static void standardTestCases() {
size_t index;
Quadratic reduce;
int order;
enum {
RunAll,
RunQuadraticLines,
RunQuadraticModLines,
RunNone
} run = RunAll;
int firstTestIndex = 0;
#if 0
run = RunQuadraticLines;
firstTestIndex = 1;
#endif
int firstQuadraticLineTest = run == RunAll ? 0 : run == RunQuadraticLines ? firstTestIndex : SK_MaxS32;
int firstQuadraticModLineTest = run == RunAll ? 0 : run == RunQuadraticModLines ? firstTestIndex : SK_MaxS32;
for (index = firstQuadraticLineTest; index < quadraticLines_count; ++index) {
const Quadratic& quad = quadraticLines[index];
order = reduceOrder(quad, reduce, kReduceOrder_TreatAsFill);
if (order != 2) {
printf("[%d] line quad order=%d\n", (int) index, order);
}
}
for (index = firstQuadraticModLineTest; index < quadraticModEpsilonLines_count; ++index) {
const Quadratic& quad = quadraticModEpsilonLines[index];
order = reduceOrder(quad, reduce, kReduceOrder_TreatAsFill);
if (order != 3) {
printf("[%d] line mod quad order=%d\n", (int) index, order);
}
}
}
static int quadPart(const Cubic& cubic, double tStart, double tEnd, Quadratic& simple) {
Cubic part;
sub_divide(cubic, tStart, tEnd, part);
Quadratic quad;
demote_cubic_to_quad(part, quad);
// FIXME: should reduceOrder be looser in this use case if quartic is going to blow up on an
// extremely shallow quadratic?
int order = reduceOrder(quad, simple, kReduceOrder_TreatAsFill);
#if DEBUG_QUAD_PART
SkDebugf("%s cubic=(%1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g) t=(%1.17g,%1.17g)\n",
__FUNCTION__, cubic[0].x, cubic[0].y, cubic[1].x, cubic[1].y, cubic[2].x, cubic[2].y,
cubic[3].x, cubic[3].y, tStart, tEnd);
SkDebugf("%s part=(%1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g)"
" quad=(%1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g)\n", __FUNCTION__, part[0].x, part[0].y,
part[1].x, part[1].y, part[2].x, part[2].y, part[3].x, part[3].y, quad[0].x, quad[0].y,
quad[1].x, quad[1].y, quad[2].x, quad[2].y);
SkDebugf("%s simple=(%1.17g,%1.17g", __FUNCTION__, simple[0].x, simple[0].y);
if (order > 1) {
SkDebugf(" %1.17g,%1.17g", simple[1].x, simple[1].y);
}
if (order > 2) {
SkDebugf(" %1.17g,%1.17g", simple[2].x, simple[2].y);
}
SkDebugf(")\n");
SkASSERT(order < 4 && order > 0);
#endif
return order;
}
static void oneOffTest() {
SkDebugf("%s FLT_EPSILON=%1.9g\n", __FUNCTION__, FLT_EPSILON);
for (size_t index = 0; index < testSetCount; ++index) {
const Quadratic& quad = testSet[index];
Quadratic reduce;
SkDEBUGCODE(int result = ) reduceOrder(quad, reduce, kReduceOrder_TreatAsFill);
SkASSERT(result == 3);
}
}
void CubicIntersection_Test() {
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);
int order2 = reduceOrder(cubic2, reduce2, kReduceOrder_NoQuadraticsAllowed);
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 void standardTestCases() {
for (size_t index = firstQuadIntersectionTest; index < quadraticTests_count; ++index) {
const Quadratic& quad1 = quadraticTests[index][0];
const Quadratic& quad2 = quadraticTests[index][1];
Quadratic reduce1, reduce2;
int order1 = reduceOrder(quad1, reduce1);
int order2 = reduceOrder(quad2, reduce2);
if (order1 < 3) {
printf("[%d] quad1 order=%d\n", (int) index, order1);
}
if (order2 < 3) {
printf("[%d] quad2 order=%d\n", (int) index, order2);
}
if (order1 == 3 && order2 == 3) {
