QuadraticIntersection_Test.cpp revision 4aaaaeace7e617ddc473645756fb7c20790bc270 
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 "CurveUtilities.h"
9#include "Intersection_Tests.h"
10#include "Intersections.h"
11#include "LineIntersection.h"
12#include "QuadraticIntersection_TestData.h"
13#include "QuadraticUtilities.h"
14#include "TestUtilities.h"
15
16const int firstQuadIntersectionTest = 9;
17
18static void standardTestCases() {
19    for (size_t index = firstQuadIntersectionTest; index < quadraticTests_count; ++index) {
20        const Quadratic& quad1 = quadraticTests[index][0];
21        const Quadratic& quad2 = quadraticTests[index][1];
22        Quadratic reduce1, reduce2;
23        int order1 = reduceOrder(quad1, reduce1, kReduceOrder_TreatAsFill);
24        int order2 = reduceOrder(quad2, reduce2, kReduceOrder_TreatAsFill);
25        if (order1 < 3) {
26            printf("[%d] quad1 order=%d\n", (int) index, order1);
27        }
28        if (order2 < 3) {
29            printf("[%d] quad2 order=%d\n", (int) index, order2);
30        }
31        if (order1 == 3 && order2 == 3) {
32            Intersections intersections;
33            intersect2(reduce1, reduce2, intersections);
34            if (intersections.intersected()) {
35                for (int pt = 0; pt < intersections.used(); ++pt) {
36                    double tt1 = intersections.fT[0][pt];
37                    double tx1, ty1;
38                    xy_at_t(quad1, tt1, tx1, ty1);
39                    double tt2 = intersections.fT[1][pt];
40                    double tx2, ty2;
41                    xy_at_t(quad2, tt2, tx2, ty2);
42                    if (!approximately_equal(tx1, tx2)) {
43                        printf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
44                            __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2);
45                    }
46                    if (!approximately_equal(ty1, ty2)) {
47                        printf("%s [%d,%d] y!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
48                            __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2);
49                    }
50                }
51            }
52        }
53    }
54}
55
56static const Quadratic testSet[] = {
57  {{1,2}, {0.984375,2.3359375}, {1.0625,2.15625}},
58  {{0,1}, {0.983539095,2.30041152}, {1.47325103,2.61316872}},
59
60  {{4.09011926,2.20971038}, {4.74608133,1.9335932}, {5.02469918,2.00694987}},
61  {{2.79472921,1.73568666}, {3.36246373,1.21251209}, {5,2}},
62
63  {{1.80814127,2.41537795}, {2.23475077,2.05922313}, {3.16529668,1.98358763}},
64  {{2.16505631,2.55782454}, {2.40541285,2.02193091}, {2.99836023,1.68247638}},
65
66{{3, 1.875}, {3.375, 1.54296875}, {3.375, 1.421875}},
67{{3.375, 1.421875}, {3.3749999999999996, 1.3007812499999998}, {3, 2}},
68
69  {{3.34,8.98}, {2.83363281,9.4265625}, {2.83796875,9.363125}},
70  {{2.83796875,9.363125}, {2.84230469,9.2996875}, {3.17875,9.1725}},
71
72{{2.7279999999999998, 3.024}, {2.5600000000000005, 2.5600000000000005}, {2.1520000000000001, 1.8560000000000001}},
73{{0.66666666666666652, 1.1481481481481481}, {1.3333333333333326, 1.3333333333333335}, {2.6666666666666665, 2.1851851851851851}},
74
75  {{2.728,3.024}, {2.56,2.56}, {2.152,1.856}},
76  {{0.666666667,1.14814815}, {1.33333333,1.33333333}, {2.66666667,2.18518519}},
77
78  {{0.875,1.5}, {1.03125,1.11022302e-16}, {1,0}},
79  {{0.875,0.859375}, {1.6875,0.73046875}, {2.5,0.625}},
80
81  {{1.64451042,0.0942001592}, {1.53635465,0.00152863961}, {1,0}},
82  {{1.27672209,0.15}, {1.32143477,9.25185854e-17}, {1,0}},
83
84{{0, 0}, {0.51851851851851849, 1.0185185185185186}, {1.2592592592592591, 1.9259259259259258}},
85{{1.2592592592592593, 1.9259259259259265}, {0.51851851851851893, 1.0185185185185195}, {0, 0}},
86
87  {{1.93281168,2.58856757}, {2.38543691,2.7096125}, {2.51967352,2.34531784}},
88  {{2.51967352,2.34531784}, {2.65263731,2.00639194}, {3.1212119,1.98608967}},
89  {{2.09544533,2.51981963}, {2.33331524,2.25252128}, {2.92003302,2.39442311}},
