Add intersections for path ops

tests/PathOpsQuadIntersectionTest.cpp

+/*
+ * Copyright 2012 Google Inc.
+ *
+ * Use of this source code is governed by a BSD-style license that can be
+ * found in the LICENSE file.
+ */
+#include "PathOpsQuadIntersectionTestData.h"
+#include "SkIntersections.h"
+#include "SkPathOpsRect.h"
+#include "SkReduceOrder.h"
+#include "Test.h"
+
+static void standardTestCases(skiatest::Reporter* reporter) {
+    bool showSkipped = false;
+    for (size_t index = 0; index < quadraticTests_count; ++index) {
+        const SkDQuad& quad1 = quadraticTests[index][0];
+        const SkDQuad& quad2 = quadraticTests[index][1];
+        SkReduceOrder reduce1, reduce2;
+        int order1 = reduce1.reduce(quad1, SkReduceOrder::kFill_Style);
+        int order2 = reduce2.reduce(quad2, SkReduceOrder::kFill_Style);
+        if (order1 < 3) {
+            if (showSkipped) {
+                SkDebugf("[%d] quad1 order=%d\n", static_cast<int>(index), order1);
+            }
+        }
+        if (order2 < 3) {
+            if (showSkipped) {
+                SkDebugf("[%d] quad2 order=%d\n", static_cast<int>(index), order2);
+            }
+        }
+        if (order1 == 3 && order2 == 3) {
+            SkIntersections intersections;
+            intersections.intersect(quad1, quad2);
+            if (intersections.used() > 0) {
+                for (int pt = 0; pt < intersections.used(); ++pt) {
+                    double tt1 = intersections[0][pt];
+                    SkDPoint xy1 = quad1.xyAtT(tt1);
+                    double tt2 = intersections[1][pt];
+                    SkDPoint xy2 = quad2.xyAtT(tt2);
+                    if (!xy1.approximatelyEqual(xy2)) {
+                        SkDebugf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
+                                __FUNCTION__, static_cast<int>(index), pt, tt1, xy1.fX, xy1.fY,
+                                tt2, xy2.fX, xy2.fY);
+                        REPORTER_ASSERT(reporter, 0);
+                    }
+                }
+            }
+        }
+    }
+}
+
+static const SkDQuad testSet[] = {
+    {{{3.0774019473063863, 3.35198509346713}, {3.0757503498668397, 3.327320623945933},
+            {3.0744102085015879, 3.3025879417907196}}},
+    {{{3.053913680774329, 3.3310471586283938}, {3.0758730889691694, 3.3273466070370152},
+            {3.0975671980059394, 3.3235031316554351}}},
+
+    {{{3.39068129, 4.44939202}, {3.03659239, 3.81843234}, {3.06844529, 3.02100922}}},
+    {{{2.10714698, 3.44196686}, {3.12180288, 3.38575704}, {3.75968569, 3.1281838}}},
+
+    {{{2.74792918, 4.77711896}, {2.82236867, 4.23882547}, {2.82848144, 3.63729341}}},
+    {{{2.62772567, 3.64823958}, {3.46652495, 3.64258364}, {4.1425079, 3.48623815}}},
+
+    {{{1.34375, 2.03125}, {2.2734375, 2.6640625}, {3.25, 3.25}}},
+    {{{3.96875, 4.65625}, {3.3359375, 3.7265625}, {2.75, 2.75}}},
+
+    {{{0, 1}, {0.324417544, 2.27953848}, {0.664376547, 2.58940267}}},
+    {{{1, 2}, {0.62109375, 2.70703125}, {0.640625, 2.546875}}},
+
+    {{{1, 2}, {0.984375, 2.3359375}, {1.0625, 2.15625}}},