Intersections intersections, intersections2;
intersect(reduce1, reduce2, intersections);
intersect2(reduce1, reduce2, intersections2);
SkASSERT(intersections.used() == intersections2.used());
if (intersections.intersected()) {
for (int pt = 0; pt < intersections.used(); ++pt) {
double tt1 = intersections.fT[0][pt];
double tx1, ty1;
xy_at_t(quad1, tt1, tx1, ty1);
double tt2 = intersections.fT[1][pt];
double tx2, ty2;
xy_at_t(quad2, tt2, tx2, ty2);
if (!approximately_equal(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 (!approximately_equal(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);
}
tt1 = intersections2.fT[0][pt];
SkASSERT(approximately_equal(intersections.fT[0][pt], tt1));
tt2 = intersections2.fT[1][pt];
SkASSERT(approximately_equal(intersections.fT[1][pt], tt2));
}
}
}
}
}
static void standardTestCases() {
for (size_t index = 0; index < quadraticTests_count; ++index) {
const Quadratic& quad1 = quadraticTests[index][0];
const Quadratic& quad2 = quadraticTests[index][1];
Quadratic reduce1, reduce2;
int order1 = reduceOrder(quad1, reduce1);
int order2 = reduceOrder(quad2, reduce2);
if (order1 < 3) {
printf("%s [%d] quad1 order=%d\n", __FUNCTION__, (int)index, order1);
}
if (order2 < 3) {
printf("%s [%d] quad2 order=%d\n", __FUNCTION__, (int)index, order2);
}
if (order1 == 3 && order2 == 3) {
double minT = 0;
double maxT = 1;
bezier_clip(reduce1, reduce2, minT, maxT);
}
}
}
void CubicBezierClip_Test() {
for (size_t index = 0; 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) {
SkDebugf("%s [%d] cubic1 order=%d\n", __FUNCTION__, (int) index, order1);
}
if (order2 < 4) {
SkDebugf("%s [%d] cubic2 order=%d\n", __FUNCTION__, (int) index, order2);
}
if (order1 == 4 && order2 == 4) {
double minT = 0;
double maxT = 1;
bezier_clip(reduce1, reduce2, minT, maxT);
}
}
}
void LineCubicIntersection_Test() {
for (size_t index = firstLineCubicIntersectionTest; index < lineCubicTests_count; ++index) {
const Cubic& cubic = lineCubicTests[index].cubic;
const _Line& line = lineCubicTests[index].line;
Cubic reduce1;
_Line reduce2;
int order1 = reduceOrder(cubic, reduce1, kReduceOrder_NoQuadraticsAllowed);
int order2 = reduceOrder(line, reduce2);
if (order1 < 4) {
printf("[%d] cubic order=%d\n", (int) index, order1);
}
if (order2 < 2) {
printf("[%d] line order=%d\n", (int) index, order2);
}
if (order1 == 4 && order2 == 2) {
double range1[2], range2[2];
int roots = intersect(reduce1, reduce2, range1, range2);
for (int pt = 0; pt < roots; ++pt) {
double tt1 = range1[pt];
double tx1, ty1;
xy_at_t(cubic, tt1, tx1, ty1);
double tt2 = range2[pt];
double tx2, ty2;
xy_at_t(line, tt2, tx2, ty2);
if (!approximately_equal(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 (!approximately_equal(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);
}
}
}
}
}
bool intersect(double minT1, double maxT1, double minT2, double maxT2) {
Quadratic smaller, larger;
// FIXME: carry last subdivide and reduceOrder result with quad
sub_divide(quad1, minT1, maxT1, intersections.swapped() ? larger : smaller);
sub_divide(quad2, minT2, maxT2, intersections.swapped() ? smaller : larger);
Quadratic smallResult;
if (reduceOrder(smaller, smallResult) <= 2) {
Quadratic largeResult;
if (reduceOrder(larger, largeResult) <= 2) {
double smallT[2], largeT[2];