90
91
92{{0.924337655,1.94072717}, {1.25185043,1.52836494}, {1.71793901,1.06149951}},
93{{0.940798831,1.67439357}, {1.25988251,1.39778567}, {1.71791672,1.06650313}},
94
95  {{0.924337655,1.94072717}, {1.39158994,1.32418496}, {2.14967426,0.687365435}},
96  {{0.940798831,1.67439357}, {1.48941875,1.16280321}, {2.47884711,0.60465921}},
97
98  {{1.7465749139282332,1.9930452039527999}, {1.8320006564080331,1.859481345189089}, {1.8731035127758437,1.6344055934266613}},
99  {{1.8731035127758437,1.6344055934266613}, {1.89928170345231,1.5006405518943067}, {1.9223833226085514,1.3495796165215643}},
100  {{1.74657491,1.9930452}, {1.87407679,1.76762853}, {1.92238332,1.34957962}},
101  {{0.60797907,1.68776977}, {1.0447864,1.50810914}, {1.87464474,1.63655092}},
102  {{1.87464474,1.63655092}, {2.70450308,1.76499271}, {4,3}},
103
104{{1.2071879545809394,0.82163474041730045}, {1.1534203513372994,0.52790870069930229}, {1.0880000000000001,0.29599999999999982}}, //t=0.63155333662549329,0.80000000000000004
105{{0.33333333333333326,0.81481481481481488}, {0.63395173631977997,0.68744136726313931}, {1.205684411948591,0.81344322326274499}},
106{{0.33333333333333326,0.81481481481481488}, {0.63396444791444551,0.68743368362444768}, {1.205732763658403,0.81345617746834109}},//t=0.33333333333333331,0.63396444791444551
107{{1.205684411948591,0.81344322326274499}, {1.2057085875611198,0.81344969999329253}, {1.205732763658403,0.81345617746834109}},
108
109  {{1.20718795,0.82163474}, {1.15342035,0.527908701}, {1.088,0.296}},
110  {{1.20568441,0.813443223}, {1.20570859,0.8134497}, {1.20573276,0.813456177}},
111
112  {{41.5072916,87.1234036}, {28.2747836,80.9545395}, {23.5780771,69.3344126}},
113  {{72.9633878,95.6593007}, {42.7738746,88.4730382}, {31.1932785,80.2458029}},
114
115  {{31.1663962,54.7302484}, {31.1662882,54.7301074}, {31.1663969,54.7302485}},
116  {{26.0404936,45.4260361}, {27.7887523,33.1863051}, {40.8833242,26.0301855}},
117
118  {{29.9404074,49.1672596}, {44.3131071,45.3915253}, {58.1067559,59.5061814}},
119  {{72.6510251,64.2972928}, {53.6989659,60.1862397}, {35.2053722,44.8391126}},
120
121{{52.14807018377202, 65.012420045148644}, {44.778669050208237, 66.315562705604378}, {51.619118408823567, 63.787827046262684}},
122{{30.004993234763383, 93.921296668202288}, {53.384822003076991, 60.732180341802753}, {58.652998934338584, 43.111073088306185}},
123
124{{80.897794748143198, 49.236332042718459}, {81.082078218891212, 64.066749904488631}, {69.972305057149981, 72.968595519850993}},
125{{72.503745601281395, 32.952320736577882}, {88.030880716061645, 38.137194847810164}, {73.193774825517906, 67.773492479591397}},
126
127{{67.426548091427676, 37.993772624988935}, {51.129513170665035, 57.542281234563646}, {44.594748190899189, 65.644267382683879}},
128{{61.336508189019057, 82.693132843213675}, {54.825078921449354, 71.663932799212432}, {47.727444217558926, 61.4049645128392}},
129
130{{67.4265481,37.9937726}, {51.1295132,57.5422812}, {44.5947482,65.6442674}},
131{{61.3365082,82.6931328}, {54.8250789,71.6639328}, {47.7274442,61.4049645}},
132
133{{53.774852327053594, 53.318060789841951}, {45.787877803416805, 51.393492026284981}, {46.703936967162392, 53.06860709822206}},
134{{46.703936967162392, 53.06860709822206}, {47.619996130907957, 54.74372217015916}, {53.020051653535361, 48.633140968832024}},
135
136{{50.934805397717923, 51.52391952648901}, {56.803308902971423, 44.246234610627596}, {69.776888596721406, 40.166645096692555}},
137{{50.230212796400401, 38.386469101526998}, {49.855620812184917, 38.818990392153609}, {56.356567496227363, 47.229909093319407}},
138
139{{36.148792695174222, 70.336952793070424}, {36.141613037691357, 70.711654739870085}, {36.154708826402597, 71.088492662905836}},
140{{35.216235592661825, 70.580199617313212}, {36.244476835123969, 71.010897787304074}, {37.230244263238326, 71.423156953613102}},
141
142// this pair is nearly coincident, and causes the quartic code to produce bad
143// data. Mathematica doesn't think they touch. Graphically, I can't tell.
