide(const SkPoint a[2], double startT, double endT,
226        SkPoint sub[2]) {
227    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
228    _Line dst;
229    sub_divide(aLine, startT, endT, dst);
230    sub[0].fX = SkDoubleToScalar(dst[0].x);
231    sub[0].fY = SkDoubleToScalar(dst[0].y);
232    sub[1].fX = SkDoubleToScalar(dst[1].x);
233    sub[1].fY = SkDoubleToScalar(dst[1].y);
234}
235
236static void QuadSubDivide(const SkPoint a[3], double startT, double endT,
237        SkPoint sub[3]) {
238    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
239            {a[2].fX, a[2].fY}};
240    Quadratic dst;
241    sub_divide(aQuad, startT, endT, dst);
242    sub[0].fX = SkDoubleToScalar(dst[0].x);
243    sub[0].fY = SkDoubleToScalar(dst[0].y);
244    sub[1].fX = SkDoubleToScalar(dst[1].x);
245    sub[1].fY = SkDoubleToScalar(dst[1].y);
246    sub[2].fX = SkDoubleToScalar(dst[2].x);
247    sub[2].fY = SkDoubleToScalar(dst[2].y);
248}
249
250static void CubicSubDivide(const SkPoint a[4], double startT, double endT,
251        SkPoint sub[4]) {
252    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
253            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
254    Cubic dst;
255    sub_divide(aCubic, startT, endT, dst);
256    sub[0].fX = SkDoubleToScalar(dst[0].x);
257    sub[0].fY = SkDoubleToScalar(dst[0].y);
258    sub[1].fX = SkDoubleToScalar(dst[1].x);
259    sub[1].fY = SkDoubleToScalar(dst[1].y);
260    sub[2].fX = SkDoubleToScalar(dst[2].x);
261    sub[2].fY = SkDoubleToScalar(dst[2].y);
262    sub[3].fX = SkDoubleToScalar(dst[3].x);
263    sub[3].fY = SkDoubleToScalar(dst[3].y);
264}
265
266static void QuadSubBounds(const SkPoint a[3], double startT, double endT,
267        SkRect& bounds) {
268    SkPoint dst[3];
269    QuadSubDivide(a, startT, endT, dst);
270    bounds.fLeft = bounds.fRight = dst[0].fX;
271    bounds.fTop = bounds.fBottom = dst[0].fY;
272    for (int index = 1; index < 3; ++index) {
273        bounds.growToInclude(dst[index].fX, dst[index].fY);
274    }
275}
276
277static void CubicSubBounds(const SkPoint a[4], double startT, double endT,
278        SkRect& bounds) {
279    SkPoint dst[4];
280    CubicSubDivide(a, startT, endT, dst);
281    bounds.fLeft = bounds.fRight = dst[0].fX;
282    bounds.fTop = bounds.fBottom = dst[0].fY;
283    for (int index = 1; index < 4; ++index) {
284        bounds.growToInclude(dst[index].fX, dst[index].fY);
285    }
286}
287
288static SkPath::Verb QuadReduceOrder(const SkPoint a[3],
289        SkTDArray<SkPoint>& reducePts) {
290    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
291            {a[2].fX, a[2].fY}};
292    Quadratic dst;
293    int order = reduceOrder(aQuad, dst);
294    for (int index = 0; index < order; ++index) {
295        SkPoint* pt = reducePts.append();
296        pt->fX = SkDoubleToScalar(dst[index].x);
297        pt->fY = SkDoubleToScalar(dst[index].y);
298    }
299    return (SkPath::Verb) (order - 1);
300}
301
302static SkPath::Verb CubicReduceOrder(const SkPoint a[4],
303        SkTDArray<SkPoint>& reducePts) {
304    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
305            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
306    Cubic dst;
307    int order = reduceOrder(aCubic, dst, kReduceOrder_QuadraticsAllowed);
308    for (int index = 0; index < order; ++index) {
309        SkPoint* pt = reducePts.append();
310        pt->fX = SkDoubleToScalar(dst[index].x);
311        pt->fY = SkDoubleToScalar(dst[index].y);
312    }
313    return (SkPath::Verb) (order - 1);
314}
315
316static bool QuadIsLinear(const SkPoint a[3]) {
317    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
318            {a[2].fX, a[2].fY}};
319    return isLinear(aQuad, 0, 2);
320}
321
322static bool CubicIsLinear(const SkPoint a[4]) {
323    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
324            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
325    return isLinear(aCubic, 0, 3);
326}
327
328static SkScalar LineLeftMost(const SkPoint a[2], double startT, double endT) {
329    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
330    double x[2];
331    xy_at_t(aLine, startT, x[0], *(double*) 0);
332    xy_at_t(aLine, endT, x[0], *(double*) 0);
333    return startT < endT ? startT : endT;
334}
335
336static SkScalar QuadLeftMost(const SkPoint a[3], double startT, double endT) {
337    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
338            {a[2].fX, a[2].fY}};
339    return leftMostT(aQuad, startT, endT);
340}
341
342static SkScalar CubicLeftMost(const SkPoint a[4], double startT, double endT) {
343    const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
344            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
345    return leftMostT(aCubic, startT, endT);
346}
347
348static SkScalar (* const SegmentLeftMost[])(const SkPoint [], double , double) = {
349    NULL,
350    LineLeftMost,
351    QuadLeftMost,
352    CubicLeftMost
353};
354
355static bool IsCoincident(const SkPoint a[2], const SkPoint& above,
356        const SkPoint& below) {
357    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
358    const _Line bLine = {{above.fX, above.fY}, {below.fX, below.fY}};
359    return implicit_matches_ulps(aLine, bLine, 32);
360}
361
362// sorting angles
363// given angles of {dx dy ddx ddy dddx dddy} sort them
364class Angle {
365public:
366    bool operator<(const Angle& rh) const {
367        if ((dy < 0) ^ (rh.dy < 0)) {
368            return dy < 0;
369        }
370        SkScalar cmp = dx * rh.dy - rh.dx * dy;
371        if (cmp) {
372            return cmp < 0;
373        }
374        if ((ddy < 0) ^ (rh.ddy < 0)) {
375            return ddy < 0;
376        }
377        cmp = ddx * rh.ddy - rh.ddx * ddy;
378        if (cmp) {
379            return cmp < 0;
380        }
381        if ((dddy < 0) ^ (rh.dddy < 0)) {
382            return ddy < 0;
383        }
384        return dddx * rh.dddy < rh.dddx * dddy;
385    }
386
387    void set(SkPoint* pts, SkPath::Verb verb) {
388        dx = pts[1].fX - pts[0].fX; // b - a
389        dy = pts[1].fY - pts[0].fY;
390        if (verb == SkPath::kLine_Verb) {
391            ddx = ddy = dddx = dddy = 0;
392            return;
393        }
394        ddx = pts[2].fX - pts[1].fX - dx; // a - 2b + c
395        ddy = pts[2].fY - pts[2].fY - dy;
396        if (verb == SkPath::kQuad_Verb) {
397            dddx = dddy = 0;
398            return;
399        }
400        dddx = pts[3].fX + 3 * (pts[1].fX - pts[2].fX) - pts[0].fX;
401        dddy = pts[3].fY + 3 * (pts[1].fY - pts[2].fY) - pts[0].fY;
402    }
403
404private:
405    SkScalar dx;
406    SkScalar dy;
407    SkScalar ddx;
408    SkScalar ddy;
409    SkScalar dddx;
410    SkScalar dddy;
411};
412
413// Bounds, unlike Rect, does not consider a vertical line to be empty.
