/*
* 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 "CurveIntersection.h"
#include "CurveUtilities.h"
#include "CubicIntersection_TestData.h"
#include "Intersection_Tests.h"
#include "Intersections.h"
#include "TestUtilities.h"
#define SHOW_ORIGINAL 1
const int firstCubicIntersectionTest = 9;
static void standardTestCases() {
for (size_t index = firstCubicIntersectionTest; index < tests_count; ++index) {
const Cubic& cubic1 = tests[index][0];
const Cubic& cubic2 = tests[index][1];
Cubic reduce1, reduce2;
int order1 = reduceOrder(cubic1, reduce1, kReduceOrder_NoQuadraticsAllowed,
kReduceOrder_TreatAsFill);
int order2 = reduceOrder(cubic2, reduce2, kReduceOrder_NoQuadraticsAllowed,
kReduceOrder_TreatAsFill);
if (order1 < 4) {
printf("%s [%d] cubic1 order=%d\n", __FUNCTION__, (int) index, order1);
continue;
}
if (order2 < 4) {
printf("%s [%d] cubic2 order=%d\n", __FUNCTION__, (int) index, order2);
continue;
}
if (implicit_matches(reduce1, reduce2)) {
printf("%s [%d] coincident\n", __FUNCTION__, (int) index);
continue;
}
Intersections tIntersections;
intersect(reduce1, reduce2, tIntersections);
if (!tIntersections.intersected()) {
printf("%s [%d] no intersection\n", __FUNCTION__, (int) index);
continue;
}
for (int pt = 0; pt < tIntersections.used(); ++pt) {
double tt1 = tIntersections.fT[0][pt];
double tx1, ty1;
xy_at_t(cubic1, tt1, tx1, ty1);
double tt2 = tIntersections.fT[1][pt];
double tx2, ty2;
xy_at_t(cubic2, tt2, tx2, ty2);
if (!AlmostEqualUlps(tx1, tx2)) {
printf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
__FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2);
}
if (!AlmostEqualUlps(ty1, ty2)) {
printf("%s [%d,%d] y!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
__FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2);
}
}
}
}
static const Cubic testSet[] = {
{{67.426548091427676, 37.993772624988935}, {23.483695892376684, 90.476863174921306}, {35.597065061143162, 79.872482633158796}, {75.38634169631932, 18.244890038969412}},
{{67.4265481, 37.9937726}, {23.4836959, 90.4768632}, {35.5970651, 79.8724826}, {75.3863417, 18.24489}},
{{0, 0}, {0, 1}, {1, 1}, {1, 0}},
{{1, 0}, {0, 0}, {0, 1}, {1, 1}},
{{0,1}, {4,5}, {1,0}, {5,3}},
{{0,1}, {3,5}, {1,0}, {5,4}},
{{0, 1}, {1, 6}, {1, 0}, {1, 0}},
{{0, 1}, {0, 1}, {1, 0}, {6, 1}},
{{0,1}, {3,4}, {1,0}, {5,1}},
{{0,1}, {1,5}, {1,0}, {4,3}},
{{0,1}, {1,2}, {1,0}, {6,1}},
{{0,1}, {1,6}, {1,0}, {2,1}},
{{0,1}, {0,5}, {1,0}, {4,0}},
{{0,1}, {0,4}, {1,0}, {5,0}},
{{0,1}, {3,4}, {1,0}, {3,0}},
{{0,1}, {0,3}, {1,0}, {4,3}},
{{0, 0}, {1, 2}, {3, 4}, {4, 4}},
{{0, 0}, {1, 2}, {3, 4}, {4, 4}},
{{4, 4}, {3, 4}, {1, 2}, {0, 0}},
{{0,1}, {2,3}, {1,0}, {1,0}},
{{0,1}, {0,1}, {1,0}, {3,2}},
{{0,2}, {0,1}, {1,0}, {1,0}},
{{0,1}, {0,1}, {2,0}, {1,0}},
{{0, 1}, {0, 2}, {1, 0}, {1, 0}},
{{0, 1}, {0, 1}, {1, 0}, {2, 0}},
{{0, 1}, {1, 6}, {1, 0}, {2, 0}},
{{0, 1}, {0, 2}, {1, 0}, {6, 1}},
{{0, 1}, {5, 6}, {1, 0}, {1, 0}},
{{0, 1}, {0, 1}, {1, 0}, {6, 5}},
{{95.837747722788592, 45.025976907939643}, {16.564570095652982, 0.72959763963222402}, {63.209855865319199, 68.047528419665767}, {57.640240647662544, 59.524565264361243}},
