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/*
* Copyright 2013 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "PathOpsTestCommon.h"
#include "SkIntersections.h"
#include "SkOpContour.h"
#include "SkOpSegment.h"
#include "SkRandom.h"
#include "SkTSort.h"
#include "Test.h"
static bool gDisableAngleTests = true;
static float next(float f)
{
int fBits = SkFloatAs2sCompliment(f);
++fBits;
float fNext = Sk2sComplimentAsFloat(fBits);
return fNext;
}
static float prev(float f)
{
int fBits = SkFloatAs2sCompliment(f);
--fBits;
float fNext = Sk2sComplimentAsFloat(fBits);
return fNext;
}
DEF_TEST(PathOpsAngleFindCrossEpsilon, reporter) {
if (gDisableAngleTests) {
return;
}
SkRandom ran;
int maxEpsilon = 0;
for (int index = 0; index < 10000000; ++index) {
SkDLine line = {{{0, 0}, {ran.nextRangeF(0.0001f, 1000), ran.nextRangeF(0.0001f, 1000)}}};
for (int inner = 0; inner < 10; ++inner) {
float t = ran.nextRangeF(0.0001f, 1);
SkDPoint dPt = line.ptAtT(t);
SkPoint pt = dPt.asSkPoint();
float xs[3] = { prev(pt.fX), pt.fX, next(pt.fX) };
float ys[3] = { prev(pt.fY), pt.fY, next(pt.fY) };
for (int xIdx = 0; xIdx < 3; ++xIdx) {
for (int yIdx = 0; yIdx < 3; ++yIdx) {
SkPoint test = { xs[xIdx], ys[yIdx] };
float p1 = SkDoubleToScalar(line[1].fX * test.fY);
float p2 = SkDoubleToScalar(line[1].fY * test.fX);
int p1Bits = SkFloatAs2sCompliment(p1);
int p2Bits = SkFloatAs2sCompliment(p2);
int epsilon = abs(p1Bits - p2Bits);
if (maxEpsilon < epsilon) {
SkDebugf("line={{0, 0}, {%1.7g, %1.7g}} t=%1.7g pt={%1.7g, %1.7g}"
" epsilon=%d\n",
line[1].fX, line[1].fY, t, test.fX, test.fY, epsilon);
maxEpsilon = epsilon;
}
}
}
}
}
}
DEF_TEST(PathOpsAngleFindQuadEpsilon, reporter) {
if (gDisableAngleTests) {
return;
}
SkRandom ran;
int maxEpsilon = 0;
double maxAngle = 0;
for (int index = 0; index < 100000; ++index) {
SkDLine line = {{{0, 0}, {ran.nextRangeF(0.0001f, 1000), ran.nextRangeF(0.0001f, 1000)}}};
float t = ran.nextRangeF(0.0001f, 1);
SkDPoint dPt = line.ptAtT(t);
float t2 = ran.nextRangeF(0.0001f, 1);
SkDPoint qPt = line.ptAtT(t2);
float t3 = ran.nextRangeF(0.0001f, 1);
SkDPoint qPt2 = line.ptAtT(t3);
qPt.fX += qPt2.fY;
qPt.fY -= qPt2.fX;
SkDQuad quad = {{line[0], dPt, qPt}};
// binary search for maximum movement of quad[1] towards test that still has 1 intersection
double moveT = 0.5f;
double deltaT = moveT / 2;
SkDPoint last;
do {
last = quad[1];
quad[1].fX = dPt.fX - line[1].fY * moveT;
quad[1].fY = dPt.fY + line[1].fX * moveT;
SkIntersections i;
i.intersect(quad, line);
REPORTER_ASSERT(reporter, i.used() > 0);
if (i.used() == 1) {
moveT += deltaT;
} else {
moveT -= deltaT;
}
deltaT /= 2;
} while (last.asSkPoint() != quad[1].asSkPoint());
float p1 = SkDoubleToScalar(line[1].fX * last.fY);
float p2 = SkDoubleToScalar(line[1].fY * last.fX);
int p1Bits = SkFloatAs2sCompliment(p1);
int p2Bits = SkFloatAs2sCompliment(p2);
int epsilon = abs(p1Bits - p2Bits);
if (maxEpsilon < epsilon) {
SkDebugf("line={{0, 0}, {%1.7g, %1.7g}} t=%1.7g/%1.7g/%1.7g moveT=%1.7g"
" pt={%1.7g, %1.7g} epsilon=%d\n",
