1/*
2 * Copyright 2013 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 "PathOpsTestCommon.h"
8#include "SkIntersections.h"
9#include "SkPathOpsCubic.h"
10#include "SkPathOpsQuad.h"
11#include "SkRandom.h"
12#include "SkReduceOrder.h"
13#include "Test.h"
14
15static struct quadCubic {
16    SkDCubic cubic;
17    SkDQuad quad;
18    int answerCount;
19    SkDPoint answers[2];
20} quadCubicTests[] = {
21#if 0  // FIXME : this should not fail (root problem behind skpcarrot_is24 )
22    {{{{1020.08099,672.161987}, {1020.08002,630.73999}, {986.502014,597.161987}, {945.080994,597.161987}}},
23     {{{1020,672}, {1020,640.93396}, {998.03302,618.96698}}}, 1,
24      {{1019.421, 662.449}}},
25#endif
26
27    {{{{778, 14089}, {778, 14091.208984375}, {776.20916748046875, 14093}, {774, 14093}}},
28     {{{778, 14089}, {777.99957275390625, 14090.65625}, {776.82843017578125, 14091.828125}}}, 2,
29     {{778, 14089}, {776.82855609581270,14091.828250841330}}},
30
31    {{{{1110, 817}, {1110.55225f, 817}, {1111, 817.447693f}, {1111, 818}}},
32     {{{1110.70715f, 817.292908f}, {1110.41406f, 817.000122f}, {1110, 817}}}, 2,
33      {{1110, 817}, {1110.70715f, 817.292908f}}},
34
35    {{{{1110, 817}, {1110.55225f, 817}, {1111, 817.447693f}, {1111, 818}}},
36     {{{1111, 818}, {1110.99988f, 817.585876f}, {1110.70715f, 817.292908f}}}, 2,
37      {{1110.70715f, 817.292908f}, {1111, 818}}},
38
39    {{{{55, 207}, {52.238574981689453, 207}, {50, 204.76142883300781}, {50, 202}}},
40     {{{55, 207}, {52.929431915283203, 206.99949645996094},
41       {51.464466094970703, 205.53553771972656}}}, 2,
42      {{55, 207}, {51.464466094970703, 205.53553771972656}}},
43
44    {{{{49, 47}, {49, 74.614250183105469}, {26.614250183105469, 97}, {-1, 97}}},
45     {{{-8.659739592076221e-015, 96.991401672363281}, {20.065492630004883, 96.645187377929688},
46       {34.355339050292969, 82.355339050292969}}}, 2,
47      {{34.355339050292969,82.355339050292969}, {34.28654835573549, 82.424006509351585}}},
48
49    {{{{10,234}, {10,229.58172607421875}, {13.581720352172852,226}, {18,226}}},
50     {{{18,226}, {14.686291694641113,226}, {12.342399597167969,228.3424072265625}}}, 1,
51      {{18,226}, {0,0}}},
52
53    {{{{10,234}, {10,229.58172607421875}, {13.581720352172852,226}, {18,226}}},
54     {{{12.342399597167969,228.3424072265625}, {10,230.68629455566406}, {10,234}}}, 1,
55      {{10,234}, {0,0}}},
56};
57
58static const int quadCubicTests_count = (int) SK_ARRAY_COUNT(quadCubicTests);
59
60static void cubicQuadIntersection(skiatest::Reporter* reporter, int index) {
61    int iIndex = static_cast<int>(index);
62    const SkDCubic& cubic = quadCubicTests[index].cubic;
63    SkASSERT(ValidCubic(cubic));
64    const SkDQuad& quad = quadCubicTests[index].quad;
65    SkASSERT(ValidQuad(quad));
66    SkReduceOrder reduce1;
67    SkReduceOrder reduce2;
68    int order1 = reduce1.reduce(cubic, SkReduceOrder::kNo_Quadratics);
69    int order2 = reduce2.reduce(quad);
70    if (order1 != 4) {
71        SkDebugf("[%d] cubic order=%d\n", iIndex, order1);
72        REPORTER_ASSERT(reporter, 0);
73    }
74    if (order2 != 3) {
75        SkDebugf("[%d] quad order=%d\n", iIndex, order2);
76        REPORTER_ASSERT(reporter, 0);
77    }
78    SkIntersections i;
79    int roots = i.intersect(cubic, quad);
80    SkASSERT(roots == quadCubicTests[index].answerCount);
81    for (int pt = 0; pt < roots; ++pt) {
82        double tt1 = i[0][pt];
83        SkDPoint xy1 = cubic.ptAtT(tt1);
84        double tt2 = i[1][pt];
85        SkDPoint xy2 = quad.ptAtT(tt2);
86        if (!xy1.approximatelyEqual(xy2)) {
87            SkDebugf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
88                __FUNCTION__, iIndex, pt, tt1, xy1.fX, xy1.fY, tt2, xy2.fX, xy2.fY);
89        }
90        REPORTER_ASSERT(reporter, xy1.approximatelyEqual(xy2));
91        bool found = false;
92        for (int idx2 = 0; idx2 < quadCubicTests[index].answerCount; ++idx2) {
93            found |= quadCubicTests[index].answers[idx2].approximatelyEqual(xy1);
94        }
95        if (!found) {
96            SkDebugf("%s [%d,%d] xy1=(%g,%g) != \n",
97                __FUNCTION__, iIndex, pt, xy1.fX, xy1.fY);
98        }
99        REPORTER_ASSERT(reporter, found);
100    }
101    reporter->bumpTestCount();
102}
103
104DEF_TEST(PathOpsCubicQuadIntersection, reporter) {