144// it may not be so bad to pretend that they don't touch, if I can detect that
145{{369.848602,145.680267}, {382.360413,121.298294}, {406.207703,121.298294}},
146{{369.850525,145.675964}, {382.362915,121.29287}, {406.211273,121.29287}},
147
148{{33.567436351153468, 62.336347586395924}, {35.200980274619084, 65.038561460144479}, {36.479571811084995, 67.632178905412445}},
149{{41.349524945572696, 67.886658677862641}, {39.125562529359087, 67.429772735149214}, {35.600314083992416, 66.705372160552685}},
150
151{{67.25299631583178, 21.109080184767524}, {43.617595267398613, 33.658034168577529}, {33.38371819435676, 44.214192553988745}},
152{{40.476838859398541, 39.543209911285999}, {36.701186108431131, 34.8817994016458}, {30.102144288878023, 26.739063172945315}},
153
154{{25.367434474345036, 50.4712103169743}, {17.865013304933097, 37.356741010559439}, {16.818988838905465, 37.682915484123129}},
155{{16.818988838905465, 37.682915484123129}, {15.772964372877833, 38.009089957686811}, {20.624104547604965, 41.825131596683121}},
156
157{{26.440225044088567, 79.695009812848298}, {26.085525979582247, 83.717928354134784}, {27.075079976297072, 84.820633667838905}},
158{{27.075079976297072, 84.820633667838905}, {28.276546859574015, 85.988574184029034}, {25.649263209500006, 87.166762066617025}},
159
160{{34.879150914024962, 83.862726601601125}, {35.095810134304429, 83.693473210169543}, {35.359284111931586, 83.488069234177502}},
161{{54.503204203015471, 76.094098492518242}, {51.366889541918894, 71.609856061299155}, {46.53086955445437, 69.949863036494207}},
162
163{{0, 0}, {1, 0}, {0, 3}},
164{{1, 0}, {0, 1}, {1, 1}},
165{{369.961151,137.980698}, {383.970093,121.298294}, {406.213287,121.298294}},
166{{353.2948,194.351074}, {353.2948,173.767563}, {364.167572,160.819855}},
167{{360.416077,166.795715}, {370.126831,147.872162}, {388.635406,147.872162}},
168{{406.236359,121.254936}, {409.445679,121.254936}, {412.975952,121.789818}},
169{{406.235992,121.254936}, {425.705902,121.254936}, {439.71994,137.087616}},
170
171{{369.8543701171875, 145.66734313964844}, {382.36788940429688, 121.28203582763672}, {406.21844482421875, 121.28203582763672}},
172{{369.96469116210938, 137.96672058105469}, {383.97555541992188, 121.28203582763672}, {406.2218017578125, 121.28203582763672}},
173
174    {{369.962311, 137.976044}, {383.971893, 121.29287}, {406.216125, 121.29287}},
175
176    {{400.121704, 149.468719}, {391.949493, 161.037186}, {391.949493, 181.202423}},
177    {{391.946747, 181.839218}, {391.946747, 155.62442}, {406.115479, 138.855438}},
178    {{360.048828125, 229.2578125}, {360.048828125, 224.4140625}, {362.607421875, 221.3671875}},
179    {{362.607421875, 221.3671875}, {365.166015625, 218.3203125}, {369.228515625, 218.3203125}},
180    {{8, 8}, {10, 10}, {8, -10}},
181    {{8, 8}, {12, 12}, {14, 4}},
182    {{8, 8}, {9, 9}, {10, 8}}
183};
184
185const size_t testSetCount = sizeof(testSet) / sizeof(testSet[0]);
186
187static void oneOffTest1(size_t outer, size_t inner) {
188    const Quadratic& quad1 = testSet[outer];
189    const Quadratic& quad2 = testSet[inner];
190    Intersections intersections2;
191    intersect2(quad1, quad2, intersections2);
192    if (intersections2.fUnsortable) {
193        SkASSERT(0);
194        return;
195    }
196    for (int pt = 0; pt < intersections2.used(); ++pt) {
