blob: 922c1030d1f9bda5664ea51a95eba02cd5604f2a [file] [log] [blame]
/*
* 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 "SkIntersections.h"
#include "SkPathOpsCubic.h"
#include "SkPathOpsLine.h"
#include "SkPathOpsPoint.h"
#include "SkPathOpsQuad.h"
#include "SkPathOpsRect.h"
#include "SkReduceOrder.h"
#include "SkTDArray.h"
#include "SkTSort.h"
#if ONE_OFF_DEBUG
static const double tLimits1[2][2] = {{0.36, 0.37}, {0.63, 0.64}};
static const double tLimits2[2][2] = {{-0.865211397, -0.865215212}, {-0.865207696, -0.865208078}};
#endif
#define DEBUG_QUAD_PART 0
#define SWAP_TOP_DEBUG 0
static int quadPart(const SkDCubic& cubic, double tStart, double tEnd, SkReduceOrder* reducer) {
SkDCubic part = cubic.subDivide(tStart, tEnd);
SkDQuad quad = part.toQuad();
// FIXME: should reduceOrder be looser in this use case if quartic is going to blow up on an
// extremely shallow quadratic?
int order = reducer->reduce(quad, SkReduceOrder::kFill_Style);
#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].fX, cubic[0].fY,
cubic[1].fX, cubic[1].fY, cubic[2].fX, cubic[2].fY,
cubic[3].fX, cubic[3].fY, 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].fX, part[0].fY, part[1].fX, part[1].fY, part[2].fX, part[2].fY,
part[3].fX, part[3].fY, quad[0].fX, quad[0].fY,
quad[1].fX, quad[1].fY, quad[2].fX, quad[2].fY);
SkDebugf("%s simple=(%1.17g,%1.17g", __FUNCTION__, reducer->fQuad[0].fX, reducer->fQuad[0].fY);
if (order > 1) {
SkDebugf(" %1.17g,%1.17g", reducer->fQuad[1].fX, reducer->fQuad[1].fY);
}
if (order > 2) {
SkDebugf(" %1.17g,%1.17g", reducer->fQuad[2].fX, reducer->fQuad[2].fY);
}
SkDebugf(")\n");
SkASSERT(order < 4 && order > 0);
#endif
return order;
}
static void intersectWithOrder(const SkDQuad& simple1, int order1, const SkDQuad& simple2,
int order2, SkIntersections& i) {
if (order1 == 3 && order2 == 3) {
i.intersect(simple1, simple2);
} else if (order1 <= 2 && order2 <= 2) {
i.intersect((const SkDLine&) simple1, (const SkDLine&) simple2);
} else if (order1 == 3 && order2 <= 2) {
i.intersect(simple1, (const SkDLine&) simple2);
} else {
SkASSERT(order1 <= 2 && order2 == 3);
i.intersect(simple2, (const SkDLine&) simple1);
i.swapPts();
}
}
// this flavor centers potential intersections recursively. In contrast, '2' may inadvertently
// chase intersections near quadratic ends, requiring odd hacks to find them.
static void intersect(const SkDCubic& cubic1, double t1s, double t1e, const SkDCubic& cubic2,
double t2s, double t2e, double precisionScale, SkIntersections& i) {
i.upDepth();
SkDCubic c1 = cubic1.subDivide(t1s, t1e);
SkDCubic c2 = cubic2.subDivide(t2s, t2e);
SkTDArray<double> ts1;
// OPTIMIZE: if c1 == c2, call once (happens when detecting self-intersection)
c1.toQuadraticTs(c1.calcPrecision() * precisionScale, &ts1);
SkTDArray<double> ts2;
c2.toQuadraticTs(c2.calcPrecision() * 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;
SkReduceOrder s1;
int o1 = quadPart(cubic1, t1Start, t1, &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;
if (&cubic1 == &cubic2 && t1Start >= t2Start) {
t2Start = t2;
continue;
}
SkReduceOrder s2;
int o2 = quadPart(cubic2, t2Start, t2, &s2);
#if ONE_OFF_DEBUG
char tab[] = " ";
if (tLimits1[0][0] >= t1Start && tLimits1[0][1] <= t1
&& tLimits1[1][0] >= t2Start && tLimits1[1][1] <= t2) {
SkDebugf("%.*s %s t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)", i.depth()*2, tab,
__FUNCTION__, t1Start, t1, t2Start, t2);
SkIntersections xlocals;
intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, xlocals);
SkDebugf(" xlocals.fUsed=%d\n", xlocals.used());
}
#endif
SkIntersections locals;
intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, locals);
double coStart[2] = { -1 };
SkDPoint coPoint;
int tCount = locals.used();
for (int tIdx = 0; tIdx < tCount; ++tIdx) {
double to1 = t1Start + (t1 - t1Start) * locals[0][tIdx];
double to2 = t2Start + (t2 - t2Start) * locals[1][tIdx];
// if the computed t is not sufficiently precise, iterate
SkDPoint p1 = cubic1.xyAtT(to1);
SkDPoint p2 = cubic2.xyAtT(to2);
if (p1.approximatelyEqual(p2)) {
if (locals.isCoincident(tIdx)) {
if (coStart[0] < 0) {
coStart[0] = to1;
coStart[1] = to2;
coPoint = p1;
} else {
i.insertCoincidentPair(coStart[0], to1, coStart[1], to2, coPoint, p1);
coStart[0] = -1;
}
} else if (&cubic1 != &cubic2 || !approximately_equal(to1, to2)) {
if (i.swapped()) { // FIXME: insert should respect swap
i.insert(to2, to1, p1);
} else {
i.insert(to1, to2, p1);
}
}
} else {
double offset = precisionScale / 16; // FIME: const is arbitrary: test, refine
double c1Bottom = tIdx == 0 ? 0 :
(t1Start + (t1 - t1Start) * locals[0][tIdx - 1] + to1) / 2;
double c1Min = SkTMax(c1Bottom, to1 - offset);
double c1Top = tIdx == tCount - 1 ? 1 :