414struct Bounds : public SkRect {
415    static bool Intersects(const Bounds& a, const Bounds& b) {
416        return a.fLeft <= b.fRight && b.fLeft <= a.fRight &&
417                a.fTop <= b.fBottom && b.fTop <= a.fBottom;
418    }
419
420    bool isEmpty() {
421        return fLeft > fRight || fTop > fBottom
422                || fLeft == fRight && fTop == fBottom
423                || isnan(fLeft) || isnan(fRight)
424                || isnan(fTop) || isnan(fBottom);
425    }
426
427    void setCubicBounds(const SkPoint a[4]) {
428        _Rect dRect;
429        Cubic cubic  = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
430            {a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
431        dRect.setBounds(cubic);
432        set(dRect.left, dRect.top, dRect.right, dRect.bottom);
433    }
434
435    void setQuadBounds(const SkPoint a[3]) {
436        const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
437                {a[2].fX, a[2].fY}};
438        _Rect dRect;
439        dRect.setBounds(quad);
440        set(dRect.left, dRect.top, dRect.right, dRect.bottom);
441    }
442};
443
444class Segment;
445
446struct Span {
447    double fT;
448    Segment* fOther;
449    double fOtherT;
450    int fWinding; // accumulated from contours surrounding this one
451    // OPTIMIZATION: done needs only 2 bits (values are -1, 0, 1)
452    int fDone; // set when t to t+fDone is processed
453    // OPTIMIZATION: done needs only 2 bits (values are -1, 0, 1)
454    int fCoincident; // -1 start of coincidence, 0 no coincidence, 1 end
455};
456
457class Segment {
458public:
459    Segment() {
460#if DEBUG_DUMP
461        fID = ++gSegmentID;
462#endif
463    }
464
465    void addAngle(SkTDArray<Angle>& angles, double start, double end) {
466        // FIXME complete this
467        // start here;
468    }
469
470    bool addCubic(const SkPoint pts[4]) {
471        fPts = pts;
472        fVerb = SkPath::kCubic_Verb;
473        fBounds.setCubicBounds(pts);
474    }
475
476    bool addLine(const SkPoint pts[2]) {
477        fPts = pts;
478        fVerb = SkPath::kLine_Verb;
479        fBounds.set(pts, 2);
480    }
481
482    // add 2 to edge or out of range values to get T extremes
483    void addOtherT(int index, double other) {
484        fTs[index].fOtherT = other;
485    }
486
487    bool addQuad(const SkPoint pts[3]) {
488        fPts = pts;
489        fVerb = SkPath::kQuad_Verb;
490        fBounds.setQuadBounds(pts);
491    }
492
493    int addT(double newT, Segment& other, int coincident) {
494        // FIXME: in the pathological case where there is a ton of intercepts,
495        //  binary search?
496        int insertedAt = -1;
497        Span* span;
498        size_t tCount = fTs.count();
499        double delta;
500        for (size_t idx2 = 0; idx2 < tCount; ++idx2) {
501            // OPTIMIZATION: if there are three or more identical Ts, then
502            // the fourth and following could be further insertion-sorted so
503            // that all the edges are clockwise or counterclockwise.
504            // This could later limit segment tests to the two adjacent
505            // neighbors, although it doesn't help with determining which
506            // circular direction to go in.
507            if (newT <= fTs[idx2].fT) {
508                insertedAt = idx2;
509                span = fTs.insert(idx2);
510                goto finish;
511            }
512        }
513        insertedAt = tCount;
514        span = fTs.append();
515finish:
516        span->fT = newT;
517        span->fOther = &other;
518        span->fWinding = 1;
519        span->fDone = 0;
520        span->fCoincident = coincident;
521        fCoincident |= coincident;
522        return insertedAt;
523    }
524
525    const Bounds& bounds() const {
526        return fBounds;
527    }
528
529    bool done() const {
530        return fDone;
531    }
532
533    int findCoincidentEnd(int start) const {
534        int tCount = fTs.count();
535        SkASSERT(start < tCount);
536        const Span& span = fTs[start];
537        SkASSERT(span.fCoincident);
538        for (int index = start + 1; index < tCount; ++index) {
539            const Span& match = fTs[index];
540            if (match.fOther == span.fOther) {
541                SkASSERT(match.fCoincident);
542                return index;
543            }
544        }
545        SkASSERT(0); // should never get here
546        return -1;
547    }
548
549    // start is the index of the beginning T of this edge
550    // it is guaranteed to have an end which describes a non-zero length (?)
551    // winding -1 means ccw, 1 means cw
552    // step is in/out -1 or 1
553    // spanIndex is returned
554    Segment* findNext(int start, int winding, int& step, int& spanIndex) {
555        SkASSERT(step == 1 || step == -1);
556        int count = fTs.count();
557        SkASSERT(step > 0 ? start < count - 1 : start > 0);
558        Span* startSpan = &fTs[start];
559        // FIXME:
560        // since Ts can be stepped either way, done markers must be careful
561        // not to assume that segment was only ascending in T. This shouldn't
562        // be a problem unless pathologically a segment can be partially
563        // ascending and partially descending -- maybe quads/cubic can do this?
564        startSpan->fDone = step;
565        SkPoint startLoc; // OPTIMIZATION: store this in the t span?
566        xyAtT(startSpan->fT, &startLoc);
567        SkPoint endLoc;
568        Span* endSpan;
569        int end = nextSpan(start, step, startLoc, startSpan, &endLoc, &endSpan);
570
571        // if we hit the end looking for span end, is that always an error?
572        SkASSERT(step > 0 ? end + 1 < count : end - 1 >= 0);
573
574        // preflight for coincidence -- if present, it may change winding
575        // considerations and whether reversed edges can be followed
576        bool foundCoincident = false;
577        int last = lastSpan(end, step, &startLoc, startSpan, foundCoincident);
578
579        // Discard opposing direction candidates if no coincidence was found.