197        double tt1 = intersections2.fT[0][pt];
198        double tx1, ty1;
199        xy_at_t(quad1, tt1, tx1, ty1);
200        int pt2 = intersections2.fFlip ? intersections2.used() - pt - 1 : pt;
201        double tt2 = intersections2.fT[1][pt2];
202        double tx2, ty2;
203        xy_at_t(quad2, tt2, tx2, ty2);
204        if (!AlmostEqualUlps(tx1, tx2)) {
205            SkDebugf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
206                __FUNCTION__, (int)outer, (int)inner, tt1, tx1, ty1, tt2, tx2, ty2);
207            SkASSERT(0);
208        }
209        if (!AlmostEqualUlps(ty1, ty2)) {
210            SkDebugf("%s [%d,%d] y!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
211                __FUNCTION__, (int)outer, (int)inner, tt1, tx1, ty1, tt2, tx2, ty2);
212            SkASSERT(0);
213        }
214#if ONE_OFF_DEBUG
215        SkDebugf("%s [%d][%d] t1=%1.9g (%1.9g, %1.9g) t2=%1.9g\n", __FUNCTION__,
216            outer, inner, tt1, tx1, ty1, tt2);
217#endif
218    }
219}
220
221void QuadraticIntersection_OneOffTest() {
222    oneOffTest1(0, 1);
223}
224
225static void oneOffTests() {
226    for (size_t outer = 0; outer < testSetCount - 1; ++outer) {
227        for (size_t inner = outer + 1; inner < testSetCount; ++inner) {
228            oneOffTest1(outer, inner);
229        }
230    }
231}
232
233static const Quadratic coincidentTestSet[] = {
234    {{369.850525, 145.675964}, {382.362915, 121.29287}, {406.211273, 121.29287}},
235    {{369.850525, 145.675964}, {382.362915, 121.29287}, {406.211273, 121.29287}},
236    {{8, 8}, {10, 10}, {8, -10}},
237    {{8, -10}, {10, 10}, {8, 8}},
238};
239
240const size_t coincidentTestSetCount = sizeof(coincidentTestSet) / sizeof(coincidentTestSet[0]);
241
242static void coincidentTest() {
243    for (size_t testIndex = 0; testIndex < coincidentTestSetCount - 1; testIndex += 2) {
244        const Quadratic& quad1 = coincidentTestSet[testIndex];
245        const Quadratic& quad2 = coincidentTestSet[testIndex + 1];
246        Intersections intersections2;
247        intersect2(quad1, quad2, intersections2);
248        SkASSERT(intersections2.coincidentUsed() == 2);
249        SkASSERT(intersections2.used() == 2);
250        for (int pt = 0; pt < intersections2.coincidentUsed(); ++pt) {
251            double tt1 = intersections2.fT[0][pt];
252            double tt2 = intersections2.fT[1][pt];
253            SkASSERT(approximately_equal(1, tt1) || approximately_zero(tt1));
254            SkASSERT(approximately_equal(1, tt2) || approximately_zero(tt2));
255        }
256    }
257}
258
259void QuadraticIntersection_Test() {
260    oneOffTests();
261    coincidentTest();
262    standardTestCases();
263}
264
265static int floatSign(double x) {
266    return x < 0 ? -1 : x > 0 ? 1 : 0;
267}
268
269static const Quadratic pointFinderTestSet[] = {
270                                                                                                                                //>=0.633974464         0.633974846 <=
271{{1.2071879545809394,0.82163474041730045}, {1.1534203513372994,0.52790870069930229}, {1.0880000000000001,0.29599999999999982}}, //t=0.63155333662549329,0.80000000000000004