+    {{{0, 1}, {0.983539095, 2.30041152}, {1.47325103, 2.61316872}}},
+
+    {{{4.09011926, 2.20971038}, {4.74608133, 1.9335932}, {5.02469918, 2.00694987}}},
+    {{{2.79472921, 1.73568666}, {3.36246373, 1.21251209}, {5, 2}}},
+
+    {{{1.80814127, 2.41537795}, {2.23475077, 2.05922313}, {3.16529668, 1.98358763}}},
+    {{{2.16505631, 2.55782454}, {2.40541285, 2.02193091}, {2.99836023, 1.68247638}}},
+
+    {{{3, 1.875}, {3.375, 1.54296875}, {3.375, 1.421875}}},
+    {{{3.375, 1.421875}, {3.3749999999999996, 1.3007812499999998}, {3, 2}}},
+
+    {{{3.34, 8.98}, {2.83363281, 9.4265625}, {2.83796875, 9.363125}}},
+    {{{2.83796875, 9.363125}, {2.84230469, 9.2996875}, {3.17875, 9.1725}}},
+
+    {{{2.7279999999999998, 3.024}, {2.5600000000000005, 2.5600000000000005},
+            {2.1520000000000001, 1.8560000000000001}}},
+    {{{0.66666666666666652, 1.1481481481481481}, {1.3333333333333326, 1.3333333333333335},
+            {2.6666666666666665, 2.1851851851851851}}},
+
+    {{{2.728, 3.024}, {2.56, 2.56}, {2.152, 1.856}}},
+    {{{0.666666667, 1.14814815}, {1.33333333, 1.33333333}, {2.66666667, 2.18518519}}},
+
+    {{{0.875, 1.5}, {1.03125, 1.11022302e-16}, {1, 0}}},
+    {{{0.875, 0.859375}, {1.6875, 0.73046875}, {2.5, 0.625}}},
+
+    {{{1.64451042, 0.0942001592}, {1.53635465, 0.00152863961}, {1, 0}}},
+    {{{1.27672209, 0.15}, {1.32143477, 9.25185854e-17}, {1, 0}}},
+
+    {{{0, 0}, {0.51851851851851849, 1.0185185185185186}, {1.2592592592592591, 1.9259259259259258}}},
+    {{{1.2592592592592593, 1.9259259259259265}, {0.51851851851851893, 1.0185185185185195}, {0, 0}}},
+
+    {{{1.93281168, 2.58856757}, {2.38543691, 2.7096125}, {2.51967352, 2.34531784}}},
+    {{{2.51967352, 2.34531784}, {2.65263731, 2.00639194}, {3.1212119, 1.98608967}}},
+    {{{2.09544533, 2.51981963}, {2.33331524, 2.25252128}, {2.92003302, 2.39442311}}},
+
+    {{{0.924337655, 1.94072717}, {1.25185043, 1.52836494}, {1.71793901, 1.06149951}}},
+    {{{0.940798831, 1.67439357}, {1.25988251, 1.39778567}, {1.71791672, 1.06650313}}},
+
+    {{{0.924337655, 1.94072717}, {1.39158994, 1.32418496}, {2.14967426, 0.687365435}}},
+    {{{0.940798831, 1.67439357}, {1.48941875, 1.16280321}, {2.47884711, 0.60465921}}},
+
+    {{{1.7465749139282332, 1.9930452039527999}, {1.8320006564080331, 1.859481345189089},
+            {1.8731035127758437, 1.6344055934266613}}},
+    {{{1.8731035127758437, 1.6344055934266613}, {1.89928170345231, 1.5006405518943067},
+            {1.9223833226085514, 1.3495796165215643}}},
+    {{{1.74657491, 1.9930452}, {1.87407679, 1.76762853}, {1.92238332, 1.34957962}}},
+    {{{0.60797907, 1.68776977}, {1.0447864, 1.50810914}, {1.87464474, 1.63655092}}},
+    {{{1.87464474, 1.63655092}, {2.70450308, 1.76499271}, {4, 3}}},
+
+    {{{1.2071879545809394, 0.82163474041730045}, {1.1534203513372994, 0.52790870069930229},
+            {1.0880000000000001, 0.29599999999999982}}}, //t=0.63155333662549329,0.80000000000000004
+    {{{0.33333333333333326, 0.81481481481481488}, {0.63395173631977997, 0.68744136726313931},
+            {1.205684411948591, 0.81344322326274499}}},