580        int candidateCount = abs(last - end);
581        if (candidateCount == 1) {
582            SkASSERT(!foundCoincident);
583            // move in winding direction until edge in correct direction
584            // balance wrong direction edges before finding correct one
585            // this requres that the intersection is angularly sorted
586            // for a single intersection, special case -- choose the opposite
587            // edge that steps the same
588            Segment* other = endSpan->fOther;
589            SkASSERT(!other->fDone);
590            spanIndex = other->matchSpan(this, endSpan->fT);
591            SkASSERT(step < 0 ? spanIndex > 0 : spanIndex < other->fTs.count() - 1);
592            return other;
593        }
594
595        // find the next T that describes a length
596        SkTDArray<Angle> angles;
597        Segment* segmentCandidate = NULL;
598        int spanCandidate = -1;
599        int directionCandidate;
600        do {
601            endSpan = &fTs[end];
602            Segment* other = endSpan->fOther;
603            if (other->fDone) {
604                continue;
605            }
606        // if there is only one live crossing, and no coincidence, continue
607        // in the same direction
608        // if there is coincidence, the only choice may be to reverse direction
609            // find edge on either side of intersection
610            int oIndex = other->matchSpan(this, endSpan->fT);
611            int oCount = other->fTs.count();
612            do {
613                Span& otherSpan = other->fTs[oIndex];
614                // if done == -1, prior span has already been processed
615                int next = other->nextSpan(oIndex, step, endLoc, &otherSpan,
616                        NULL, NULL);
617                if (next < 0) {
618                    continue;
619                }
620                bool otherIsCoincident;
621                last = other->lastSpan(next, step, &endLoc, &otherSpan,
622                        otherIsCoincident);
623                if (last < 0) {
624                    continue;
625                }
626            #if 0
627                Span& prior = other->fTs[oIndex - 1];
628                    if (otherSpan.fDone >= 0 && oIndex > 0) {
629                        // FIXME: this needs to loop on -- until t && pt are different
630                        if (prior.fDone > 0) {
631                            continue;
632                        }
633
634                    }
635                } else { // step == 1
636                    if (otherSpan.fDone <= 0 && oIndex < oCount - 1) {
637                        // FIXME: this needs to loop on ++ until t && pt are different
638                        Span& next = other->fTs[oIndex + 1];
639                        if (next.fDone < 0) {
640                            continue;
641                        }
642                    }
643                }
644            #endif
645                if (!segmentCandidate) {
646                    segmentCandidate = other;
647                    spanCandidate = oIndex;
648                    directionCandidate = step;
649                    continue;
650                }
651                // there's two or more matches
652                if (spanCandidate >= 0) { // retrieve first stored candidate
653                    // add edge leading into junction
654                    addAngle(angles, endSpan->fT, startSpan->fT);
655                    // add edge leading away from junction
656                    double nextT = nextSpan(end, step, endLoc, endSpan, NULL,
657                            NULL);
658                    if (nextT >= 0) {
659                        addAngle(angles, endSpan->fT, nextT);
660                    }
661                    // add first stored candidate into junction
662                    segmentCandidate->addAngle(angles,
663                            segmentCandidate->fTs[spanCandidate - 1].fT,
664                            segmentCandidate->fTs[spanCandidate].fT);
665                    // add first stored candidate away from junction
666                    segmentCandidate->addAngle(angles,
667                            segmentCandidate->fTs[spanCandidate].fT,
668                            segmentCandidate->fTs[spanCandidate + 1].fT);
669                }
670                // add candidate into and away from junction
671
672
673           //     start here;
674                // more than once viable candidate -- need to
675                //  measure angles to find best
676                // noncoincident quads/cubics may have the same initial angle
677                // as lines, so must sort by derivatives as well
678                // while we're here, figure out all connections given the
679                //  initial winding info
680                // so the span needs to contain the pairing info found here
681                // this should include the winding computed for the edge, and
682                //  what edge it connects to, and whether it is discarded
683                //  (maybe discarded == abs(winding) > 1) ?
684                // only need derivatives for duration of sorting, add a new struct
685                // for pairings, remove extra spans that have zero length and
686                //  reference an unused other
687                // for coincident, the last span on the other may be marked done
688                //  (always?)
689            } while (++oIndex < oCount);
690        } while ((end += step) != last);
691        // if loop is exhausted, contour may be closed.
692        // FIXME: pass in close point so we can check for closure
693
694        // given a segment, and a sense of where 'inside' is, return the next
695        // segment. If this segment has an intersection, or ends in multiple
696        // segments, find the mate that continues the outside.
697        // note that if there are multiples, but no coincidence, we can limit
698        // choices to connections in the correct direction
699
700        // mark found segments as done
701    }
702
703    void findTooCloseToCall(int winding) {
704        int count = fTs.count();
705        if (count < 3) { // require t=0, x, 1 at minimum
706            return;
707        }
708        int matchIndex = 0;
709        int moCount;
710        Span* match;
711        Segment* mOther;
712        do {
713            match = &fTs[matchIndex];
714            mOther = match->fOther;
715            moCount = mOther->fTs.count();
716        } while (moCount >= 3 || ++matchIndex < count - 1); // require t=0, x, 1 at minimum
717        SkPoint matchPt;
718        // OPTIMIZATION: defer matchPt until qualifying toCount is found?
719        xyAtT(match->fT, &matchPt);
720        // look for a pair of nearby T values that map to the same (x,y) value
721        // if found, see if the pair of other segments share a common point. If
722        // so, the span from here to there is coincident.
723        for (int index = matchIndex + 1; index < count; ++index) {
724            Span* test = &fTs[index];
725            Segment* tOther = test->fOther;
726            int toCount = tOther->fTs.count();
727            if (toCount < 3) { // require t=0, x, 1 at minimum
728                continue;
729            }
730            SkPoint testPt;
731            xyAtT(test->fT, &testPt);
732            if (matchPt != testPt) {
733                matchIndex = index;
734                moCount = toCount;
735                match = test;
736                mOther = tOther;
737                matchPt = testPt;
738                continue;
739            }
740            int moStart = -1; // FIXME: initialization is debugging only
741            for (int moIndex = 0; moIndex < moCount; ++moIndex) {
742                Span& moSpan = mOther->fTs[moIndex];
743                if (moSpan.fOther == this) {
744                    if (moSpan.fOtherT == match->fT) {
745                        moStart = moIndex;
746                    }
747                    continue;
748                }
749                if (moSpan.fOther != tOther) {
750                    continue;
751                }
752                int toStart = -1;
753                int toIndex; // FIXME: initialization is debugging only
754                bool found = false;
755                for (toIndex = 0; toIndex < toCount; ++toIndex) {
756                    Span& toSpan = tOther->fTs[toIndex];
757                    if (toSpan.fOther == this) {
758                        if (toSpan.fOtherT == test->fT) {
759                            toStart = toIndex;
760                        }
761                        continue;
762                    }
763                    if (toSpan.fOther == mOther && toSpan.fOtherT
764                            == moSpan.fT) {
765                        found = true;
766                        break;
767                    }
768                }
769                if (!found) {
770                    continue;
771                }
772                SkASSERT(moStart >= 0);
773                SkASSERT(toStart >= 0);
774                // test to see if the segment between there and here is linear
775                if (!mOther->isLinear(moStart, moIndex)
776                        || !tOther->isLinear(toStart, toIndex)) {
777                    continue;
778                }
779                mOther->fTs[moStart].fCoincident = -1;
780                tOther->fTs[toStart].fCoincident = -1;
781                mOther->fTs[moIndex].fCoincident = 1;
782                tOther->fTs[toIndex].fCoincident = 1;
783            }
784    nextStart:
785            ;
786        }
787    }
788
789    int findByT(double t, const Segment* match) const {
790        // OPTIMIZATION: bsearch if count is honkin huge
791        int count = fTs.count();
792        for (int index = 0; index < count; ++index) {
793            const Span& span = fTs[index];
794            if (t == span.fT && match == span.fOther) {
795                return index;
796            }
797        }
798        SkASSERT(0); // should never get here
799        return -1;
800    }
801
802    // find the adjacent T that is leftmost, with a point != base
803    int findLefty(int tIndex, const SkPoint& base) const {
804        int bestTIndex;
805        SkPoint test;
806        SkScalar bestX = DBL_MAX;
807        int testTIndex = tIndex;
808        while (--testTIndex >= 0) {
809            xyAtT(testTIndex, &test);
810            if (test != base) {
811                continue;
812            }
813            bestX = test.fX;
814            bestTIndex = testTIndex;
815            break;
816        }
817        int count = fTs.count();
818        testTIndex = tIndex;
819        while (++testTIndex < count) {
820            xyAtT(testTIndex, &test);
821            if (test == base) {
822                continue;
823            }
824            return bestX > test.fX ? testTIndex : bestTIndex;