{{51.593891741518817, 38.53849970667553}, {62.34752929878772, 74.924924725166022}, {74.810149322641152, 34.17966562983564}, {29.368398119401373, 94.66719277886078}},
{{39.765160968417838, 33.060396198677083}, {5.1922921581157908, 66.854301452103215}, {31.619281802149157, 25.269248720849514}, {81.541621071073038, 70.025341524754353}},
{{46.078911165743556, 48.259962651999651}, {20.24450549867214, 49.403916182650214}, {0.26325131778756683, 24.46489805563581}, {15.915006546264051, 83.515023059917155}},
{{65.454505973241524, 93.881892270353575}, {45.867360264932437, 92.723972719499827}, {2.1464054482739447, 74.636369140183717}, {33.774068594804994, 40.770872887582925}},
{{72.963387832494163, 95.659300729473728}, {11.809496633619768, 82.209921247423594}, {13.456139067865974, 57.329313623406605}, {36.060621606214262, 70.867335643091849}},
{{32.484981432782945, 75.082940782924624}, {42.467313093350882, 48.131159948246157}, {3.5963115764764657, 43.208665839959245}, {79.442476890721579, 89.709102357602262}},
{{18.98573861410177, 93.308887208490106}, {40.405250173250792, 91.039661826118675}, {8.0467721950480584, 42.100282172719147}, {40.883324221187891, 26.030185504830527}},
{{7.5374809128872498, 82.441702896003477}, {22.444346930107265, 22.138854312775123}, {66.76091829629658, 50.753805856571446}, {78.193478508942519, 97.7932997968948}},
{{97.700573130371311, 53.53260215070685}, {87.72443481149358, 84.575876772671876}, {19.215031396232092, 47.032676472809484}, {11.989686410869325, 10.659507480757082}},
{{26.192053931854691, 9.8504326817814416}, {10.174241480498686, 98.476562741434464}, {21.177712558385782, 33.814968789841501}, {75.329030899018534, 55.02231980442177}},
{{56.222082700683771, 24.54395039218662}, {95.589995289030483, 81.050822735322086}, {28.180450866082897, 28.837706255185282}, {60.128952916771617, 87.311672180570511}},
{{42.449716172390481, 52.379709366885805}, {27.896043159019225, 48.797373636065686}, {92.770268299044233, 89.899302036454571}, {12.102066544863426, 99.43241951960718}},
{{45.77532924980639, 45.958701495993274}, {37.458701356062065, 68.393691335056758}, {37.569326692060258, 27.673713456687381}, {60.674866037757539, 62.47349659096146}},
{{67.426548091427676, 37.993772624988935}, {23.483695892376684, 90.476863174921306}, {35.597065061143162, 79.872482633158796}, {75.38634169631932, 18.244890038969412}},
{{61.336508189019057, 82.693132843213675}, {44.639380902349664, 54.074825790745592}, {16.815615499771951, 20.049704667203923}, {41.866884958868326, 56.735503699973002}},
{{67.4265481, 37.9937726}, {23.4836959, 90.4768632}, {35.5970651, 79.8724826}, {75.3863417, 18.24489}},
{{61.3365082, 82.6931328}, {44.6393809, 54.0748258}, {16.8156155, 20.0497047}, {41.866885, 56.7355037}},
{{18.1312339, 31.6473732}, {95.5711034, 63.5350219}, {92.3283165, 62.0158945}, {18.5656052, 32.1268808}},
{{97.402018, 35.7169972}, {33.1127443, 25.8935163}, {1.13970027, 54.9424981}, {56.4860195, 60.529264}},
};
const size_t testSetCount = sizeof(testSet) / sizeof(testSet[0]);
static const Cubic newTestSet[] = {
{{1,3}, {5,6}, {5,3}, {5,4}},
{{3,5}, {4,5}, {3,1}, {6,5}},
{{0,5}, {0,5}, {5,4}, {6,4}},