line[1].fX, line[1].fY, t, t2, t3, moveT, last.fX, last.fY, epsilon);
maxEpsilon = epsilon;
}
double a1 = atan2(line[1].fY, line[1].fX);
double a2 = atan2(last.fY, last.fX);
double angle = fabs(a1 - a2);
if (maxAngle < angle) {
SkDebugf("line={{0, 0}, {%1.7g, %1.7g}} t=%1.7g/%1.7g/%1.7g moveT=%1.7g"
" pt={%1.7g, %1.7g} angle=%1.7g\n",
line[1].fX, line[1].fY, t, t2, t3, moveT, last.fX, last.fY, angle);
maxAngle = angle;
}
}
}
static int find_slop(double x, double y, double rx, double ry) {
int slopBits = 0;
bool less1, less2;
double absX = fabs(x);
double absY = fabs(y);
double length = absX < absY ? absX / 2 + absY : absX + absY / 2;
int exponent;
(void) frexp(length, &exponent);
double epsilon = ldexp(FLT_EPSILON, exponent);
do {
// get the length as the larger plus half the smaller (both same signs)
// find the ulps of the length
// compute the offsets from there
double xSlop = epsilon * slopBits;
double ySlop = x * y < 0 ? -xSlop : xSlop; // OPTIMIZATION: use copysign / _copysign ?
double x1 = x - xSlop;
double y1 = y + ySlop;
double x_ry1 = x1 * ry;
double rx_y1 = rx * y1;
less1 = x_ry1 < rx_y1;
double x2 = x + xSlop;
double y2 = y - ySlop;
double x_ry2 = x2 * ry;
double rx_y2 = rx * y2;
less2 = x_ry2 < rx_y2;
} while (less1 == less2 && ++slopBits);
return slopBits;
}
// from http://stackoverflow.com/questions/1427422/cheap-algorithm-to-find-measure-of-angle-between-vectors
static double diamond_angle(double y, double x)
{
if (y >= 0)
return (x >= 0 ? y/(x+y) : 1-x/(-x+y));
else
return (x < 0 ? 2-y/(-x-y) : 3+x/(x-y));
}
static const double slopTests[][4] = {
// x y rx ry
{-0.058554756452593892, -0.18804585843827226, -0.018568569646021160, -0.059615294434479438},
{-0.0013717412948608398, 0.0041152238845825195, -0.00045837944195925573, 0.0013753175735478074},
{-2.1033774145221198, -1.4046019261273715e-008, -0.70062688352066704, -1.2706324683777995e-008},
};
DEF_TEST(PathOpsAngleFindSlop, reporter) {
if (gDisableAngleTests) {
return;
}
for (int index = 0; index < (int) SK_ARRAY_COUNT(slopTests); ++index) {
const double* slopTest = slopTests[index];
double x = slopTest[0];
double y = slopTest[1];
double rx = slopTest[2];
double ry = slopTest[3];
SkDebugf("%s xy %d=%d\n", __FUNCTION__, index, find_slop(x, y, rx, ry));
SkDebugf("%s rxy %d=%d\n", __FUNCTION__, index, find_slop(rx, ry, x, y));
double angle = diamond_angle(y, x);
double rAngle = diamond_angle(ry, rx);
double diff = fabs(angle - rAngle);
SkDebugf("%s diamond xy=%1.9g rxy=%1.9g diff=%1.9g factor=%d\n", __FUNCTION__,
angle, rAngle, diff, (int) (diff / FLT_EPSILON));
}
}
class PathOpsAngleTester {
public:
static int After(SkOpAngle& lh, SkOpAngle& rh) {
return lh.after(&rh);
}
static int ConvexHullOverlaps(SkOpAngle& lh, SkOpAngle& rh) {
return lh.convexHullOverlaps(&rh);
}
static int Orderable(SkOpAngle& lh, SkOpAngle& rh) {
return lh.orderable(&rh);
}
static int EndsIntersect(SkOpAngle& lh, SkOpAngle& rh) {
return lh.endsIntersect(&rh);
}
static void SetNext(SkOpAngle& lh, SkOpAngle& rh) {
lh.fNext = &rh;