825        }
826        SkASSERT(0); // can't get here (?)
827        return -1;
828    }
829
830    // OPTIMIZATION : for a pair of lines, can we compute points at T (cached)
831    // and use more concise logic like the old edge walker code?
832    // FIXME: this needs to deal with coincident edges
833    const Segment* findTop(int& tIndex) const {
834        // iterate through T intersections and return topmost
835        // topmost tangent from y-min to first pt is closer to horizontal
836        int firstT = 0;
837        int lastT = 0;
838        SkScalar topY = fPts[0].fY;
839        int count = fTs.count();
840        int index;
841        for (index = 1; index < count; ++index) {
842            const Span& span = fTs[index];
843            double t = span.fT;
844            SkScalar yIntercept = yAtT(t);
845            if (topY > yIntercept) {
846                topY = yIntercept;
847                firstT = lastT = index;
848            } else if (topY == yIntercept) {
849                lastT = index;
850            }
851        }
852        // if there's only a pair of segments, go with the endpoint chosen above
853        if (firstT == lastT && (firstT == 0 || firstT == count - 1)) {
854            tIndex = firstT;
855            return this;
856        }
857        // if the topmost T is not on end, or is three-way or more, find left
858        SkPoint leftBase;
859        xyAtT(firstT, &leftBase);
860        int tLeft = findLefty(firstT, leftBase);
861        const Segment* leftSegment = this;
862        // look for left-ness from tLeft to firstT (matching y of other)
863        for (index = firstT; index <= lastT; ++index) {
864            const Segment* other = fTs[index].fOther;
865            double otherT = fTs[index].fOtherT;
866            int otherTIndex = other->findByT(otherT, this);
867            // pick companionT closest (but not too close) on either side
868            int otherTLeft = other->findLefty(otherTIndex, leftBase);
869            // within this span, find highest y
870            SkPoint testPt, otherPt;
871            testPt.fY = yAtT(tLeft);
872            otherPt.fY = other->yAtT(otherTLeft);
873            // FIXME: incomplete
874            // find the y intercept with the opposite segment
875            if (testPt.fY < otherPt.fY) {
876
877            } else if (testPt.fY > otherPt.fY) {
878
879            }
880            // FIXME: leftMost no good. Use y intercept instead
881#if 0
882            SkScalar otherMost = other->leftMost(otherTIndex, otherTLeft);
883            if (otherMost < left) {
884                leftSegment = other;
885            }
886#endif
887        }
888        return leftSegment;
889    }
890
891    bool intersected() const {
892        return fTs.count() > 0;
893    }
894
895    bool isLinear(int start, int end) const {
896        if (fVerb == SkPath::kLine_Verb) {
897            return true;
898        }
899        if (fVerb == SkPath::kQuad_Verb) {
900            SkPoint qPart[3];
901            QuadSubDivide(fPts, fTs[start].fT, fTs[end].fT, qPart);
902            return QuadIsLinear(qPart);
903        } else {
904            SkASSERT(fVerb == SkPath::kCubic_Verb);
905            SkPoint cPart[4];
906            CubicSubDivide(fPts, fTs[start].fT, fTs[end].fT, cPart);
907            return CubicIsLinear(cPart);
908        }
909    }
910
911    bool isHorizontal() const {
912        return fBounds.fTop == fBounds.fBottom;
913    }
914
915    bool isVertical() const {
916        return fBounds.fLeft == fBounds.fRight;
917    }
918
919    int lastSpan(int end, int step, const SkPoint* startLoc,
920            const Span* startSpan, bool& coincident) {
921        int last = end;
922        int count = fTs.count();
923        coincident = false;
924        SkPoint lastLoc;
925        do {
926            if (fTs[last].fCoincident == -step) {
927                coincident = true;
928            }
929            if (step > 0 ? ++last < count : --last >= 0) {
930                return -1;
931            }
932            const Span& lastSpan = fTs[last];
933            if (lastSpan.fDone == -step) {
934                return -1;
935            }
936            if (lastSpan.fT == startSpan->fT) {
937                continue;
938            }
939            xyAtT(lastSpan.fT, &lastLoc);
940        } while (*startLoc == lastLoc);
941        return last;
942    }
943
944    SkScalar leftMost(int start, int end) const {
945        return (*SegmentLeftMost[fVerb])(fPts, fTs[start].fT, fTs[end].fT);
946    }
947
948    int matchSpan(const Segment* match, double matchT)
949    {
950        int count = fTs.count();
951        for (int index = 0; index < count; ++index) {
952            Span& span = fTs[index];
953            if (span.fOther != match) {
954                continue;
955            }
956            if (span.fOtherT != matchT) {
957                continue;
958            }
959            return index;
960        }
961        SkASSERT(0); // should never get here
962        return -1;
963    }
964
965    int nextSpan(int from, int step, const SkPoint& fromLoc,
966            const Span* fromSpan, SkPoint* toLoc, Span** toSpan) {
967        int count = fTs.count();
968        int to = from;
969        while (step > 0 ? ++to < count : --to >= 0) {
970            Span* span = &fTs[to];
971            if (span->fT == fromSpan->fT) {
972                continue;
973            }
974            SkPoint loc;
975            xyAtT(span->fT, &loc);
976            if (fromLoc == loc) {
977                continue;
978            }
979            if (toLoc) {
980                *toLoc = loc;
981            }
982            if (toSpan) {
983                *toSpan = span;
984            }
985            return to;
986        }
987        return -1;
988    }
989
990    const SkPoint* pts() const {
991        return fPts;
992    }
993
994    void reset() {
995        fPts = NULL;
996        fVerb = (SkPath::Verb) -1;
997        fBounds.set(SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, SK_ScalarMax);
998        fTs.reset();