+    {{{0.33333333333333326, 0.81481481481481488}, {0.63396444791444551, 0.68743368362444768},
+            {1.205732763658403, 0.81345617746834109}}}, //t=0.33333333333333331, 0.63396444791444551
+    {{{1.205684411948591, 0.81344322326274499}, {1.2057085875611198, 0.81344969999329253},
+            {1.205732763658403, 0.81345617746834109}}},
+
+    {{{1.20718795, 0.82163474}, {1.15342035, 0.527908701}, {1.088, 0.296}}},
+    {{{1.20568441, 0.813443223}, {1.20570859, 0.8134497}, {1.20573276, 0.813456177}}},
+
+    {{{41.5072916, 87.1234036}, {28.2747836, 80.9545395}, {23.5780771, 69.3344126}}},
+    {{{72.9633878, 95.6593007}, {42.7738746, 88.4730382}, {31.1932785, 80.2458029}}},
+
+    {{{31.1663962, 54.7302484}, {31.1662882, 54.7301074}, {31.1663969, 54.7302485}}},
+    {{{26.0404936, 45.4260361}, {27.7887523, 33.1863051}, {40.8833242, 26.0301855}}},
+
+    {{{29.9404074, 49.1672596}, {44.3131071, 45.3915253}, {58.1067559, 59.5061814}}},
+    {{{72.6510251, 64.2972928}, {53.6989659, 60.1862397}, {35.2053722, 44.8391126}}},
+
+    {{{52.14807018377202, 65.012420045148644}, {44.778669050208237, 66.315562705604378},
+            {51.619118408823567, 63.787827046262684}}},
+    {{{30.004993234763383, 93.921296668202288}, {53.384822003076991, 60.732180341802753},
+            {58.652998934338584, 43.111073088306185}}},
+
+    {{{80.897794748143198, 49.236332042718459}, {81.082078218891212, 64.066749904488631},
+            {69.972305057149981, 72.968595519850993}}},
+    {{{72.503745601281395, 32.952320736577882}, {88.030880716061645, 38.137194847810164},
+            {73.193774825517906, 67.773492479591397}}},
+
+    {{{67.426548091427676, 37.993772624988935}, {51.129513170665035, 57.542281234563646},
+            {44.594748190899189, 65.644267382683879}}},
+    {{{61.336508189019057, 82.693132843213675}, {54.825078921449354, 71.663932799212432},
+            {47.727444217558926, 61.4049645128392}}},
+
+    {{{67.4265481, 37.9937726}, {51.1295132, 57.5422812}, {44.5947482, 65.6442674}}},
+    {{{61.3365082, 82.6931328}, {54.8250789, 71.6639328}, {47.7274442, 61.4049645}}},
+
+    {{{53.774852327053594, 53.318060789841951}, {45.787877803416805, 51.393492026284981},
+            {46.703936967162392, 53.06860709822206}}},
+    {{{46.703936967162392, 53.06860709822206}, {47.619996130907957, 54.74372217015916},
+            {53.020051653535361, 48.633140968832024}}},
+
+    {{{50.934805397717923, 51.52391952648901}, {56.803308902971423, 44.246234610627596},
+            {69.776888596721406, 40.166645096692555}}},
+    {{{50.230212796400401, 38.386469101526998}, {49.855620812184917, 38.818990392153609},
+            {56.356567496227363, 47.229909093319407}}},
+
+    {{{36.148792695174222, 70.336952793070424}, {36.141613037691357, 70.711654739870085},
+            {36.154708826402597, 71.088492662905836}}},
+    {{{35.216235592661825, 70.580199617313212}, {36.244476835123969, 71.010897787304074},
+            {37.230244263238326, 71.423156953613102}}},
+
+    // this pair is nearly coincident, and causes the quartic code to produce bad
+    // data. Mathematica doesn't think they touch. Graphically, I can't tell.