{{4,5}, {4,6}, {5,0}, {5,0}},
{{0,4}, {1,3}, {5,4}, {4,2}},
{{4,5}, {2,4}, {4,0}, {3,1}},
{{0,2}, {1,5}, {3,2}, {4,1}},
{{2,3}, {1,4}, {2,0}, {5,1}},
{{0,2}, {2,3}, {5,1}, {3,2}},
{{1,5}, {2,3}, {2,0}, {3,2}},
{{2,6}, {4,5}, {1,0}, {6,1}},
{{0,1}, {1,6}, {6,2}, {5,4}},
{{0,1}, {1,2}, {6,5}, {5,4}},
{{5,6}, {4,5}, {1,0}, {2,1}},
{{2.5119999999999996, 1.5710000000000002}, {2.6399999999999983, 1.6599999999999997}, {2.8000000000000007, 1.8000000000000003}, {3, 2}},
{{2.4181876227114887, 1.9849772580462195}, {2.8269904869227211, 2.009330650246834}, {3.2004679292461624, 1.9942047174679169}, {3.4986199496818058, 2.0035994597094731}},
{{2,3}, {1,4}, {1,0}, {6,0}},
{{0,1}, {0,6}, {3,2}, {4,1}},
{{0,2}, {1,5}, {1,0}, {6,1}},
{{0,1}, {1,6}, {2,0}, {5,1}},
{{0,1}, {1,5}, {2,1}, {4,0}},
{{1,2}, {0,4}, {1,0}, {5,1}},
{{0,1}, {3,5}, {2,1}, {3,1}},
{{1,2}, {1,3}, {1,0}, {5,3}},
{{0,1}, {2,5}, {6,0}, {5,3}},
{{0,6}, {3,5}, {1,0}, {5,2}},
{{0,1}, {3,6}, {1,0}, {5,2}},
{{0,1}, {2,5}, {1,0}, {6,3}},
{{1,2},{5,6},{1,0},{1,0}},
{{0,1},{0,1},{2,1},{6,5}},
{{0,6},{1,2},{1,0},{1,0}},
{{0,1},{0,1},{6,0},{2,1}},
{{0,2},{0,1},{3,0},{1,0}},
{{0,3},{0,1},{2,0},{1,0}},
};
const size_t newTestSetCount = sizeof(newTestSet) / sizeof(newTestSet[0]);
#if 0
static void oneOff(const Cubic& cubic1, const Cubic& cubic2) {
SkTDArray<Quadratic> quads1;
cubic_to_quadratics(cubic1, calcPrecision(cubic1), quads1);
#if SHOW_ORIGINAL
SkDebugf("computed quadratics given\n");
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}, {%1.9g,%1.9g}},\n",
cubic1[0].x, cubic1[0].y, cubic1[1].x, cubic1[1].y,
cubic1[2].x, cubic1[2].y, cubic1[3].x, cubic1[3].y));
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}, {%1.9g,%1.9g}},\n",
cubic2[0].x, cubic2[0].y, cubic2[1].x, cubic2[1].y,
cubic2[2].x, cubic2[2].y, cubic2[3].x, cubic2[3].y));
#endif
#if ONE_OFF_DEBUG
SkDebugf("computed quadratics set 1\n");
for (int index = 0; index < quads1.count(); ++index) {
const Quadratic& q = quads1[index];
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y,
q[1].x, q[1].y, q[2].x, q[2].y);
}
#endif
SkTDArray<Quadratic> quads2;
cubic_to_quadratics(cubic2, calcPrecision(cubic2), quads2);
#if ONE_OFF_DEBUG
SkDebugf("computed quadratics set 2\n");
for (int index = 0; index < quads2.count(); ++index) {
const Quadratic& q = quads2[index];
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y,
q[1].x, q[1].y, q[2].x, q[2].y);
}
#endif
Intersections intersections2, intersections3;
intersect2(cubic1, cubic2, intersections2);
intersect3(cubic1, cubic2, intersections3);
int pt1, pt2, pt3;
bool found;
double tt1, tt2, last = -1;
_Point xy1, xy2;
for (pt1 = 0; pt1 < intersections2.used(); ++pt1) {
tt1 = intersections2.fT[0][pt1];
SkASSERT(!approximately_equal(last, tt1));
last = tt1;
xy_at_t(cubic1, tt1, xy1.x, xy1.y);
pt2 = intersections2.fFlip ? intersections2.used() - pt1 - 1 : pt1;
tt2 = intersections2.fT[1][pt2];
xy_at_t(cubic2, tt2, xy2.x, xy2.y);
#if ONE_OFF_DEBUG
SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n",
__FUNCTION__, tt1, xy1.x, xy1.y, intersections2.fPt[pt1].x,
intersections2.fPt[pt1].y, xy2.x, xy2.y, tt2);
#endif
SkASSERT(xy1.approximatelyEqual(xy2));