999        fDone = false;
1000        fCoincident = 0;
1001    }
1002
1003    // OPTIMIZATION: remove this function if it's never called
1004    double t(int tIndex) const {
1005        return fTs[tIndex].fT;
1006    }
1007
1008    SkPath::Verb verb() const {
1009        return fVerb;
1010    }
1011
1012    SkScalar xAtT(double t) const {
1013        return (*SegmentXAtT[fVerb])(fPts, t);
1014    }
1015
1016    void xyAtT(double t, SkPoint* pt) const {
1017        (*SegmentXYAtT[fVerb])(fPts, t, pt);
1018    }
1019
1020    SkScalar yAtT(double t) const {
1021        return (*SegmentYAtT[fVerb])(fPts, t);
1022    }
1023
1024#if DEBUG_DUMP
1025    void dump() const {
1026        const char className[] = "Segment";
1027        const int tab = 4;
1028        for (int i = 0; i < fTs.count(); ++i) {
1029            SkPoint out;
1030            (*SegmentXYAtT[fVerb])(fPts, t(i), &out);
1031            SkDebugf("%*s [%d] %s.fTs[%d]=%1.9g (%1.9g,%1.9g) other=%d"
1032                    " otherT=%1.9g winding=%d\n",
1033                    tab + sizeof(className), className, fID,
1034                    kLVerbStr[fVerb], i, fTs[i].fT, out.fX, out.fY,
1035                    fTs[i].fOther->fID, fTs[i].fOtherT, fTs[i].fWinding);
1036        }
1037        SkDebugf("%*s [%d] fBounds=(l:%1.9g, t:%1.9g r:%1.9g, b:%1.9g)",
1038                tab + sizeof(className), className, fID,
1039                fBounds.fLeft, fBounds.fTop, fBounds.fRight, fBounds.fBottom);
1040    }
1041#endif
1042
1043private:
1044    const SkPoint* fPts;
1045    SkPath::Verb fVerb;
1046    Bounds fBounds;
1047    SkTDArray<Span> fTs; // two or more (always includes t=0 t=1)
1048    // FIXME: coincident only needs two bits (-1, 0, 1)
1049    int fCoincident; // non-zero if some coincident span inside
1050    bool fDone;
1051#if DEBUG_DUMP
1052    int fID;
1053#endif
1054};
1055
1056class Contour {
1057public:
1058    Contour() {
1059        reset();
1060#if DEBUG_DUMP
1061        fID = ++gContourID;
1062#endif
1063    }
1064
1065    bool operator<(const Contour& rh) const {
1066        return fBounds.fTop == rh.fBounds.fTop
1067                ? fBounds.fLeft < rh.fBounds.fLeft
1068                : fBounds.fTop < rh.fBounds.fTop;
1069    }
1070
1071    void addCubic(const SkPoint pts[4]) {
1072        fSegments.push_back().addCubic(pts);
1073        fContainsCurves = true;
1074    }
1075
1076    void addLine(const SkPoint pts[2]) {
1077        fSegments.push_back().addLine(pts);
1078    }
1079
1080    void addQuad(const SkPoint pts[3]) {
1081        fSegments.push_back().addQuad(pts);
1082        fContainsCurves = true;
1083    }
1084
1085    const Bounds& bounds() const {
1086        return fBounds;
1087    }
1088
1089    void complete() {
1090        setBounds();
1091        fContainsIntercepts = false;
1092    }
1093
1094    void containsIntercepts() {
1095        fContainsIntercepts = true;
1096    }
1097
1098    void findTooCloseToCall(int winding) {
1099        int segmentCount = fSegments.count();
1100        for (int sIndex = 0; sIndex < segmentCount; ++sIndex) {
1101            fSegments[sIndex].findTooCloseToCall(winding);
1102        }
1103    }
1104
1105    void reset() {
1106        fSegments.reset();
1107        fBounds.set(SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, SK_ScalarMax);
1108        fContainsCurves = fContainsIntercepts = false;
1109    }
1110
1111    // OPTIMIZATION: feel pretty uneasy about this. It seems like once again
1112    // we need to sort and walk edges in y, but that on the surface opens the
1113    // same can of worms as before. But then, this is a rough sort based on
1114    // segments' top, and not a true sort, so it could be ameniable to regular
1115    // sorting instead of linear searching. Still feel like I'm missing something
1116    Segment* topSegment() {
1117        int segmentCount = fSegments.count();
1118        SkASSERT(segmentCount > 0);
1119        int best = -1;
1120        Segment* bestSegment = NULL;
1121        while (++best < segmentCount) {
1122            Segment* testSegment = &fSegments[best];
1123            if (testSegment->done()) {
1124                continue;
1125            }
1126            bestSegment = testSegment;
1127            break;
1128        }
1129        if (!bestSegment) {
1130            return NULL;
1131        }
1132        SkScalar bestTop = bestSegment->bounds().fTop;
1133        for (int test = best + 1; test < segmentCount; ++test) {
1134            Segment* testSegment = &fSegments[test];
1135            if (testSegment->done()) {
1136                continue;
1137            }
1138            SkScalar testTop = testSegment->bounds().fTop;
1139            if (bestTop > testTop) {
1140                bestTop = testTop;
1141                bestSegment = testSegment;
1142            }
1143        }
1144        return bestSegment;
1145    }
1146
1147#if DEBUG_DUMP
1148    void dump() {
1149        int i;
1150        const char className[] = "Contour";
1151        const int tab = 4;
1152        SkDebugf("%s %p (contour=%d)\n", className, this, fID);
1153        for (i = 0; i < fSegments.count(); ++i) {
1154            SkDebugf("%*s.fSegments[%d]:\n", tab + sizeof(className),
1155                    className, i);
1156            fSegments[i].dump();
1157        }
1158        SkDebugf("%*s.fBounds=(l:%1.9g, t:%1.9g r:%1.9g, b:%1.9g)\n",
1159                tab + sizeof(className), className,
1160                fBounds.fLeft, fBounds.fTop,
1161                fBounds.fRight, fBounds.fBottom);
1162        SkDebugf("%*s.fContainsIntercepts=%d\n", tab + sizeof(className),
1163                className, fContainsIntercepts);
1164        SkDebugf("%*s.fContainsCurves=%d\n", tab + sizeof(className),
1165                className, fContainsCurves);
1166    }
1167#endif
1168
1169protected:
1170    void setBounds() {
1171        int count = fSegments.count();
1172        if (count == 0) {
1173            SkDebugf("%s empty contour\n", __FUNCTION__);
1174            SkASSERT(0);
1175            // FIXME: delete empty contour?