+    // it may not be so bad to pretend that they don't touch, if I can detect that
+    {{{369.848602, 145.680267}, {382.360413, 121.298294}, {406.207703, 121.298294}}},
+    {{{369.850525, 145.675964}, {382.362915, 121.29287}, {406.211273, 121.29287}}},
+
+    {{{33.567436351153468, 62.336347586395924}, {35.200980274619084, 65.038561460144479},
+            {36.479571811084995, 67.632178905412445}}},
+    {{{41.349524945572696, 67.886658677862641}, {39.125562529359087, 67.429772735149214},
+            {35.600314083992416, 66.705372160552685}}},
+
+    {{{67.25299631583178, 21.109080184767524}, {43.617595267398613, 33.658034168577529},
+            {33.38371819435676, 44.214192553988745}}},
+    {{{40.476838859398541, 39.543209911285999}, {36.701186108431131, 34.8817994016458},
+            {30.102144288878023, 26.739063172945315}}},
+
+    {{{25.367434474345036, 50.4712103169743}, {17.865013304933097, 37.356741010559439},
+            {16.818988838905465, 37.682915484123129}}},
+    {{{16.818988838905465, 37.682915484123129}, {15.772964372877833, 38.009089957686811},
+            {20.624104547604965, 41.825131596683121}}},
+
+    {{{26.440225044088567, 79.695009812848298}, {26.085525979582247, 83.717928354134784},
+            {27.075079976297072, 84.820633667838905}}},
+    {{{27.075079976297072, 84.820633667838905}, {28.276546859574015, 85.988574184029034},
+            {25.649263209500006, 87.166762066617025}}},
+
+    {{{34.879150914024962, 83.862726601601125}, {35.095810134304429, 83.693473210169543},
+            {35.359284111931586, 83.488069234177502}}},
+    {{{54.503204203015471, 76.094098492518242}, {51.366889541918894, 71.609856061299155},
+            {46.53086955445437, 69.949863036494207}}},
+
+    {{{0, 0}, {1, 0}, {0, 3}}},
+    {{{1, 0}, {0, 1}, {1, 1}}},
+    {{{369.961151, 137.980698}, {383.970093, 121.298294}, {406.213287, 121.298294}}},
+    {{{353.2948, 194.351074}, {353.2948, 173.767563}, {364.167572, 160.819855}}},
+    {{{360.416077, 166.795715}, {370.126831, 147.872162}, {388.635406, 147.872162}}},
+    {{{406.236359, 121.254936}, {409.445679, 121.254936}, {412.975952, 121.789818}}},
+    {{{406.235992, 121.254936}, {425.705902, 121.254936}, {439.71994, 137.087616}}},
+
+    {{{369.8543701171875, 145.66734313964844}, {382.36788940429688, 121.28203582763672},
+            {406.21844482421875, 121.28203582763672}}},
+    {{{369.96469116210938, 137.96672058105469}, {383.97555541992188, 121.28203582763672},
+            {406.2218017578125, 121.28203582763672}}},
+
+    {{{369.962311, 137.976044}, {383.971893, 121.29287}, {406.216125, 121.29287}}},
+
+    {{{400.121704, 149.468719}, {391.949493, 161.037186}, {391.949493, 181.202423}}},
+    {{{391.946747, 181.839218}, {391.946747, 155.62442}, {406.115479, 138.855438}}},
+    {{{360.048828125, 229.2578125}, {360.048828125, 224.4140625}, {362.607421875, 221.3671875}}},
+    {{{362.607421875, 221.3671875}, {365.166015625, 218.3203125}, {369.228515625, 218.3203125}}},
+    {{{8, 8}, {10, 10}, {8, -10}}},
+    {{{8, 8}, {12, 12}, {14, 4}}},
+    {{{8, 8}, {9, 9}, {10, 8}}}
+};
+
+const size_t testSetCount = sizeof(testSet) / sizeof(testSet[0]);
+
+static void oneOffTest1(skiatest::Reporter* reporter, size_t outer, size_t inner) {
+    const SkDQuad& quad1 = testSet[outer];