const _Line& smallLine = (const _Line&) smallResult;
const _Line& largeLine = (const _Line&) largeResult;
// FIXME: this doesn't detect or deal with coincident lines
if (!::intersect(smallLine, largeLine, smallT, largeT)) {
return false;
}
if (intersections.swapped()) {
smallT[0] = interp(minT2, maxT2, smallT[0]);
largeT[0] = interp(minT1, maxT1, largeT[0]);
} else {
smallT[0] = interp(minT1, maxT1, smallT[0]);
largeT[0] = interp(minT2, maxT2, largeT[0]);
}
intersections.add(smallT[0], largeT[0]);
return true;
}
}
double minT, maxT;
if (!bezier_clip(smaller, larger, minT, maxT)) {
if (minT == maxT) {
if (intersections.swapped()) {
minT1 = (minT1 + maxT1) / 2;
minT2 = interp(minT2, maxT2, minT);
} else {
minT1 = interp(minT1, maxT1, minT);
minT2 = (minT2 + maxT2) / 2;
}
intersections.add(minT1, minT2);
return true;
}
return false;
}
int split;
if (intersections.swapped()) {
double newMinT1 = interp(minT1, maxT1, minT);
double newMaxT1 = interp(minT1, maxT1, maxT);
split = (newMaxT1 - newMinT1 > (maxT1 - minT1) * tClipLimit) << 1;
#define VERBOSE 0
#if VERBOSE
printf("%s d=%d s=%d new1=(%g,%g) old1=(%g,%g) split=%d\n", __FUNCTION__, depth,
splits, newMinT1, newMaxT1, minT1, maxT1, split);
#endif
minT1 = newMinT1;
maxT1 = newMaxT1;
} else {
double newMinT2 = interp(minT2, maxT2, minT);
double newMaxT2 = interp(minT2, maxT2, maxT);
split = newMaxT2 - newMinT2 > (maxT2 - minT2) * tClipLimit;
#define VERBOSE 0
#if VERBOSE
printf("%s d=%d s=%d new2=(%g,%g) old2=(%g,%g) split=%d\n", __FUNCTION__, depth,
splits, newMinT2, newMaxT2, minT2, maxT2, split);
#endif
minT2 = newMinT2;
maxT2 = newMaxT2;
}
return chop(minT1, maxT1, minT2, maxT2, split);
}
// this flavor approximates the cubics with quads to find the intersecting ts
// OPTIMIZE: if this strategy proves successful, the quad approximations, or the ts used
// to create the approximations, could be stored in the cubic segment
// FIXME: this strategy needs to intersect the convex hull on either end with the opposite to
// account for inset quadratics that cause the endpoint intersection to avoid detection
// the segments can be very short -- the length of the maximum quadratic error (precision)
// FIXME: this needs to recurse on itself, taking a range of T values and computing the new
// t range ala is linear inner. The range can be figured by taking the dx/dy and determining
// the fraction that matches the precision. That fraction is the change in t for the smaller cubic.
static bool intersect2(const Cubic& cubic1, double t1s, double t1e, const Cubic& cubic2,
double t2s, double t2e, double precisionScale, Intersections& i) {
Cubic c1, c2;
sub_divide(cubic1, t1s, t1e, c1);
sub_divide(cubic2, t2s, t2e, c2);
SkTDArray<double> ts1;
cubic_to_quadratics(c1, calcPrecision(c1) * precisionScale, ts1);
SkTDArray<double> ts2;
cubic_to_quadratics(c2, calcPrecision(c2) * precisionScale, ts2);
double t1Start = t1s;
int ts1Count = ts1.count();
for (int i1 = 0; i1 <= ts1Count; ++i1) {
const double tEnd1 = i1 < ts1Count ? ts1[i1] : 1;
const double t1 = t1s + (t1e - t1s) * tEnd1;
Cubic part1;
sub_divide(cubic1, t1Start, t1, part1);
Quadratic q1;
demote_cubic_to_quad(part1, q1);
// start here;
// should reduceOrder be looser in this use case if quartic is going to blow up on an
// extremely shallow quadratic?