1176            return;
1177        }
1178        fBounds = fSegments.front().bounds();
1179        for (int index = 1; index < count; ++index) {
1180            fBounds.growToInclude(fSegments[index].bounds());
1181        }
1182    }
1183
1184public:
1185    SkTArray<Segment> fSegments; // not worth accessor functions?
1186
1187private:
1188    Bounds fBounds;
1189    bool fContainsIntercepts;
1190    bool fContainsCurves;
1191#if DEBUG_DUMP
1192    int fID;
1193#endif
1194};
1195
1196class EdgeBuilder {
1197public:
1198
1199EdgeBuilder(const SkPath& path, SkTArray<Contour>& contours)
1200    : fPath(path)
1201    , fCurrentContour(NULL)
1202    , fContours(contours)
1203{
1204#if DEBUG_DUMP
1205    gContourID = 0;
1206    gSegmentID = 0;
1207#endif
1208    walk();
1209}
1210
1211protected:
1212
1213void complete() {
1214    if (fCurrentContour && fCurrentContour->fSegments.count()) {
1215        fCurrentContour->complete();
1216        fCurrentContour = NULL;
1217    }
1218}
1219
1220void startContour() {
1221    if (!fCurrentContour) {
1222        fCurrentContour = fContours.push_back_n(1);
1223    }
1224}
1225
1226void walk() {
1227    // FIXME:remove once we can access path pts directly
1228    SkPath::RawIter iter(fPath); // FIXME: access path directly when allowed
1229    SkPoint pts[4];
1230    SkPath::Verb verb;
1231    do {
1232        verb = iter.next(pts);
1233        *fPathVerbs.append() = verb;
1234        if (verb == SkPath::kMove_Verb) {
1235            *fPathPts.append() = pts[0];
1236        } else if (verb >= SkPath::kLine_Verb && verb <= SkPath::kCubic_Verb) {
1237            fPathPts.append(verb, &pts[1]);
1238        }
1239    } while (verb != SkPath::kDone_Verb);
1240    // FIXME: end of section to remove once path pts are accessed directly
1241
1242    SkPath::Verb reducedVerb;
1243    uint8_t* verbPtr = fPathVerbs.begin();
1244    const SkPoint* pointsPtr = fPathPts.begin();
1245    while ((verb = (SkPath::Verb) *verbPtr++) != SkPath::kDone_Verb) {
1246        switch (verb) {
1247            case SkPath::kMove_Verb:
1248                complete();
1249                startContour();
1250                pointsPtr += 1;
1251                continue;
1252            case SkPath::kLine_Verb:
1253                // skip degenerate points
1254                if (pointsPtr[-1].fX != pointsPtr[0].fX
1255                        || pointsPtr[-1].fY != pointsPtr[0].fY) {
1256                    fCurrentContour->addLine(&pointsPtr[-1]);
1257                }
1258                break;
1259            case SkPath::kQuad_Verb:
1260                reducedVerb = QuadReduceOrder(&pointsPtr[-1], fReducePts);
1261                if (reducedVerb == 0) {
1262                    break; // skip degenerate points
1263                }
1264                if (reducedVerb == 1) {
1265                    fCurrentContour->addLine(fReducePts.end() - 2);
1266                    break;
1267                }
1268                fCurrentContour->addQuad(&pointsPtr[-1]);
1269                break;
1270            case SkPath::kCubic_Verb:
1271                reducedVerb = CubicReduceOrder(&pointsPtr[-1], fReducePts);
1272                if (reducedVerb == 0) {
1273                    break; // skip degenerate points
1274                }
1275                if (reducedVerb == 1) {
1276                    fCurrentContour->addLine(fReducePts.end() - 2);
1277                    break;
1278                }
1279                if (reducedVerb == 2) {
1280                    fCurrentContour->addQuad(fReducePts.end() - 3);
1281                    break;
1282                }
1283                fCurrentContour->addCubic(&pointsPtr[-1]);
1284                break;
1285            case SkPath::kClose_Verb:
1286                SkASSERT(fCurrentContour);
1287                complete();
1288                continue;
1289            default:
1290                SkDEBUGFAIL("bad verb");
1291                return;
1292        }
1293        pointsPtr += verb;
1294        SkASSERT(fCurrentContour);
1295    }
1296    complete();
1297    if (fCurrentContour && !fCurrentContour->fSegments.count()) {
1298        fContours.pop_back();
1299    }
1300}
1301
1302private:
1303    const SkPath& fPath;
1304    SkTDArray<SkPoint> fPathPts; // FIXME: point directly to path pts instead
1305    SkTDArray<uint8_t> fPathVerbs; // FIXME: remove
1306    Contour* fCurrentContour;
1307    SkTArray<Contour>& fContours;
1308    SkTDArray<SkPoint> fReducePts; // segments created on the fly
1309};
1310
1311class Work {
1312public:
1313    enum SegmentType {
1314        kHorizontalLine_Segment = -1,
1315        kVerticalLine_Segment = 0,
1316        kLine_Segment = SkPath::kLine_Verb,
1317        kQuad_Segment = SkPath::kQuad_Verb,
1318        kCubic_Segment = SkPath::kCubic_Verb,
1319    };
1320
1321    void addOtherT(int index, double other) {
1322        fContour->fSegments[fIndex].addOtherT(index, other);
1323    }
1324
1325    // Avoid collapsing t values that are close to the same since
1326    // we walk ts to describe consecutive intersections. Since a pair of ts can
1327    // be nearly equal, any problems caused by this should be taken care
1328    // of later.
1329    // On the edge or out of range values are negative; add 2 to get end
1330    int addT(double newT, const Work& other, int coincident) {
1331        fContour->containsIntercepts();
1332        return fContour->fSegments[fIndex].addT(newT,
1333                other.fContour->fSegments[other.fIndex], coincident);
1334    }
1335
1336    bool advance() {
1337        return ++fIndex < fLast;
1338    }
1339
1340    SkScalar bottom() const {
1341        return bounds().fBottom;
1342    }
1343
1344    const Bounds& bounds() const {
1345        return fContour->fSegments[fIndex].bounds();
1346    }
1347
1348    const SkPoint* cubic() const {
1349        return fCubic;
1350    }
1351
1352    void init(Contour* contour) {
1353        fContour = contour;
1354        fIndex = 0;
1355        fLast = contour->fSegments.count();
1356    }
1357
1358    SkScalar left() const {
1359        return bounds().fLeft;
1360    }
1361
1362    void promoteToCubic() {
1363        fCubic[0] = pts()[0];
1364        fCubic[2] = pts()[1];
1365        fCubic[3] = pts()[2];
1366        fCubic[1].fX = (fCubic[0].fX + fCubic[2].fX * 2) / 3;
1367        fCubic[1].fY = (fCubic[0].fY + fCubic[2].fY * 2) / 3;
1368        fCubic[2].fX = (fCubic[3].fX + fCubic[2].fX * 2) / 3;
1369        fCubic[2].fY = (fCubic[3].fY + fCubic[2].fY * 2) / 3;
1370    }
1371
1372    const SkPoint* pts() const {
1373        return fContour->fSegments[fIndex].pts();
1374    }
1375
1376    SkScalar right() const {
1377        return bounds().fRight;
1378    }
1379
1380    ptrdiff_t segmentIndex() const {
1381        return fIndex;
1382    }
1383
1384    SegmentType segmentType() const {
1385        const Segment& segment = fContour->fSegments[fIndex];
1386        SegmentType type = (SegmentType) segment.verb();
1387        if (type != kLine_Segment) {
1388            return type;
1389        }
1390        if (segment.isHorizontal()) {
1391            return kHorizontalLine_Segment;
1392        }
1393        if (segment.isVertical()) {
1394            return kVerticalLine_Segment;
1395        }
1396        return kLine_Segment;
1397    }
1398
1399    bool startAfter(const Work& after) {
1400        fIndex = after.fIndex;
1401        return advance();