#if SK_DEBUG
found = false;
for (pt3 = 0; pt3 < intersections3.used(); ++pt3) {
if (roughly_equal(tt1, intersections3.fT[0][pt3])) {
found = true;
break;
}
}
SkASSERT(found);
#endif
}
last = -1;
for (pt3 = 0; pt3 < intersections3.used(); ++pt3) {
found = false;
double tt3 = intersections3.fT[0][pt3];
SkASSERT(!approximately_equal(last, tt3));
last = tt3;
for (pt1 = 0; pt1 < intersections2.used(); ++pt1) {
if (approximately_equal(tt3, intersections2.fT[0][pt1])) {
found = true;
break;
}
}
if (!found) {
tt1 = intersections3.fT[0][pt3];
xy_at_t(cubic1, tt1, xy1.x, xy1.y);
pt2 = intersections3.fFlip ? intersections3.used() - pt3 - 1 : pt3;
tt2 = intersections3.fT[1][pt2];
xy_at_t(cubic2, tt2, xy2.x, xy2.y);
#if ONE_OFF_DEBUG
SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n",
__FUNCTION__, tt1, xy1.x, xy1.y, intersections3.fPt[pt1].x,
intersections3.fPt[pt1].y, xy2.x, xy2.y, tt2);
#endif
SkASSERT(xy1.approximatelyEqual(xy2));
SkDebugf("%s missing in intersect2\n", __FUNCTION__);
}
}
}
#endif
static void oneOff3(const Cubic& cubic1, const Cubic& cubic2) {
#if ONE_OFF_DEBUG
SkDebugf("computed quadratics given\n");
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
cubic1[0].x, cubic1[0].y, cubic1[1].x, cubic1[1].y,
cubic1[2].x, cubic1[2].y, cubic1[3].x, cubic1[3].y);
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
cubic2[0].x, cubic2[0].y, cubic2[1].x, cubic2[1].y,
cubic2[2].x, cubic2[2].y, cubic2[3].x, cubic2[3].y);
#endif
SkTDArray<Quadratic> quads1;
cubic_to_quadratics(cubic1, calcPrecision(cubic1), quads1);
#if ONE_OFF_DEBUG
SkDebugf("computed quadratics set 1\n");
for (int index = 0; index < quads1.count(); ++index) {
const Quadratic& q = quads1[index];
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y,
q[1].x, q[1].y, q[2].x, q[2].y);
}
#endif
SkTDArray<Quadratic> quads2;
cubic_to_quadratics(cubic2, calcPrecision(cubic2), quads2);
#if ONE_OFF_DEBUG
SkDebugf("computed quadratics set 2\n");
for (int index = 0; index < quads2.count(); ++index) {
const Quadratic& q = quads2[index];
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y,
q[1].x, q[1].y, q[2].x, q[2].y);
}
#endif
Intersections intersections3;
intersect3(cubic1, cubic2, intersections3);
int pt2, pt3;
double tt1, tt2, last = -1;
_Point xy1, xy2;
for (pt3 = 0; pt3 < intersections3.used(); ++pt3) {
double tt3 = intersections3.fT[0][pt3];
// SkASSERT(!approximately_equal(last, tt3));
last = tt3;
tt1 = intersections3.fT[0][pt3];
xy_at_t(cubic1, tt1, xy1.x, xy1.y);
pt2 = intersections3.fFlip ? intersections3.used() - pt3 - 1 : pt3;
tt2 = intersections3.fT[1][pt2];
xy_at_t(cubic2, tt2, xy2.x, xy2.y);
#if ONE_OFF_DEBUG
SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n",
__FUNCTION__, tt1, xy1.x, xy1.y, intersections3.fPt[pt3].x,
intersections3.fPt[pt3].y, xy2.x, xy2.y, tt2);
#endif
SkASSERT(xy1.approximatelyEqual(xy2));
}
}
#if 0
static int fails[][2] = { {0, 23}, // fails in intersect2 recursing
{2, 7}, // answers differ, but neither is correct ('3' is closer)
{3, 26}, // fails in intersect2 recursing
{4, 9}, // fails in intersect2 recursing
{4, 10}, // fails in intersect2 recursing
{10, 17}, // fails in intersect2 recursing