+    const SkDQuad& quad2 = testSet[inner];
+    SkIntersections intersections2;
+    intersections2.intersect(quad1, quad2);
+    for (int pt = 0; pt < intersections2.used(); ++pt) {
+        double tt1 = intersections2[0][pt];
+        SkDPoint xy1 = quad1.xyAtT(tt1);
+        double tt2 = intersections2[1][pt];
+        SkDPoint xy2 = quad2.xyAtT(tt2);
+        if (!xy1.approximatelyEqual(xy2)) {
+            SkDebugf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
+                    __FUNCTION__, static_cast<int>(outer), static_cast<int>(inner),
+                    tt1, xy1.fX, xy1.fY, tt2, xy2.fX, xy2.fY);
+            REPORTER_ASSERT(reporter, 0);
+        }
+#if ONE_OFF_DEBUG
+        SkDebugf("%s [%d][%d] t1=%1.9g (%1.9g, %1.9g) t2=%1.9g\n", __FUNCTION__,
+            outer, inner, tt1, xy1.fX, xy1.fY, tt2);
+#endif
+    }
+}
+
+static void QuadraticIntersection_OneOffTest(skiatest::Reporter* reporter) {
+    oneOffTest1(reporter, 0, 1);
+    oneOffTest1(reporter, 1, 0);
+}
+
+static void oneOffTests(skiatest::Reporter* reporter) {
+    for (size_t outer = 0; outer < testSetCount - 1; ++outer) {
+        for (size_t inner = outer + 1; inner < testSetCount; ++inner) {
+            oneOffTest1(reporter, outer, inner);
+        }
+    }
+}
+
+static const SkDQuad coincidentTestSet[] = {
+    {{{369.850525, 145.675964}, {382.362915, 121.29287}, {406.211273, 121.29287}}},
+    {{{369.850525, 145.675964}, {382.362915, 121.29287}, {406.211273, 121.29287}}},
+    {{{8, 8}, {10, 10}, {8, -10}}},
+    {{{8, -10}, {10, 10}, {8, 8}}},
+};
+
+const size_t coincidentTestSetCount = sizeof(coincidentTestSet) / sizeof(coincidentTestSet[0]);
+
+static void coincidentTest(skiatest::Reporter* reporter) {
+    for (size_t testIndex = 0; testIndex < coincidentTestSetCount - 1; testIndex += 2) {
+        const SkDQuad& quad1 = coincidentTestSet[testIndex];
+        const SkDQuad& quad2 = coincidentTestSet[testIndex + 1];
+        SkIntersections intersections2;
+        intersections2.intersect(quad1, quad2);
+        REPORTER_ASSERT(reporter, intersections2.coincidentUsed() == 2);
+        REPORTER_ASSERT(reporter, intersections2.used() == 2);
+        for (int pt = 0; pt < intersections2.coincidentUsed(); ++pt) {
+            double tt1 = intersections2[0][pt];
+            double tt2 = intersections2[1][pt];
+            REPORTER_ASSERT(reporter, approximately_equal(1, tt1) || approximately_zero(tt1));
+            REPORTER_ASSERT(reporter, approximately_equal(1, tt2) || approximately_zero(tt2));
+        }
+    }
+}
+
+static int floatSign(double x) {
+    return x < 0 ? -1 : x > 0 ? 1 : 0;
+}
+
+static const SkDQuad pointFinderTestSet[] = {
+                                                                                                                                //>=0.633974464         0.633974846 <=
+{{{1.2071879545809394, 0.82163474041730045}, {1.1534203513372994, 0.52790870069930229},
+        {1.0880000000000001, 0.29599999999999982}}},  //t=0.63155333662549329, 0.80000000000000004
+{{{1.2071879545809394, 0.82163474041730045}, {1.2065040319428038, 0.81766753259119995},
+        {1.2058123269101506, 0.81370135061854221}}},  //t=0.63155333662549329, 0.6339049773632347