}
};
class PathOpsSegmentTester {
public:
static void DebugReset(SkOpSegment* segment) {
segment->debugReset();
}
};
struct CircleData {
const SkDCubic fPts;
const int fPtCount;
SkPoint fShortPts[4];
};
static CircleData circleDataSet[] = {
{ {{{313.0155029296875, 207.90290832519531}, {320.05078125, 227.58743286132812}}}, 2, {} },
{ {{{313.0155029296875, 207.90290832519531}, {313.98246891063195, 219.33615203830394},
{320.05078125, 227.58743286132812}}}, 3, {} },
};
static const int circleDataSetSize = (int) SK_ARRAY_COUNT(circleDataSet);
DEF_TEST(PathOpsAngleCircle, reporter) {
SkChunkAlloc allocator(4096);
SkOpContour contour;
SkOpGlobalState state(NULL SkDEBUGPARAMS(&contour));
contour.init(&state, false, false);
for (int index = 0; index < circleDataSetSize; ++index) {
CircleData& data = circleDataSet[index];
for (int idx2 = 0; idx2 < data.fPtCount; ++idx2) {
data.fShortPts[idx2] = data.fPts.fPts[idx2].asSkPoint();
}
switch (data.fPtCount) {
case 2:
contour.addLine(data.fShortPts, &allocator);
break;
case 3:
contour.addQuad(data.fShortPts, &allocator);
break;
case 4:
contour.addCubic(data.fShortPts, &allocator);
break;
}
}
SkOpSegment* first = contour.first();
first->debugAddAngle(0, 1, &allocator);
SkOpSegment* next = first->next();
next->debugAddAngle(0, 1, &allocator);
PathOpsAngleTester::Orderable(*first->debugLastAngle(), *next->debugLastAngle());
}
struct IntersectData {
const SkDCubic fPts;
const int fPtCount;
double fTStart;
double fTEnd;
SkPoint fShortPts[4];
};
static IntersectData intersectDataSet1[] = {
{ {{{322.935669,231.030273}, {312.832214,220.393295}, {312.832214,203.454178}}}, 3,
0.865309956, 0.154740299, {} },
{ {{{322.12738,233.397751}, {295.718353,159.505829}}}, 2,
0.345028807, 0.0786326511, {} },
{ {{{322.935669,231.030273}, {312.832214,220.393295}, {312.832214,203.454178}}}, 3,
0.865309956, 1, {} },
{ {{{322.12738,233.397751}, {295.718353,159.505829}}}, 2,
0.345028807, 1, {} },
};
static IntersectData intersectDataSet2[] = {
{ {{{364.390686,157.898193}, {375.281769,136.674606}, {396.039917,136.674606}}}, 3,
0.578520747, 1, {} },
{ {{{364.390686,157.898193}, {375.281769,136.674606}, {396.039917,136.674606}}}, 3,
0.578520747, 0.536512973, {} },
{ {{{366.608826,151.196014}, {378.803101,136.674606}, {398.164948,136.674606}}}, 3,
0.490456543, 1, {} },
};
static IntersectData intersectDataSet3[] = {
{ {{{2.000000,0.000000}, {1.33333333,0.66666667}}}, 2, 1, 0, {} },
{ {{{1.33333333,0.66666667}, {0.000000,2.000000}}}, 2, 0, 0.25, {} },
{ {{{2.000000,2.000000}, {1.33333333,0.66666667}}}, 2, 1, 0, {} },
};
static IntersectData intersectDataSet4[] = {
{ {{{1.3333333,0.6666667}, {0.000,2.000}}}, 2, 0.250000006, 0, {} },
{ {{{1.000,0.000}, {1.000,1.000}}}, 2, 1, 0, {} },
{ {{{1.000,1.000}, {0.000,0.000}}}, 2, 0, 1, {} },
};
static IntersectData intersectDataSet5[] = {
{ {{{0.000,0.000}, {1.000,0.000}, {1.000,1.000}}}, 3, 1, 0.666666667, {} },
{ {{{0.000,0.000}, {2.000,1.000}, {0.000,2.000}}}, 3, 0.5, 1, {} },
{ {{{0.000,0.000}, {2.000,1.000}, {0.000,2.000}}}, 3, 0.5, 0, {} },