1402    }
1403
1404    SkScalar top() const {
1405        return bounds().fTop;
1406    }
1407
1408    SkPath::Verb verb() const {
1409        return fContour->fSegments[fIndex].verb();
1410    }
1411
1412    SkScalar x() const {
1413        return bounds().fLeft;
1414    }
1415
1416    bool xFlipped() const {
1417        return x() != pts()[0].fX;
1418    }
1419
1420    SkScalar y() const {
1421        return bounds().fTop;
1422    }
1423
1424    bool yFlipped() const {
1425        return y() != pts()[0].fX;
1426    }
1427
1428protected:
1429    Contour* fContour;
1430    SkPoint fCubic[4];
1431    int fIndex;
1432    int fLast;
1433};
1434
1435static void debugShowLineIntersection(int pts, const Work& wt,
1436        const Work& wn, const double wtTs[2], const double wnTs[2]) {
1437#if DEBUG_ADD_INTERSECTING_TS
1438    if (!pts) {
1439        return;
1440    }
1441    SkPoint wtOutPt, wnOutPt;
1442    LineXYAtT(wt.pts(), wtTs[0], &wtOutPt);
1443    LineXYAtT(wn.pts(), wnTs[0], &wnOutPt);
1444    SkDebugf("%s wtTs[0]=%g (%g,%g, %g,%g) (%g,%g)\n",
1445            __FUNCTION__,
1446            wtTs[0], wt.pts()[0].fX, wt.pts()[0].fY,
1447            wt.pts()[1].fX, wt.pts()[1].fY, wtOutPt.fX, wtOutPt.fY);
1448    if (pts == 2) {
1449        SkDebugf("%s wtTs[1]=%g\n", __FUNCTION__, wtTs[1]);
1450    }
1451    SkDebugf("%s wnTs[0]=%g (%g,%g, %g,%g) (%g,%g)\n",
1452            __FUNCTION__,
1453            wnTs[0], wn.pts()[0].fX, wn.pts()[0].fY,
1454            wn.pts()[1].fX, wn.pts()[1].fY, wnOutPt.fX, wnOutPt.fY);
1455    if (pts == 2) {
1456        SkDebugf("%s wnTs[1]=%g\n", __FUNCTION__, wnTs[1]);
1457    }
1458#endif
1459}
1460
1461static bool addIntersectTs(Contour* test, Contour* next, int winding) {
1462    if (test != next) {
1463        if (test->bounds().fBottom < next->bounds().fTop) {
1464            return false;
1465        }
1466        if (!Bounds::Intersects(test->bounds(), next->bounds())) {
1467            return true;
1468        }
1469    }
1470    Work wt, wn;
1471    wt.init(test);
1472    wn.init(next);
1473    do {
1474        if (test == next && !wn.startAfter(wt)) {
1475            continue;
1476        }
1477        do {
1478            if (!Bounds::Intersects(wt.bounds(), wn.bounds())) {
1479                continue;
1480            }
1481            int pts;
1482            Intersections ts;
1483            bool swap = false;
1484            switch (wt.segmentType()) {
1485                case Work::kHorizontalLine_Segment:
1486                    swap = true;
1487                    switch (wn.segmentType()) {
1488                        case Work::kHorizontalLine_Segment:
1489                        case Work::kVerticalLine_Segment:
1490                        case Work::kLine_Segment: {
1491                            pts = HLineIntersect(wn.pts(), wt.left(),
1492                                    wt.right(), wt.y(), wt.xFlipped(), ts);
1493                            break;
1494                        }
1495                        case Work::kQuad_Segment: {
1496                            pts = HQuadIntersect(wn.pts(), wt.left(),
1497                                    wt.right(), wt.y(), wt.xFlipped(), ts);
1498                            break;
1499                        }
1500                        case Work::kCubic_Segment: {
1501                            pts = HCubicIntersect(wn.pts(), wt.left(),
1502                                    wt.right(), wt.y(), wt.xFlipped(), ts);
1503                            break;
1504                        }
1505                        default:
1506                            SkASSERT(0);
1507                    }
1508                    break;
1509                case Work::kVerticalLine_Segment:
1510                    swap = true;
1511                    switch (wn.segmentType()) {
1512                        case Work::kHorizontalLine_Segment:
1513                        case Work::kVerticalLine_Segment:
1514                        case Work::kLine_Segment: {
1515                            pts = VLineIntersect(wn.pts(), wt.top(),
1516                                    wt.bottom(), wt.x(), wt.yFlipped(), ts);
1517                            break;
1518                        }
1519                        case Work::kQuad_Segment: {
1520                            pts = VQuadIntersect(wn.pts(), wt.top(),
1521                                    wt.bottom(), wt.x(), wt.yFlipped(), ts);
1522                            break;
1523                        }
1524                        case Work::kCubic_Segment: {
1525                            pts = VCubicIntersect(wn.pts(), wt.top(),
1526                                    wt.bottom(), wt.x(), wt.yFlipped(), ts);
1527                            break;
1528                        }
1529                        default:
1530                            SkASSERT(0);
1531                    }
1532                    break;
1533                case Work::kLine_Segment:
1534                    switch (wn.segmentType()) {
1535                        case Work::kHorizontalLine_Segment:
1536                            pts = HLineIntersect(wt.pts(), wn.left(),
1537                                    wn.right(), wn.y(), wn.xFlipped(), ts);
1538                            break;
1539                        case Work::kVerticalLine_Segment:
1540                            pts = VLineIntersect(wt.pts(), wn.top(),
1541                                    wn.bottom(), wn.x(), wn.yFlipped(), ts);
1542                            break;
1543                        case Work::kLine_Segment: {
1544                            pts = LineIntersect(wt.pts(), wn.pts(), ts);
1545                            debugShowLineIntersection(pts, wt, wn,
1546                                    ts.fT[1], ts.fT[0]);
1547                            break;
1548                        }
1549                        case Work::kQuad_Segment: {
1550                            swap = true;
1551                            pts = QuadLineIntersect(wn.pts(), wt.pts(), ts);
1552                            break;
1553                        }
1554                        case Work::kCubic_Segment: {
1555                            swap = true;
1556                            pts = CubicLineIntersect(wn.pts(), wt.pts(), ts);
1557                            break;
1558                        }
1559                        default:
1560                            SkASSERT(0);
1561                    }
1562                    break;
1563                case Work::kQuad_Segment:
1564                    switch (wn.segmentType()) {
1565                        case Work::kHorizontalLine_Segment:
1566                            pts = HQuadIntersect(wt.pts(), wn.left(),
1567                                    wn.right(), wn.y(), wn.xFlipped(), ts);
1568                            break;
1569                        case Work::kVerticalLine_Segment:
1570                            pts = VQuadIntersect(wt.pts(), wn.top(),
1571                                    wn.bottom(), wn.x(), wn.yFlipped(), ts);
1572                            break;
1573                        case Work::kLine_Segment: {
1574                            pts = QuadLineIntersect(wt.pts(), wn.pts(), ts);
1575                            break;
1576                        }
1577                        case Work::kQuad_Segment: {
1578                            pts = QuadIntersect(wt.pts(), wn.pts(), ts);