272{{1.2071879545809394,0.82163474041730045}, {1.2065040319428038,0.81766753259119995}, {1.2058123269101506,0.81370135061854221}}, //t=0.63155333662549329,0.6339049773632347
273{{1.2058123269101506,0.81370135061854221}, {1.152376363978022,0.5244097415381026}, {1.0880000000000001,0.29599999999999982}},   //t=0.6339049773632347, 0.80000000000000004
274                                                                                                                                //>=0.633974083         0.633975227 <=
275{{0.33333333333333326,0.81481481481481488}, {0.63395173631977997,0.68744136726313931}, {1.205684411948591,0.81344322326274499}},//t=0.33333333333333331,0.63395173631977986
276{{0.33333333333333326,0.81481481481481488}, {0.63396444791444551,0.68743368362444768}, {1.205732763658403,0.81345617746834109}},//t=0.33333333333333331,0.63396444791444551
277{{1.205684411948591,0.81344322326274499}, {1.2057085875611198,0.81344969999329253}, {1.205732763658403,0.81345617746834109}},   //t=0.63395173631977986,0.63396444791444551
278{{1.205732763658403,0.81345617746834109}, {1.267928895828891,0.83008534558465619}, {1.3333333333333333,0.85185185185185175}},   //t=0.63396444791444551,0.66666666666666663
279};
280
281static void pointFinder(const Quadratic& q1, const Quadratic& q2) {
282    for (int index = 0; index < 3; ++index) {
283        double t = nearestT(q1, q2[index]);
284        _Point onQuad;
285        xy_at_t(q1, t, onQuad.x, onQuad.y);
286        SkDebugf("%s t=%1.9g (%1.9g,%1.9g) dist=%1.9g\n", __FUNCTION__, t, onQuad.x, onQuad.y,
287                onQuad.distance(q2[index]));
288        double left[3];
289        left[0] = is_left((const _Line&) q1[0], q2[index]);
290        left[1] = is_left((const _Line&) q1[1], q2[index]);
291        _Line diag = {q1[0], q1[2]};
292        left[2] = is_left(diag, q2[index]);
293        SkDebugf("%s left=(%d, %d, %d) inHull=%s\n", __FUNCTION__, floatSign(left[0]),
294                floatSign(left[1]), floatSign(left[2]),
295                point_in_hull(q1, q2[index]) ? "true" : "false");
296    }
297    SkDebugf("\n");
298}
299
300static void hullIntersect(const Quadratic& q1, const Quadratic& q2) {
301    SkDebugf("%s", __FUNCTION__);
302    Intersections ts;
303    for (int i1 = 0; i1 < 3; ++i1) {
304        _Line l1 = {q1[i1], q1[(i1 + 1) % 3]};
305        for (int i2 = 0; i2 < 3; ++i2) {
306            _Line l2 = {q2[i2], q2[(i2 + 1) % 3]};
307            if (intersect(l1, l2, ts)) {
308                SkDebugf(" [%d,%d]", i1, i2);
309            }
310        }
311    }
312    SkDebugf("\n");
313}
314
315void QuadraticIntersection_PointFinder() {
316    pointFinder(pointFinderTestSet[0], pointFinderTestSet[4]);
317    pointFinder(pointFinderTestSet[4], pointFinderTestSet[0]);
318    pointFinder(pointFinderTestSet[0], pointFinderTestSet[6]);
319    pointFinder(pointFinderTestSet[6], pointFinderTestSet[0]);
320    hullIntersect(pointFinderTestSet[0], pointFinderTestSet[4]);
321    hullIntersect(pointFinderTestSet[0], pointFinderTestSet[6]);
322}
323
324static void intersectionFinder(int test1, int test2) {
325    const Quadratic& quad1 = testSet[test1];
326    const Quadratic& quad2 = testSet[test2];
327
328    double t1Seed = 0.966;
329    double t2Seed = 0.99;
330    double t1Step = 0.1;
331    double t2Step = 0.01;
332    _Point t1[3], t2[3];
333    bool toggle = true;