{12, 14}, // loops indefinitely
{12, 21}, // fails in intersect2 recursing
{13, 21}, // fails in intersect2 recursing
{14, 21}, // fails in intersect2 recursing
{17, 25}, // fails in intersect2 recursing
{23, 25}, // fails in intersect2 recursing
};
static int failCount = sizeof(fails) / sizeof(fails[0]);
#endif
static void oneOff(int outer, int inner) {
const Cubic& cubic1 = testSet[outer];
const Cubic& cubic2 = testSet[inner];
#if 0
bool failing = false;
for (int i = 0; i < failCount; ++i) {
if ((fails[i][0] == outer && fails[i][1] == inner)
|| (fails[i][1] == outer && fails[i][0] == inner)) {
failing = true;
break;
}
}
if (!failing) {
oneOff(cubic1, cubic2);
} else {
#endif
oneOff3(cubic1, cubic2);
// }
}
void CubicIntersection_OneOffTest() {
oneOff(0, 1);
}
static void newOneOff(int outer, int inner) {
const Cubic& cubic1 = newTestSet[outer];
const Cubic& cubic2 = newTestSet[inner];
oneOff3(cubic1, cubic2);
}
void CubicIntersection_NewOneOffTest() {
newOneOff(0, 1);
}
static void oneOffTests() {
for (size_t outer = 0; outer < testSetCount - 1; ++outer) {
for (size_t inner = outer + 1; inner < testSetCount; ++inner) {
oneOff(outer, inner);
}
}
}
void CubicIntersection_OneOffTests() {
oneOffTests();
}
#define DEBUG_CRASH 0
class CubicChopper {
public:
// only finds one intersection
CubicChopper(const Cubic& c1, const Cubic& c2)
: cubic1(c1)
, cubic2(c2)
, depth(0) {
}
bool intersect(double minT1, double maxT1, double minT2, double maxT2) {
Cubic sub1, sub2;
// FIXME: carry last subdivide and reduceOrder result with cubic
sub_divide(cubic1, minT1, maxT1, sub1);
sub_divide(cubic2, minT2, maxT2, sub2);
Intersections i;
intersect3(sub1, sub2, i);
if (i.used() == 0) {
return false;
}
double x1, y1, x2, y2;
t1 = minT1 + i.fT[0][0] * (maxT1 - minT1);
t2 = minT2 + i.fT[1][0] * (maxT2 - minT2);
xy_at_t(cubic1, t1, x1, y1);
xy_at_t(cubic2, t2, x2, y2);
if (AlmostEqualUlps(x1, x2) && AlmostEqualUlps(y1, y2)) {
return true;
}
double half1 = (minT1 + maxT1) / 2;
double half2 = (minT2 + maxT2) / 2;
++depth;
bool result;
if (depth & 1) {
result = intersect(minT1, half1, minT2, maxT2) || intersect(half1, maxT1, minT2, maxT2)
|| intersect(minT1, maxT1, minT2, half2) || intersect(minT1, maxT1, half2, maxT2);
} else {
result = intersect(minT1, maxT1, minT2, half2) || intersect(minT1, maxT1, half2, maxT2)
|| intersect(minT1, half1, minT2, maxT2) || intersect(half1, maxT1, minT2, maxT2);
}
--depth;
return result;
}
const Cubic& cubic1;
const Cubic& cubic2;
double t1;
double t2;
int depth;
};
#define TRY_OLD 0 // old way fails on test == 1
void CubicIntersection_RandTestOld() {
srand(0);
const int tests = 1000000; // 10000000;
double largestFactor = DBL_MAX;
for (int test = 0; test < tests; ++test) {
Cubic cubic1, cubic2;
for (int i = 0; i < 4; ++i) {
cubic1[i].x = (double) rand() / RAND_MAX * 100;
cubic1[i].y = (double) rand() / RAND_MAX * 100;
cubic2[i].x = (double) rand() / RAND_MAX * 100;
cubic2[i].y = (double) rand() / RAND_MAX * 100;
}
if (test == 2513) { // the pair crosses three times, but the quadratic approximation
continue; // only sees one -- should be OK to ignore the other two?