1579                            break;
1580                        }
1581                        case Work::kCubic_Segment: {
1582                            wt.promoteToCubic();
1583                            pts = CubicIntersect(wt.cubic(), wn.pts(), ts);
1584                            break;
1585                        }
1586                        default:
1587                            SkASSERT(0);
1588                    }
1589                    break;
1590                case Work::kCubic_Segment:
1591                    switch (wn.segmentType()) {
1592                        case Work::kHorizontalLine_Segment:
1593                            pts = HCubicIntersect(wt.pts(), wn.left(),
1594                                    wn.right(), wn.y(), wn.xFlipped(), ts);
1595                            break;
1596                        case Work::kVerticalLine_Segment:
1597                            pts = VCubicIntersect(wt.pts(), wn.top(),
1598                                    wn.bottom(), wn.x(), wn.yFlipped(), ts);
1599                            break;
1600                        case Work::kLine_Segment: {
1601                            pts = CubicLineIntersect(wt.pts(), wn.pts(), ts);
1602                            break;
1603                        }
1604                        case Work::kQuad_Segment: {
1605                            wn.promoteToCubic();
1606                            pts = CubicIntersect(wt.pts(), wn.cubic(), ts);
1607                            break;
1608                        }
1609                        case Work::kCubic_Segment: {
1610                            pts = CubicIntersect(wt.pts(), wn.pts(), ts);
1611                            break;
1612                        }
1613                        default:
1614                            SkASSERT(0);
1615                    }
1616                    break;
1617                default:
1618                    SkASSERT(0);
1619            }
1620            // in addition to recording T values, record matching segment
1621            int coincident = pts == 2 && wn.segmentType() <= Work::kLine_Segment
1622                    && wt.segmentType() <= Work::kLine_Segment ? -1 :0;
1623            for (int pt = 0; pt < pts; ++pt) {
1624                SkASSERT(ts.fT[0][pt] >= 0 && ts.fT[0][pt] <= 1);
1625                SkASSERT(ts.fT[1][pt] >= 0 && ts.fT[1][pt] <= 1);
1626                int testTAt = wt.addT(ts.fT[swap][pt], wn, coincident);
1627                int nextTAt = wn.addT(ts.fT[!swap][pt], wt, coincident);
1628                wt.addOtherT(testTAt, ts.fT[!swap][pt]);
1629                wn.addOtherT(nextTAt, ts.fT[swap][pt]);
1630                coincident = -coincident;
1631            }
1632        } while (wn.advance());
1633    } while (wt.advance());
1634    return true;
1635}
1636
1637// see if coincidence is formed by clipping non-concident segments
1638static void coincidenceCheck(SkTDArray<Contour*>& contourList, int winding) {
1639    int contourCount = contourList.count();
1640    for (size_t cIndex = 0; cIndex < contourCount; ++cIndex) {
1641        Contour* contour = contourList[cIndex];
1642        contour->findTooCloseToCall(winding);
1643    }
1644}
1645
1646// Each segment may have an inside or an outside. Segments contained within
1647// winding may have insides on either side, and form a contour that should be
1648// ignored. Segments that are coincident with opposing direction segments may
1649// have outsides on either side, and should also disappear.
1650// 'Normal' segments will have one inside and one outside. Subsequent connections
1651// when winding should follow the intersection direction. If more than one edge
1652// is an option, choose first edge that continues the inside.
1653
1654static void bridge(SkTDArray<Contour*>& contourList) {
1655    int contourCount = contourList.count();
1656    do {
1657    // OPTIMIZATION: not crazy about linear search here to find top active y.
1658    // seems like we should break down and do the sort, or maybe sort each
1659    // contours' segments?
1660    // Once the segment array is built, there's no reason I can think of not to
1661    // sort it in Y. hmmm
1662        int cIndex = 0;
1663        Segment* topStart;
1664        do {
1665            Contour* topContour = contourList[cIndex];
1666            topStart = topContour->topSegment();
1667        } while (!topStart && ++cIndex < contourCount);
1668        if (!topStart) {
1669            break;
1670        }
1671        SkScalar top = topStart->bounds().fTop;
1672        for (int cTest = cIndex + 1; cTest < contourCount; ++cTest) {
1673            Contour* contour = contourList[cTest];
1674            if (top < contour->bounds().fTop) {
1675                continue;
1676            }
1677            Segment* test = contour->topSegment();
1678            if (top > test->bounds().fTop) {
1679                cIndex = cTest;
1680                topStart = test;
1681                top = test->bounds().fTop;
1682            }
1683        }
1684        int index;
1685        const Segment* topSegment = topStart->findTop(index);
1686        // Start at the top. Above the top is outside, below is inside.
1687        // follow edges to intersection
1688        // at intersection, stay on outside, but mark remaining edges as inside
1689            // or, only mark first pair as inside?
1690            // how is this going to work for contained (but not intersecting)
1691            //  segments?
1692 //   start here ;
1693    // find span
1694    // mark neighbors winding coverage
1695    // output span
1696    // mark span as processed
1697
1698    } while (true);
1699
1700
1701}
1702
1703static void makeContourList(SkTArray<Contour>& contours, Contour& sentinel,
1704        SkTDArray<Contour*>& list) {
1705    int count = contours.count();
1706    if (count == 0) {
1707        return;
1708    }
1709    for (int index = 0; index < count; ++index) {
1710        *list.append() = &contours[index];
1711    }
1712    *list.append() = &sentinel;
1713    QSort<Contour>(list.begin(), list.end() - 1);
1714}
1715
1716void simplifyx(const SkPath& path, bool asFill, SkPath& simple) {
1717    // returns 1 for evenodd, -1 for winding, regardless of inverse-ness
1718    int winding = (path.getFillType() & 1) ? 1 : -1;
1719    simple.reset();
1720    simple.setFillType(SkPath::kEvenOdd_FillType);
1721
1722    // turn path into list of segments
1723    SkTArray<Contour> contours;
1724    // FIXME: add self-intersecting cubics' T values to segment
1725    EdgeBuilder builder(path, contours);
1726    SkTDArray<Contour*> contourList;
1727    Contour sentinel;
1728    sentinel.reset();
1729    makeContourList(contours, sentinel, contourList);
1730    Contour** currentPtr = contourList.begin();
1731    if (!currentPtr) {
1732        return;
1733    }
1734    // find all intersections between segments
1735    do {
1736        Contour** nextPtr = currentPtr;
1737        Contour* current = *currentPtr++;
1738        Contour* next;
1739        do {
1740            next = *nextPtr++;
1741        } while (next != &sentinel && addIntersectTs(current, next, winding));
1742    } while (*currentPtr != &sentinel);
1743    // eat through coincident edges
1744    coincidenceCheck(contourList, winding);
1745    // construct closed contours
1746    bridge(contourList);
1747}
1748
1749