105    for (int index = 0; index < quadCubicTests_count; ++index) {
106        cubicQuadIntersection(reporter, index);
107        reporter->bumpTestCount();
108    }
109}
110
111DEF_TEST(PathOpsCubicQuadIntersectionOneOff, reporter) {
112    cubicQuadIntersection(reporter, 0);
113}
114
115static bool gPathOpCubicQuadSlopVerbose = false;
116static const int kCubicToQuadSubdivisionDepth = 8; // slots reserved for cubic to quads subdivision
117
118// determine that slop required after quad/quad finds a candidate intersection
119// use the cross of the tangents plus the distance from 1 or 0 as knobs
120DEF_TEST(PathOpsCubicQuadSlop, reporter) {
121    // create a random non-selfintersecting cubic
122    // break it into quadratics
123    // offset the quadratic, measuring the slop required to find the intersection
124    if (!gPathOpCubicQuadSlopVerbose) {  // takes a while to run -- so exclude it by default
125        return;
126    }
127    int results[101];
128    sk_bzero(results, sizeof(results));
129    double minCross[101];
130    sk_bzero(minCross, sizeof(minCross));
131    double maxCross[101];
132    sk_bzero(maxCross, sizeof(maxCross));
133    double sumCross[101];
134    sk_bzero(sumCross, sizeof(sumCross));
135    int foundOne = 0;
136    int slopCount = 1;
137    SkRandom ran;
138    for (int index = 0; index < 10000000; ++index) {
139        if (index % 1000 == 999) SkDebugf(".");
140        SkDCubic cubic = {{
141                {ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)},
142                {ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)},
143                {ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)},
144                {ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)}
145        }};
146        SkIntersections i;
147        if (i.intersect(cubic)) {
148            continue;
149        }
150        SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts;
151        cubic.toQuadraticTs(cubic.calcPrecision(), &ts);
152        double tStart = 0;
153        int tsCount = ts.count();
154        for (int i1 = 0; i1 <= tsCount; ++i1) {
155            const double tEnd = i1 < tsCount ? ts[i1] : 1;
156            SkDCubic part = cubic.subDivide(tStart, tEnd);
157            SkDQuad quad = part.toQuad();
158            SkReduceOrder reducer;
159            int order = reducer.reduce(quad);
160            if (order != 3) {
161                continue;
162            }
163            for (int i2 = 0; i2 < 100; ++i2) {
164                SkDPoint endDisplacement = {ran.nextRangeF(-100, 100), ran.nextRangeF(-100, 100)};
165                SkDQuad nearby = {{
166                        {quad[0].fX + endDisplacement.fX, quad[0].fY + endDisplacement.fY},
167                        {quad[1].fX + ran.nextRangeF(-100, 100), quad[1].fY + ran.nextRangeF(-100, 100)},
168                        {quad[2].fX - endDisplacement.fX, quad[2].fY - endDisplacement.fY}
169                }};
170                order = reducer.reduce(nearby);
171                if (order != 3) {
172                    continue;
173                }
174                SkIntersections locals;
175                locals.allowNear(false);
176                locals.intersect(quad, nearby);
177                if (locals.used() != 1) {
178                    continue;
179                }
180                // brute force find actual intersection
181                SkDLine cubicLine = {{ {0, 0}, {cubic[0].fX, cubic[0].fY } }};
182                SkIntersections liner;
183                int i3;
184                int found = -1;
185                int foundErr = true;
186                for (i3 = 1; i3 <= 1000; ++i3) {
187                    cubicLine[0] = cubicLine[1];
188                    cubicLine[1] = cubic.ptAtT(i3 / 1000.);
189                    liner.reset();
190                    liner.allowNear(false);
191                    liner.intersect(nearby, cubicLine);
192                    if (liner.used() == 0) {
193                        continue;
194                    }
195                    if (liner.used() > 1) {
196                        foundErr = true;
197                        break;
198                    }
199                    if (found > 0) {
200                        foundErr = true;
201                        break;
202                    }
203                    foundErr = false;