}
if (test == 12932) { // this exposes a weakness when one cubic touches the other but
continue; // does not touch the quad approximation. Captured in qc.htm as cubic15
}
#if DEBUG_CRASH
char str[1024];
sprintf(str, "{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n"
"{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n",
cubic1[0].x, cubic1[0].y, cubic1[1].x, cubic1[1].y, cubic1[2].x, cubic1[2].y,
cubic1[3].x, cubic1[3].y,
cubic2[0].x, cubic2[0].y, cubic2[1].x, cubic2[1].y, cubic2[2].x, cubic2[2].y,
cubic2[3].x, cubic2[3].y);
#endif
_Rect rect1, rect2;
rect1.setBounds(cubic1);
rect2.setBounds(cubic2);
bool boundsIntersect = rect1.left <= rect2.right && rect2.left <= rect2.right
&& rect1.top <= rect2.bottom && rect2.top <= rect1.bottom;
Intersections i1, i2;
#if TRY_OLD
bool oldIntersects = intersect(cubic1, cubic2, i1);
#else
bool oldIntersects = false;
#endif
if (test == -1) {
SkDebugf("ready...\n");
}
bool newIntersects = intersect3(cubic1, cubic2, i2);
if (!boundsIntersect && (oldIntersects || newIntersects)) {
#if DEBUG_CRASH
SkDebugf("%s %d unexpected intersection boundsIntersect=%d oldIntersects=%d"
" newIntersects=%d\n%s %s\n", __FUNCTION__, test, boundsIntersect,
oldIntersects, newIntersects, __FUNCTION__, str);
#endif
SkASSERT(0);
}
if (oldIntersects && !newIntersects) {
#if DEBUG_CRASH
SkDebugf("%s %d missing intersection oldIntersects=%d newIntersects=%d\n%s %s\n",
__FUNCTION__, test, oldIntersects, newIntersects, __FUNCTION__, str);
#endif
SkASSERT(0);
}
if (!oldIntersects && !newIntersects) {
continue;
}
if (i2.used() > 1) {
continue;
// just look at single intercepts for simplicity
}
Intersections self1, self2; // self-intersect checks
if (intersect(cubic1, self1)) {
continue;
}
if (intersect(cubic2, self2)) {
continue;
}
// binary search for range necessary to enclose real intersection
CubicChopper c(cubic1, cubic2);
bool result = c.intersect(0, 1, 0, 1);
if (!result) {
// FIXME: a failure here probably means that a core routine used by CubicChopper is failing
continue;
}
double delta1 = fabs(c.t1 - i2.fT[0][0]);
double delta2 = fabs(c.t2 - i2.fT[1][0]);
double calc1 = calcPrecision(cubic1);
double calc2 = calcPrecision(cubic2);
double factor1 = calc1 / delta1;
double factor2 = calc2 / delta2;
SkDebugf("%s %d calc1=%1.9g delta1=%1.9g factor1=%1.9g calc2=%1.9g delta2=%1.9g"
" factor2=%1.9g\n", __FUNCTION__, test,
calc1, delta1, factor1, calc2, delta2, factor2);
if (factor1 < largestFactor) {
SkDebugf("WE HAVE A WINNER! %1.9g\n", factor1);
#if DEBUG_CRASH
SkDebugf("%s\n", str);
#endif
oneOff3(cubic1, cubic2);
largestFactor = factor1;
}
if (factor2 < largestFactor) {
SkDebugf("WE HAVE A WINNER! %1.9g\n", factor2);
#if DEBUG_CRASH
SkDebugf("%s\n", str);
#endif
oneOff3(cubic1, cubic2);
largestFactor = factor2;
}
}
}
void CubicIntersection_RandTest() {