+{{{1.2058123269101506, 0.81370135061854221}, {1.152376363978022, 0.5244097415381026},
+        {1.0880000000000001, 0.29599999999999982}}},  //t=0.6339049773632347,  0.80000000000000004
+                                                                                                                                //>=0.633974083         0.633975227 <=
+{{{0.33333333333333326, 0.81481481481481488}, {0.63395173631977997, 0.68744136726313931},
+        {1.205684411948591, 0.81344322326274499}}},   //t=0.33333333333333331, 0.63395173631977986
+{{{0.33333333333333326, 0.81481481481481488}, {0.63396444791444551, 0.68743368362444768},
+        {1.205732763658403, 0.81345617746834109}}},   //t=0.33333333333333331, 0.63396444791444551
+{{{1.205684411948591, 0.81344322326274499}, {1.2057085875611198, 0.81344969999329253},
+        {1.205732763658403, 0.81345617746834109}}},   //t=0.63395173631977986, 0.63396444791444551
+{{{1.205732763658403, 0.81345617746834109}, {1.267928895828891, 0.83008534558465619},
+        {1.3333333333333333, 0.85185185185185175}}},  //t=0.63396444791444551, 0.66666666666666663
+};
+
+static void pointFinder(const SkDQuad& q1, const SkDQuad& q2) {
+    for (int index = 0; index < 3; ++index) {
+        double t = q1.nearestT(q2[index]);
+        SkDPoint onQuad = q1.xyAtT(t);
+        SkDebugf("%s t=%1.9g (%1.9g,%1.9g) dist=%1.9g\n", __FUNCTION__, t, onQuad.fX, onQuad.fY,
+                onQuad.distance(q2[index]));
+        double left[3];
+        left[0] = ((const SkDLine&) q1[0]).isLeft(q2[index]);
+        left[1] = ((const SkDLine&) q1[1]).isLeft(q2[index]);
+        SkDLine diag = {{q1[0], q1[2]}};
+        left[2] = diag.isLeft(q2[index]);
+        SkDebugf("%s left=(%d, %d, %d) inHull=%s\n", __FUNCTION__, floatSign(left[0]),
+                floatSign(left[1]), floatSign(left[2]),
+                q1.pointInHull(q2[index]) ? "true" : "false");
+    }
+    SkDebugf("\n");
+}
+
+static void hullIntersect(const SkDQuad& q1, const SkDQuad& q2) {
+    SkDebugf("%s", __FUNCTION__);
+    SkIntersections ts;
+    for (int i1 = 0; i1 < 3; ++i1) {
+        SkDLine l1 = {{q1[i1], q1[(i1 + 1) % 3]}};
+        for (int i2 = 0; i2 < 3; ++i2) {
+            SkDLine l2 = {{q2[i2], q2[(i2 + 1) % 3]}};
+            if (ts.intersect(l1, l2)) {
+                SkDebugf(" [%d,%d]", i1, i2);
+            }
+        }
+    }
+    SkDebugf("\n");
+}
+
+static void QuadraticIntersection_PointFinder() {
+    pointFinder(pointFinderTestSet[0], pointFinderTestSet[4]);
+    pointFinder(pointFinderTestSet[4], pointFinderTestSet[0]);
+    pointFinder(pointFinderTestSet[0], pointFinderTestSet[6]);
+    pointFinder(pointFinderTestSet[6], pointFinderTestSet[0]);
+    hullIntersect(pointFinderTestSet[0], pointFinderTestSet[4]);
+    hullIntersect(pointFinderTestSet[0], pointFinderTestSet[6]);
+}
+
+static void intersectionFinder(int test1, int test2) {
+    const SkDQuad& quad1 = testSet[test1];
+    const SkDQuad& quad2 = testSet[test2];
+
+    double t1Seed = 0.5;
+    double t2Seed = 0.8;
+    double t1Step = 0.1;
+    double t2Step = 0.1;
+    SkDPoint t1[3], t2[3];
+    bool toggle = true;
+    do {
+        t1[0] = quad1.xyAtT(t1Seed - t1Step);
+        t1[1] = quad1.xyAtT(t1Seed);
+        t1[2] = quad1.xyAtT(t1Seed + t1Step);
+        t2[0] = quad2.xyAtT(t2Seed - t2Step);