334    do {
335        xy_at_t(quad1, t1Seed - t1Step, t1[0].x, t1[0].y);
336        xy_at_t(quad1, t1Seed,          t1[1].x, t1[1].y);
337        xy_at_t(quad1, t1Seed + t1Step, t1[2].x, t1[2].y);
338        xy_at_t(quad2, t2Seed - t2Step, t2[0].x, t2[0].y);
339        xy_at_t(quad2, t2Seed,          t2[1].x, t2[1].y);
340        xy_at_t(quad2, t2Seed + t2Step, t2[2].x, t2[2].y);
341        double dist[3][3];
342        dist[1][1] = t1[1].distance(t2[1]);
343        int best_i = 1, best_j = 1;
344        for (int i = 0; i < 3; ++i) {
345            for (int j = 0; j < 3; ++j) {
346                if (i == 1 && j == 1) {
347                    continue;
348                }
349                dist[i][j] = t1[i].distance(t2[j]);
350                if (dist[best_i][best_j] > dist[i][j]) {
351                    best_i = i;
352                    best_j = j;
353                }
354            }
355        }
356        if (best_i == 0) {
357            t1Seed -= t1Step;
358        } else if (best_i == 2) {
359            t1Seed += t1Step;
360        }
361        if (best_j == 0) {
362            t2Seed -= t2Step;
363        } else if (best_j == 2) {
364            t2Seed += t2Step;
365        }
366        if (best_i == 1 && best_j == 1) {
367            if ((toggle ^= true)) {
368                t1Step /= 2;
369            } else {
370                t2Step /= 2;
371            }
372        }
373    } while (!t1[1].approximatelyEqual(t2[1]));
374    t1Step = t2Step = 0.1;
375    double t10 = t1Seed - t1Step * 2;
376    double t12 = t1Seed + t1Step * 2;
377    double t20 = t2Seed - t2Step * 2;
378    double t22 = t2Seed + t2Step * 2;
379    _Point test;
380    while (!approximately_zero(t1Step)) {
381        xy_at_t(quad1, t10, test.x, test.y);
382        t10 += t1[1].approximatelyEqual(test) ? -t1Step : t1Step;
383        t1Step /= 2;
384    }
385    t1Step = 0.1;
386    while (!approximately_zero(t1Step)) {
387        xy_at_t(quad1, t12, test.x, test.y);
388        t12 -= t1[1].approximatelyEqual(test) ? -t1Step : t1Step;
389        t1Step /= 2;
390    }
391    while (!approximately_zero(t2Step)) {
392        xy_at_t(quad2, t20, test.x, test.y);
393        t20 += t2[1].approximatelyEqual(test) ? -t2Step : t2Step;
394        t2Step /= 2;
395    }
396    t2Step = 0.1;
397    while (!approximately_zero(t2Step)) {
398        xy_at_t(quad2, t22, test.x, test.y);
399        t22 -= t2[1].approximatelyEqual(test) ? -t2Step : t2Step;
400        t2Step /= 2;
401    }
402#if ONE_OFF_DEBUG
403    SkDebugf("%s t1=(%1.9g<%1.9g<%1.9g) t2=(%1.9g<%1.9g<%1.9g)\n", __FUNCTION__,
404        t10, t1Seed, t12, t20, t2Seed, t22);
405    _Point p10 = xy_at_t(quad1, t10);
406    _Point p1Seed = xy_at_t(quad1, t1Seed);
407    _Point p12 = xy_at_t(quad1, t12);
408    SkDebugf("%s p1=(%1.9g,%1.9g)<(%1.9g,%1.9g)<(%1.9g,%1.9g)\n", __FUNCTION__,
409        p10.x, p10.y, p1Seed.x, p1Seed.y, p12.x, p12.y);
410    _Point p20 = xy_at_t(quad2, t20);
411    _Point p2Seed = xy_at_t(quad2, t2Seed);
412    _Point p22 = xy_at_t(quad2, t22);
413    SkDebugf("%s p2=(%1.9g,%1.9g)<(%1.9g,%1.9g)<(%1.9g,%1.9g)\n", __FUNCTION__,
414        p20.x, p20.y, p2Seed.x, p2Seed.y, p22.x, p22.y);
415#endif
416}
417
418void QuadraticIntersection_IntersectionFinder() {
419    intersectionFinder(0, 1);
420}
421