srand(0);
const int tests = 10000000;
for (int test = 0; test < tests; ++test) {
Cubic cubic1, cubic2;
for (int i = 0; i < 4; ++i) {
cubic1[i].x = (double) rand() / RAND_MAX * 100;
cubic1[i].y = (double) rand() / RAND_MAX * 100;
cubic2[i].x = (double) rand() / RAND_MAX * 100;
cubic2[i].y = (double) rand() / RAND_MAX * 100;
}
#if DEBUG_CRASH
char str[1024];
sprintf(str, "{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n"
"{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n",
cubic1[0].x, cubic1[0].y, cubic1[1].x, cubic1[1].y, cubic1[2].x, cubic1[2].y,
cubic1[3].x, cubic1[3].y,
cubic2[0].x, cubic2[0].y, cubic2[1].x, cubic2[1].y, cubic2[2].x, cubic2[2].y,
cubic2[3].x, cubic2[3].y);
#endif
_Rect rect1, rect2;
rect1.setBounds(cubic1);
rect2.setBounds(cubic2);
bool boundsIntersect = rect1.left <= rect2.right && rect2.left <= rect2.right
&& rect1.top <= rect2.bottom && rect2.top <= rect1.bottom;
if (test == -1) {
SkDebugf("ready...\n");
}
Intersections intersections2;
bool newIntersects = intersect3(cubic1, cubic2, intersections2);
if (!boundsIntersect && newIntersects) {
#if DEBUG_CRASH
SkDebugf("%s %d unexpected intersection boundsIntersect=%d "
" newIntersects=%d\n%s %s\n", __FUNCTION__, test, boundsIntersect,
newIntersects, __FUNCTION__, str);
#endif
SkASSERT(0);
}
for (int pt = 0; pt < intersections2.used(); ++pt) {
double tt1 = intersections2.fT[0][pt];
_Point xy1, xy2;
xy_at_t(cubic1, tt1, xy1.x, xy1.y);
int pt2 = intersections2.fFlip ? intersections2.used() - pt - 1 : pt;
double tt2 = intersections2.fT[1][pt2];
xy_at_t(cubic2, tt2, xy2.x, xy2.y);
#if 0
SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n", __FUNCTION__,
tt1, xy1.x, xy1.y, xy2.x, xy2.y, tt2);
#endif
SkASSERT(xy1.approximatelyEqual(xy2));
}
}
}
static void intersectionFinder(int index0, int index1, double t1Seed, double t2Seed,
double t1Step, double t2Step) {
const Cubic& cubic1 = newTestSet[index0];
const Cubic& cubic2 = newTestSet[index1];
_Point t1[3], t2[3];
bool toggle = true;
do {
xy_at_t(cubic1, t1Seed - t1Step, t1[0].x, t1[0].y);
xy_at_t(cubic1, t1Seed, t1[1].x, t1[1].y);
xy_at_t(cubic1, t1Seed + t1Step, t1[2].x, t1[2].y);
xy_at_t(cubic2, t2Seed - t2Step, t2[0].x, t2[0].y);
xy_at_t(cubic2, t2Seed, t2[1].x, t2[1].y);
xy_at_t(cubic2, t2Seed + t2Step, t2[2].x, t2[2].y);
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;
_Point test;
while (!approximately_zero(t1Step)) {
xy_at_t(cubic1, t10, test.x, test.y);
t10 += t1[1].approximatelyEqual(test) ? -t1Step : t1Step;
t1Step /= 2;
}
t1Step = 0.1;
while (!approximately_zero(t1Step)) {
xy_at_t(cubic1, t12, test.x, test.y);
t12 -= t1[1].approximatelyEqual(test) ? -t1Step : t1Step;
t1Step /= 2;
}
while (!approximately_zero(t2Step)) {
xy_at_t(cubic2, t20, test.x, test.y);
t20 += t2[1].approximatelyEqual(test) ? -t2Step : t2Step;