Quadratic s1;
int o1 = reduceOrder(q1, s1);
double t2Start = t2s;
int ts2Count = ts2.count();
for (int i2 = 0; i2 <= ts2Count; ++i2) {
const double tEnd2 = i2 < ts2Count ? ts2[i2] : 1;
const double t2 = t2s + (t2e - t2s) * tEnd2;
Cubic part2;
sub_divide(cubic2, t2Start, t2, part2);
Quadratic q2;
demote_cubic_to_quad(part2, q2);
Quadratic s2;
double o2 = reduceOrder(q2, s2);
Intersections locals;
if (o1 == 3 && o2 == 3) {
intersect2(q1, q2, locals);
} else if (o1 <= 2 && o2 <= 2) {
locals.fUsed = intersect((const _Line&) s1, (const _Line&) s2, locals.fT[0],
locals.fT[1]);
} else if (o1 == 3 && o2 <= 2) {
intersect(q1, (const _Line&) s2, locals);
} else {
SkASSERT(o1 <= 2 && o2 == 3);
intersect(q2, (const _Line&) s1, locals);
for (int s = 0; s < locals.fUsed; ++s) {
SkTSwap(locals.fT[0][s], locals.fT[1][s]);
}
}
for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
double to1 = t1Start + (t1 - t1Start) * locals.fT[0][tIdx];
double to2 = t2Start + (t2 - t2Start) * locals.fT[1][tIdx];
// if the computed t is not sufficiently precise, iterate
_Point p1, p2;
xy_at_t(cubic1, to1, p1.x, p1.y);
xy_at_t(cubic2, to2, p2.x, p2.y);
if (p1.approximatelyEqual(p2)) {
i.insert(i.swapped() ? to2 : to1, i.swapped() ? to1 : to2);
} else {
double dt1, dt2;
computeDelta(cubic1, to1, (t1e - t1s), cubic2, to2, (t2e - t2s), dt1, dt2);
double scale = precisionScale;
if (dt1 > 0.125 || dt2 > 0.125) {
scale /= 2;
SkDebugf("%s scale=%1.9g\n", __FUNCTION__, scale);
}
#if SK_DEBUG
++debugDepth;
assert(debugDepth < 10);
#endif
i.swap();
intersect2(cubic2, SkTMax(to2 - dt2, 0.), SkTMin(to2 + dt2, 1.),
cubic1, SkTMax(to1 - dt1, 0.), SkTMin(to1 + dt1, 1.), scale, i);
i.swap();
#if SK_DEBUG
--debugDepth;
#endif
}
}
t2Start = t2;
}
t1Start = t1;
}
return i.intersected();
}
void CubicReduceOrder_Test() {
size_t index;
Cubic reduce;
int order;
enum {
RunAll,
RunPointDegenerates,
RunNotPointDegenerates,
RunLines,
RunNotLines,
RunModEpsilonLines,
RunLessEpsilonLines,
RunNegEpsilonLines,
RunQuadraticLines,
RunQuadraticModLines,
RunComputedLines,
RunNone
} run = RunAll;
int firstTestIndex = 0;
#if 0
run = RunComputedLines;
firstTestIndex = 18;
#endif
int firstPointDegeneratesTest = run == RunAll ? 0 : run == RunPointDegenerates ? firstTestIndex : SK_MaxS32;
int firstNotPointDegeneratesTest = run == RunAll ? 0 : run == RunNotPointDegenerates ? firstTestIndex : SK_MaxS32;
int firstLinesTest = run == RunAll ? 0 : run == RunLines ? firstTestIndex : SK_MaxS32;
int firstNotLinesTest = run == RunAll ? 0 : run == RunNotLines ? firstTestIndex : SK_MaxS32;
int firstModEpsilonTest = run == RunAll ? 0 : run == RunModEpsilonLines ? firstTestIndex : SK_MaxS32;
int firstLessEpsilonTest = run == RunAll ? 0 : run == RunLessEpsilonLines ? firstTestIndex : SK_MaxS32;
int firstNegEpsilonTest = run == RunAll ? 0 : run == RunNegEpsilonLines ? firstTestIndex : SK_MaxS32;
int firstQuadraticLineTest = run == RunAll ? 0 : run == RunQuadraticLines ? firstTestIndex : SK_MaxS32;
int firstQuadraticModLineTest = run == RunAll ? 0 : run == RunQuadraticModLines ? firstTestIndex : SK_MaxS32;
int firstComputedLinesTest = run == RunAll ? 0 : run == RunComputedLines ? firstTestIndex : SK_MaxS32;
for (index = firstPointDegeneratesTest; index < pointDegenerates_count; ++index) {
const Cubic& cubic = pointDegenerates[index];
order = reduceOrder(cubic, reduce, kReduceOrder_QuadraticsAllowed,
kReduceOrder_TreatAsFill);
if (order != 1) {
SkDebugf("[%d] pointDegenerates order=%d\n", (int) index, order);
}
}
for (index = firstNotPointDegeneratesTest; index < notPointDegenerates_count; ++index) {
const Cubic& cubic = notPointDegenerates[index];
order = reduceOrder(cubic, reduce, kReduceOrder_QuadraticsAllowed,
kReduceOrder_TreatAsFill);
if (order == 1) {