};
static IntersectData intersectDataSet6[] = { // pathops_visualizer.htm:3658
{ {{{0.000,1.000}, {3.000,4.000}, {1.000,0.000}, {3.000,0.000}}}, 4, 0.0925339054, 0, {} }, // pathops_visualizer.htm:3616
{ {{{0.000,1.000}, {0.000,3.000}, {1.000,0.000}, {4.000,3.000}}}, 4, 0.453872386, 0, {} }, // pathops_visualizer.htm:3616
{ {{{0.000,1.000}, {3.000,4.000}, {1.000,0.000}, {3.000,0.000}}}, 4, 0.0925339054, 0.417096368, {} }, // pathops_visualizer.htm:3616
};
static IntersectData intersectDataSet7[] = { // pathops_visualizer.htm:3748
{ {{{2.000,1.000}, {0.000,1.000}}}, 2, 0.5, 0, {} }, // pathops_visualizer.htm:3706
{ {{{2.000,0.000}, {0.000,2.000}}}, 2, 0.5, 1, {} }, // pathops_visualizer.htm:3706
{ {{{0.000,1.000}, {0.000,2.000}, {2.000,0.000}, {2.000,1.000}}}, 4, 0.5, 1, {} }, // pathops_visualizer.htm:3706
}; //
static IntersectData intersectDataSet8[] = { // pathops_visualizer.htm:4194
{ {{{0.000,1.000}, {2.000,3.000}, {5.000,1.000}, {4.000,3.000}}}, 4, 0.311007457, 0.285714286, {} }, // pathops_visualizer.htm:4152
{ {{{1.000,5.000}, {3.000,4.000}, {1.000,0.000}, {3.000,2.000}}}, 4, 0.589885081, 0.999982974, {} }, // pathops_visualizer.htm:4152
{ {{{1.000,5.000}, {3.000,4.000}, {1.000,0.000}, {3.000,2.000}}}, 4, 0.589885081, 0.576935809, {} }, // pathops_visualizer.htm:4152
}; //
static IntersectData intersectDataSet9[] = { // pathops_visualizer.htm:4142
{ {{{0.000,1.000}, {2.000,3.000}, {5.000,1.000}, {4.000,3.000}}}, 4, 0.476627072, 0.311007457, {} }, // pathops_visualizer.htm:4100
{ {{{1.000,5.000}, {3.000,4.000}, {1.000,0.000}, {3.000,2.000}}}, 4, 0.999982974, 1, {} }, // pathops_visualizer.htm:4100
{ {{{0.000,1.000}, {2.000,3.000}, {5.000,1.000}, {4.000,3.000}}}, 4, 0.476627072, 1, {} }, // pathops_visualizer.htm:4100
}; //
static IntersectData intersectDataSet10[] = { // pathops_visualizer.htm:4186
{ {{{0.000,1.000}, {1.000,6.000}, {1.000,0.000}, {1.000,0.000}}}, 4, 0.788195121, 0.726275769, {} }, // pathops_visualizer.htm:4144
{ {{{0.000,1.000}, {0.000,1.000}, {1.000,0.000}, {6.000,1.000}}}, 4, 0.473378977, 1, {} }, // pathops_visualizer.htm:4144
{ {{{0.000,1.000}, {1.000,6.000}, {1.000,0.000}, {1.000,0.000}}}, 4, 0.788195121, 1, {} }, // pathops_visualizer.htm:4144
}; //
static IntersectData intersectDataSet11[] = { // pathops_visualizer.htm:4704
{ {{{979.305,561.000}, {1036.695,291.000}}}, 2, 0.888888874, 0.11111108, {} }, // pathops_visualizer.htm:4662
{ {{{1006.695,291.000}, {1023.264,291.000}, {1033.840,304.431}, {1030.318,321.000}}}, 4, 1, 0, {} }, // pathops_visualizer.htm:4662
{ {{{979.305,561.000}, {1036.695,291.000}}}, 2, 0.888888874, 1, {} }, // pathops_visualizer.htm:4662
}; //
static IntersectData intersectDataSet12[] = { // pathops_visualizer.htm:5481
{ {{{67.000,912.000}, {67.000,913.000}}}, 2, 1, 0, {} }, // pathops_visualizer.htm:5439
{ {{{67.000,913.000}, {67.000,917.389}, {67.224,921.726}, {67.662,926.000}}}, 4, 0, 1, {} }, // pathops_visualizer.htm:5439