t2Step /= 2;
}
t2Step = 0.1;
while (!approximately_zero(t2Step)) {
xy_at_t(cubic2, t22, test.x, test.y);
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);
_Point p10 = xy_at_t(cubic1, t10);
_Point p1Seed = xy_at_t(cubic1, t1Seed);
_Point p12 = xy_at_t(cubic1, t12);
SkDebugf("%s p1=(%1.9g,%1.9g)<(%1.9g,%1.9g)<(%1.9g,%1.9g)\n", __FUNCTION__,
p10.x, p10.y, p1Seed.x, p1Seed.y, p12.x, p12.y);
_Point p20 = xy_at_t(cubic2, t20);
_Point p2Seed = xy_at_t(cubic2, t2Seed);
_Point p22 = xy_at_t(cubic2, t22);
SkDebugf("%s p2=(%1.9g,%1.9g)<(%1.9g,%1.9g)<(%1.9g,%1.9g)\n", __FUNCTION__,
p20.x, p20.y, p2Seed.x, p2Seed.y, p22.x, p22.y);
#endif
}
void CubicIntersection_IntersectionFinder() {
// double t1Seed = 0.87;
// double t2Seed = 0.87;
double t1Step = 0.000001;
double t2Step = 0.000001;
intersectionFinder(0, 1, 0.855895664, 0.864850875, t1Step, t2Step);
intersectionFinder(0, 1, 0.865207906, 0.865207887, t1Step, t2Step);
intersectionFinder(0, 1, 0.865213351, 0.865208087, t1Step, t2Step);
}
static void coincidentTest() {
#if 0
Cubic cubic1 = {{0, 1}, {0, 2}, {1, 0}, {1, 0}};
Cubic cubic2 = {{0, 1}, {0, 2}, {1, 0}, {6, 1}};
#endif
}
void CubicIntersection_SelfTest() {
const Cubic selfSet[] = {
{{0,2}, {2,3}, {5,1}, {3,2}},
{{0,2}, {3,5}, {5,0}, {4,2}},
{{3.34,8.98}, {1.95,10.27}, {3.76,7.65}, {4.96,10.64}},
{{3.13,2.74}, {1.08,4.62}, {3.71,0.94}, {2.01,3.81}},
{{6.71,3.14}, {7.99,2.75}, {8.27,1.96}, {6.35,3.57}},
{{12.81,7.27}, {7.22,6.98}, {12.49,8.97}, {11.42,6.18}},
};
size_t selfSetCount = sizeof(selfSet) / sizeof(selfSet[0]);
size_t firstFail = 1;
for (size_t index = firstFail; index < selfSetCount; ++index) {
const Cubic& cubic = selfSet[index];
#if ONE_OFF_DEBUG
int idx2;
double max[3];
int ts = find_cubic_max_curvature(cubic, max);
for (idx2 = 0; idx2 < ts; ++idx2) {
SkDebugf("%s max[%d]=%1.9g (%1.9g, %1.9g)\n", __FUNCTION__, idx2,
max[idx2], xy_at_t(cubic, max[idx2]).x, xy_at_t(cubic, max[idx2]).y);
}
SkTDArray<double> ts1;
SkTDArray<Quadratic> quads1;
cubic_to_quadratics(cubic, calcPrecision(cubic), ts1);
for (idx2 = 0; idx2 < ts1.count(); ++idx2) {
SkDebugf("%s t[%d]=%1.9g\n", __FUNCTION__, idx2, ts1[idx2]);
}
cubic_to_quadratics(cubic, calcPrecision(cubic), quads1);
for (idx2 = 0; idx2 < quads1.count(); ++idx2) {
const Quadratic& q = quads1[idx2];
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
q[0].x, q[0].y, q[1].x, q[1].y, q[2].x, q[2].y);
}
SkDebugf("\n");
#endif
Intersections i;
SkDEBUGCODE(int result = ) intersect(cubic, i);
SkASSERT(result == 1);
SkASSERT(i.used() == 1);
SkASSERT(!approximately_equal(i.fT[0][0], i.fT[1][0]));
_Point pt1 = xy_at_t(cubic, i.fT[0][0]);
_Point pt2 = xy_at_t(cubic, i.fT[1][0]);
SkASSERT(pt1.approximatelyEqual(pt2));
}
}
void CubicIntersection_Test() {
oneOffTests();
coincidentTest();
standardTestCases();
}