SkDebugf("[%d] notPointDegenerates order=%d\n", (int) index, order);
}
}
for (index = firstLinesTest; index < lines_count; ++index) {
const Cubic& cubic = lines[index];
order = reduceOrder(cubic, reduce, kReduceOrder_QuadraticsAllowed,
kReduceOrder_TreatAsFill);
if (order != 2) {
SkDebugf("[%d] lines order=%d\n", (int) index, order);
}
}
for (index = firstNotLinesTest; index < notLines_count; ++index) {
const Cubic& cubic = notLines[index];
order = reduceOrder(cubic, reduce, kReduceOrder_QuadraticsAllowed,
kReduceOrder_TreatAsFill);
if (order == 2) {
SkDebugf("[%d] notLines order=%d\n", (int) index, order);
}
}
for (index = firstModEpsilonTest; index < modEpsilonLines_count; ++index) {
const Cubic& cubic = modEpsilonLines[index];
order = reduceOrder(cubic, reduce, kReduceOrder_QuadraticsAllowed,
kReduceOrder_TreatAsFill);
if (order == 2) {
SkDebugf("[%d] line mod by epsilon order=%d\n", (int) index, order);
}
}
for (index = firstLessEpsilonTest; index < lessEpsilonLines_count; ++index) {
const Cubic& cubic = lessEpsilonLines[index];
order = reduceOrder(cubic, reduce, kReduceOrder_QuadraticsAllowed,
kReduceOrder_TreatAsFill);
if (order != 2) {
SkDebugf("[%d] line less by epsilon/2 order=%d\n", (int) index, order);
}
}
for (index = firstNegEpsilonTest; index < negEpsilonLines_count; ++index) {
const Cubic& cubic = negEpsilonLines[index];
order = reduceOrder(cubic, reduce, kReduceOrder_QuadraticsAllowed,
kReduceOrder_TreatAsFill);
if (order != 2) {
SkDebugf("[%d] line neg by epsilon/2 order=%d\n", (int) index, order);
}
}
for (index = firstQuadraticLineTest; index < quadraticLines_count; ++index) {
const Quadratic& quad = quadraticLines[index];
Cubic cubic;
quad_to_cubic(quad, cubic);
order = reduceOrder(cubic, reduce, kReduceOrder_QuadraticsAllowed,
kReduceOrder_TreatAsFill);
if (order != 2) {
SkDebugf("[%d] line quad order=%d\n", (int) index, order);
}
}
for (index = firstQuadraticModLineTest; index < quadraticModEpsilonLines_count; ++index) {
const Quadratic& quad = quadraticModEpsilonLines[index];
Cubic cubic;
quad_to_cubic(quad, cubic);
order = reduceOrder(cubic, reduce, kReduceOrder_QuadraticsAllowed,
kReduceOrder_TreatAsFill);
if (order != 3) {
SkDebugf("[%d] line mod quad order=%d\n", (int) index, order);
}
}
// test if computed line end points are valid
for (index = firstComputedLinesTest; index < lines_count; ++index) {
const Cubic& cubic = lines[index];
bool controlsInside = controls_inside(cubic);
order = reduceOrder(cubic, reduce, kReduceOrder_QuadraticsAllowed,
kReduceOrder_TreatAsFill);
if (reduce[0].x == reduce[1].x && reduce[0].y == reduce[1].y) {
SkDebugf("[%d] line computed ends match order=%d\n", (int) index, order);
}
if (controlsInside) {
if ( (reduce[0].x != cubic[0].x && reduce[0].x != cubic[3].x)
|| (reduce[0].y != cubic[0].y && reduce[0].y != cubic[3].y)
|| (reduce[1].x != cubic[0].x && reduce[1].x != cubic[3].x)
|| (reduce[1].y != cubic[0].y && reduce[1].y != cubic[3].y)) {
SkDebugf("[%d] line computed ends order=%d\n", (int) index, order);
}
} else {
// binary search for extrema, compare against actual results
// while a control point is outside of bounding box formed by end points, split
_Rect bounds = {DBL_MAX, DBL_MAX, -DBL_MAX, -DBL_MAX};
find_tight_bounds(cubic, bounds);
if ( (!AlmostEqualUlps(reduce[0].x, bounds.left) && !AlmostEqualUlps(reduce[0].x, bounds.right))
|| (!AlmostEqualUlps(reduce[0].y, bounds.top) && !AlmostEqualUlps(reduce[0].y, bounds.bottom))
|| (!AlmostEqualUlps(reduce[1].x, bounds.left) && !AlmostEqualUlps(reduce[1].x, bounds.right))
|| (!AlmostEqualUlps(reduce[1].y, bounds.top) && !AlmostEqualUlps(reduce[1].y, bounds.bottom))) {
SkDebugf("[%d] line computed tight bounds order=%d\n", (int) index, order);
}
}
}
}