{ {{{194.000,1041.000}, {123.860,1041.000}, {67.000,983.692}, {67.000,913.000}}}, 4, 1, 0, {} }, // pathops_visualizer.htm:5439
}; //
static IntersectData intersectDataSet13[] = { // pathops_visualizer.htm:5735
{ {{{6.000,0.000}, {0.000,4.000}}}, 2, 0.625, 0.25, {} }, // pathops_visualizer.htm:5693
{ {{{0.000,1.000}, {0.000,6.000}, {4.000,0.000}, {6.000,1.000}}}, 4, 0.5, 0.833333333, {} }, // pathops_visualizer.htm:5693
{ {{{0.000,1.000}, {0.000,6.000}, {4.000,0.000}, {6.000,1.000}}}, 4, 0.5, 0.379043969, {} }, // pathops_visualizer.htm:5693
}; //
static IntersectData intersectDataSet14[] = { // pathops_visualizer.htm:5875
{ {{{0.000,1.000}, {4.000,6.000}, {2.000,1.000}, {2.000,0.000}}}, 4, 0.0756502183, 0.0594570973, {} }, // pathops_visualizer.htm:5833
{ {{{1.000,2.000}, {0.000,2.000}, {1.000,0.000}, {6.000,4.000}}}, 4, 0.0756502184, 0, {} }, // pathops_visualizer.htm:5833
{ {{{0.000,1.000}, {4.000,6.000}, {2.000,1.000}, {2.000,0.000}}}, 4, 0.0756502183, 0.531917258, {} }, // pathops_visualizer.htm:5833
}; //
static IntersectData intersectDataSet15[] = { // pathops_visualizer.htm:6580
{ {{{490.435,879.407}, {405.593,909.436}}}, 2, 0.500554405, 1, {} }, // pathops_visualizer.htm:6538
{ {{{447.967,894.438}, {448.007,894.424}, {448.014,894.422}}}, 3, 0, 1, {} }, // pathops_visualizer.htm:6538
{ {{{490.435,879.407}, {405.593,909.436}}}, 2, 0.500554405, 0.500000273, {} }, // pathops_visualizer.htm:6538
}; //
static IntersectData intersectDataSet16[] = { // pathops_visualizer.htm:7419
{ {{{1.000,4.000}, {4.000,5.000}, {3.000,2.000}, {6.000,3.000}}}, 4, 0.5, 0, {} }, // pathops_visualizer.htm:7377
{ {{{2.000,3.000}, {3.000,6.000}, {4.000,1.000}, {5.000,4.000}}}, 4, 0.5, 0.112701665, {} }, // pathops_visualizer.htm:7377
{ {{{5.000,4.000}, {2.000,3.000}}}, 2, 0.5, 0, {} }, // pathops_visualizer.htm:7377
}; //
// from skpi_gino_com_16
static IntersectData intersectDataSet17[] = {
{ /*seg=7*/ {{{270.974121f, 770.025879f}, {234.948273f, 734}, {184, 734}}}
, 3, 0.74590454, 0.547660352, {} },
{ /*seg=8*/ {{{185, 734}, {252.93103f, 734}, {308, 789.06897f}, {308, 857}}}
, 4, 0.12052623, 0, {} },
{ /*seg=7*/ {{{270.974121f, 770.025879f}, {234.948273f, 734}, {184, 734}}}
, 3, 0.74590454, 1, {} },
};
static IntersectData intersectDataSet18[] = {
{ /*seg=7*/ {{{270.974121f, 770.025879f}, {234.948273f, 734}, {184, 734}}}
, 3, 0.74590454, 1, {} },
{ /*seg=8*/ {{{185, 734}, {252.93103f, 734}, {308, 789.06897f}, {308, 857}}}
, 4, 0.12052623, 0.217351928, {} },
{ /*seg=7*/ {{{270.974121f, 770.025879f}, {234.948273f, 734}, {184, 734}}}
, 3, 0.74590454, 0.547660352, {} },
};
static IntersectData intersectDataSet19[] = {
{ /*seg=1*/ {{{0, 1}, {3, 5}, {2, 1}, {3, 1}}}
, 4, 0.135148995, 0.134791946, {} },
{ /*seg=3*/ {{{1, 2}, {1, 2.15061641f}, {1, 2.21049166f}, {1.01366711f, 2.21379328f}}}
, 4, 0.956740456, 0.894913214, {} },
{ /*seg=1*/ {{{0, 1}, {3, 5}, {2, 1}, {3, 1}}}
, 4, 0.135148995, 0.551812363, {} },
};
#define I(x) intersectDataSet##x
static IntersectData* intersectDataSets[] = {
I(1), I(2), I(3), I(4), I(5), I(6), I(7), I(8), I(9), I(10),