204                    found = i3;
205                }
206                if (foundErr) {
207                    continue;
208                }
209                SkDVector dist = liner.pt(0) - locals.pt(0);
210                SkDVector qV = nearby.dxdyAtT(locals[0][0]);
211                double cubicT = (found - 1 + liner[1][0]) / 1000.;
212                SkDVector cV = cubic.dxdyAtT(cubicT);
213                double qxc = qV.crossCheck(cV);
214                double qvLen = qV.length();
215                double cvLen = cV.length();
216                double maxLen = SkTMax(qvLen, cvLen);
217                qxc /= maxLen;
218                double quadT = tStart + (tEnd - tStart) * locals[0][0];
219                double diffT = fabs(cubicT - quadT);
220                int diffIdx = (int) (diffT * 100);
221                results[diffIdx]++;
222                double absQxc = fabs(qxc);
223                if (sumCross[diffIdx] == 0) {
224                    minCross[diffIdx] = maxCross[diffIdx] = sumCross[diffIdx] = absQxc;
225                } else {
226                    minCross[diffIdx] = SkTMin(minCross[diffIdx], absQxc);
227                    maxCross[diffIdx] = SkTMax(maxCross[diffIdx], absQxc);
228                    sumCross[diffIdx] +=  absQxc;
229                }
230                if (diffIdx >= 20) {
231#if 01
232                    SkDebugf("cubic={{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}}"
233                        " quad={{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}}"
234                        " {{{%1.9g,%1.9g}, {%1.9g,%1.9g}}}"
235                        " qT=%1.9g cT=%1.9g dist=%1.9g cross=%1.9g\n",
236                        cubic[0].fX, cubic[0].fY, cubic[1].fX, cubic[1].fY,
237                        cubic[2].fX, cubic[2].fY, cubic[3].fX, cubic[3].fY,
238                        nearby[0].fX, nearby[0].fY, nearby[1].fX, nearby[1].fY,
239                        nearby[2].fX, nearby[2].fY,
240                        liner.pt(0).fX, liner.pt(0).fY,
241                        locals.pt(0).fX, locals.pt(0).fY, quadT, cubicT, dist.length(), qxc);
242#else
243                    SkDebugf("qT=%1.9g cT=%1.9g dist=%1.9g cross=%1.9g\n",
244                        quadT, cubicT, dist.length(), qxc);
245                    SkDebugf("<div id=\"slop%d\">\n", ++slopCount);
246                    SkDebugf("{{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}}\n"
247                        "{{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}}\n"
248                        "{{{%1.9g,%1.9g}, {%1.9g,%1.9g}}}\n",
249                        cubic[0].fX, cubic[0].fY, cubic[1].fX, cubic[1].fY,
250                        cubic[2].fX, cubic[2].fY, cubic[3].fX, cubic[3].fY,
251                        nearby[0].fX, nearby[0].fY, nearby[1].fX, nearby[1].fY,
252                        nearby[2].fX, nearby[2].fY,
253                        liner.pt(0).fX, liner.pt(0).fY,
254                        locals.pt(0).fX, locals.pt(0).fY);
255                    SkDebugf("</div>\n\n");
256#endif
257                }
258                ++foundOne;
259            }
260            tStart = tEnd;
261        }
262        if (++foundOne >= 100000) {
263            break;
264        }
265    }
266#if 01
267    SkDebugf("slopCount=%d\n", slopCount);
268    int max = 100;
269    while (results[max] == 0) {
270        --max;
271    }
272    for (int i = 0; i <= max; ++i) {
273        if (i > 0 && i % 10 == 0) {
274            SkDebugf("\n");
275        }
276        SkDebugf("%d ", results[i]);
277    }
278    SkDebugf("min\n");
279    for (int i = 0; i <= max; ++i) {
280        if (i > 0 && i % 10 == 0) {
281            SkDebugf("\n");
282        }
283        SkDebugf("%1.9g ", minCross[i]);
284    }
285    SkDebugf("max\n");
286    for (int i = 0; i <= max; ++i) {
287        if (i > 0 && i % 10 == 0) {
288            SkDebugf("\n");
289        }
290        SkDebugf("%1.9g ", maxCross[i]);
291    }
292    SkDebugf("avg\n");
293    for (int i = 0; i <= max; ++i) {
294        if (i > 0 && i % 10 == 0) {
295            SkDebugf("\n");
296        }
297        SkDebugf("%1.9g ", sumCross[i] / results[i]);
298    }
299#else
300    for (int i = 1; i < slopCount; ++i) {
301        SkDebugf("        slop%d,\n", i);
302    }
303#endif
304    SkDebugf("\n");
305}
306