+        t2[1] = quad2.xyAtT(t2Seed);
+        t2[2] = quad2.xyAtT(t2Seed + t2Step);
+        double dist[3][3];
+        dist[1][1] = t1[1].distance(t2[1]);
+        int best_i = 1, best_j = 1;
+        for (int i = 0; i < 3; ++i) {
+            for (int j = 0; j < 3; ++j) {
+                if (i == 1 && j == 1) {
+                    continue;
+                }
+                dist[i][j] = t1[i].distance(t2[j]);
+                if (dist[best_i][best_j] > dist[i][j]) {
+                    best_i = i;
+                    best_j = j;
+                }
+            }
+        }
+        if (best_i == 0) {
+            t1Seed -= t1Step;
+        } else if (best_i == 2) {
+            t1Seed += t1Step;
+        }
+        if (best_j == 0) {
+            t2Seed -= t2Step;
+        } else if (best_j == 2) {
+            t2Seed += t2Step;
+        }
+        if (best_i == 1 && best_j == 1) {
+            if ((toggle ^= true)) {
+                t1Step /= 2;
+            } else {
+                t2Step /= 2;
+            }
+        }
+    } while (!t1[1].approximatelyEqual(t2[1]));
+    t1Step = t2Step = 0.1;
+    double t10 = t1Seed - t1Step * 2;
+    double t12 = t1Seed + t1Step * 2;
+    double t20 = t2Seed - t2Step * 2;
+    double t22 = t2Seed + t2Step * 2;
+    SkDPoint test;
+    while (!approximately_zero(t1Step)) {
+        test = quad1.xyAtT(t10);
+        t10 += t1[1].approximatelyEqual(test) ? -t1Step : t1Step;
+        t1Step /= 2;
+    }
+    t1Step = 0.1;
+    while (!approximately_zero(t1Step)) {
+        test = quad1.xyAtT(t12);
+        t12 -= t1[1].approximatelyEqual(test) ? -t1Step : t1Step;
+        t1Step /= 2;
+    }
+    while (!approximately_zero(t2Step)) {
+        test = quad2.xyAtT(t20);
+        t20 += t2[1].approximatelyEqual(test) ? -t2Step : t2Step;
+        t2Step /= 2;
+    }
+    t2Step = 0.1;
+    while (!approximately_zero(t2Step)) {
+        test = quad2.xyAtT(t22);
+        t22 -= t2[1].approximatelyEqual(test) ? -t2Step : t2Step;
+        t2Step /= 2;
+    }
+#if ONE_OFF_DEBUG
+    SkDebugf("%s t1=(%1.9g<%1.9g<%1.9g) t2=(%1.9g<%1.9g<%1.9g)\n", __FUNCTION__,
+        t10, t1Seed, t12, t20, t2Seed, t22);
+    SkDPoint p10 = quad1.xyAtT(t10);
+    SkDPoint p1Seed = quad1.xyAtT(t1Seed);
+    SkDPoint p12 = quad1.xyAtT(t12);
+    SkDebugf("%s p1=(%1.9g,%1.9g)<(%1.9g,%1.9g)<(%1.9g,%1.9g)\n", __FUNCTION__,
+        p10.fX, p10.fY, p1Seed.fX, p1Seed.fY, p12.fX, p12.fY);
+    SkDPoint p20 = quad2.xyAtT(t20);
+    SkDPoint p2Seed = quad2.xyAtT(t2Seed);
+    SkDPoint p22 = quad2.xyAtT(t22);
+    SkDebugf("%s p2=(%1.9g,%1.9g)<(%1.9g,%1.9g)<(%1.9g,%1.9g)\n", __FUNCTION__,
+        p20.fX, p20.fY, p2Seed.fX, p2Seed.fY, p22.fX, p22.fY);
+#endif
+}
+
+static void QuadraticIntersection_IntersectionFinder() {
+    intersectionFinder(0, 1);
+}
+
+static void TestQuadIntersection(skiatest::Reporter* reporter) {
+    oneOffTests(reporter);
+    coincidentTest(reporter);
+    standardTestCases(reporter);
+    if (false) QuadraticIntersection_IntersectionFinder();
+    if (false) QuadraticIntersection_PointFinder();
+    if (false) QuadraticIntersection_OneOffTest(reporter);
+}
+
+
+#include "TestClassDef.h"
+DEFINE_TESTCLASS("PathOpsQuadIntersection", QuadIntersectionTestClass, TestQuadIntersection)
+