I(11), I(12), I(13), I(14), I(15), I(16), I(17), I(18), I(19),
};
#undef I
#define I(x) (int) SK_ARRAY_COUNT(intersectDataSet##x)
static const int intersectDataSetSizes[] = {
I(1), I(2), I(3), I(4), I(5), I(6), I(7), I(8), I(9), I(10),
I(11), I(12), I(13), I(14), I(15), I(16), I(17), I(18), I(19),
};
#undef I
static const int intersectDataSetsSize = (int) SK_ARRAY_COUNT(intersectDataSetSizes);
struct FourPoints {
SkPoint pts[4];
};
DEF_TEST(PathOpsAngleAfter, reporter) {
SkChunkAlloc allocator(4096);
SkOpContour contour;
SkOpGlobalState state(NULL SkDEBUGPARAMS(&contour));
contour.init(&state, false, false);
for (int index = intersectDataSetsSize - 1; index >= 0; --index) {
IntersectData* dataArray = intersectDataSets[index];
const int dataSize = intersectDataSetSizes[index];
for (int index2 = 0; index2 < dataSize - 2; ++index2) {
allocator.reset();
contour.reset();
for (int index3 = 0; index3 < 3; ++index3) {
IntersectData& data = dataArray[index2 + index3];
SkPoint* temp = (SkPoint*) SkOpTAllocator<FourPoints>::Allocate(&allocator);
for (int idx2 = 0; idx2 < data.fPtCount; ++idx2) {
temp[idx2] = data.fPts.fPts[idx2].asSkPoint();
}
switch (data.fPtCount) {
case 2: {
contour.addLine(temp, &allocator);
} break;
case 3: {
contour.addQuad(temp, &allocator);
} break;
case 4: {
contour.addCubic(temp, &allocator);
} break;
}
}
SkOpSegment* seg1 = contour.first();
seg1->debugAddAngle(dataArray[index2 + 0].fTStart, dataArray[index2 + 0].fTEnd, &allocator);
SkOpSegment* seg2 = seg1->next();
seg2->debugAddAngle(dataArray[index2 + 1].fTStart, dataArray[index2 + 1].fTEnd, &allocator);
SkOpSegment* seg3 = seg2->next();
seg3->debugAddAngle(dataArray[index2 + 2].fTStart, dataArray[index2 + 2].fTEnd, &allocator);
SkOpAngle& angle1 = *seg1->debugLastAngle();
SkOpAngle& angle2 = *seg2->debugLastAngle();
SkOpAngle& angle3 = *seg3->debugLastAngle();
PathOpsAngleTester::SetNext(angle1, angle3);
// These data sets are seeded when the set itself fails, so likely the dataset does not
// match the expected result. The tests above return 1 when first added, but
// return 0 after the bug is fixed.
SkDEBUGCODE(int result =) PathOpsAngleTester::After(angle2, angle1);
SkASSERT(result == 0 || result == 1);
}
}
}
void SkOpSegment::debugAddAngle(double startT, double endT, SkChunkAlloc* allocator) {
SkOpPtT* startPtT = startT == 0 ? fHead.ptT() : startT == 1 ? fTail.ptT()
: this->addT(startT, kNoAlias, allocator);
SkOpPtT* endPtT = endT == 0 ? fHead.ptT() : endT == 1 ? fTail.ptT()
: this->addT(endT, kNoAlias, allocator);
SkOpAngle* angle = SkOpTAllocator<SkOpAngle>::Allocate(allocator);
SkOpSpanBase* startSpan = &fHead;
while (startSpan->ptT() != startPtT) {
startSpan = startSpan->upCast()->next();
}
SkOpSpanBase* endSpan = &fHead;
while (endSpan->ptT() != endPtT) {
endSpan = endSpan->upCast()->next();
}
angle->set(startSpan, endSpan);
if (startT < endT) {
startSpan->upCast()->setToAngle(angle);
endSpan->setFromAngle(angle);
} else {
endSpan->upCast()->setToAngle(angle);
startSpan->setFromAngle(angle);
}
}