(t1Start + (t1 - t1Start) * locals[0][tIdx + 1] + to1) / 2;
double c1Max = SkTMin(c1Top, to1 + offset);
double c2Min = SkTMax(0., to2 - offset);
double c2Max = SkTMin(1., to2 + offset);
#if ONE_OFF_DEBUG
SkDebugf("%.*s %s 1 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab,
__FUNCTION__,
c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max
&& c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max,
to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset
&& to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset,
c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max
&& c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max,
to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset
&& to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset);
SkDebugf("%.*s %s 1 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g"
" 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n",
i.depth()*2, tab, __FUNCTION__, c1Bottom, c1Top, 0., 1.,
to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
SkDebugf("%.*s %s 1 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
" c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min,
c1Max, c2Min, c2Max);
#endif
intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
#if ONE_OFF_DEBUG
SkDebugf("%.*s %s 1 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__,
i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1);
#endif
if (tCount > 1) {
c1Min = SkTMax(0., to1 - offset);
c1Max = SkTMin(1., to1 + offset);
double c2Bottom = tIdx == 0 ? to2 :
(t2Start + (t2 - t2Start) * locals[1][tIdx - 1] + to2) / 2;
double c2Top = tIdx == tCount - 1 ? to2 :
(t2Start + (t2 - t2Start) * locals[1][tIdx + 1] + to2) / 2;
if (c2Bottom > c2Top) {
SkTSwap(c2Bottom, c2Top);
}
if (c2Bottom == to2) {
c2Bottom = 0;
}
if (c2Top == to2) {
c2Top = 1;
}
c2Min = SkTMax(c2Bottom, to2 - offset);
c2Max = SkTMin(c2Top, to2 + offset);
#if ONE_OFF_DEBUG
SkDebugf("%.*s %s 2 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab,
__FUNCTION__,
c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max
&& c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max,
to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset
&& to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset,
c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max
&& c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max,
to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset
&& to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset);
SkDebugf("%.*s %s 2 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g"
" 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n",
i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top,
to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
SkDebugf("%.*s %s 2 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
" c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min,
c1Max, c2Min, c2Max);
#endif
intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
#if ONE_OFF_DEBUG
SkDebugf("%.*s %s 2 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__,
i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1);
#endif
c1Min = SkTMax(c1Bottom, to1 - offset);
c1Max = SkTMin(c1Top, to1 + offset);
#if ONE_OFF_DEBUG
SkDebugf("%.*s %s 3 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab,
__FUNCTION__,
c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max
&& c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max,
to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset
&& to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset,
c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max
&& c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max,
to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset
&& to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset);
SkDebugf("%.*s %s 3 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g"
" 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n",
i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top,
to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
SkDebugf("%.*s %s 3 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
" c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min,
c1Max, c2Min, c2Max);
#endif
intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
#if ONE_OFF_DEBUG
SkDebugf("%.*s %s 3 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__,
i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1);
#endif
}
intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
// FIXME: if no intersection is found, either quadratics intersected where
// cubics did not, or the intersection was missed. In the former case, expect
// the quadratics to be nearly parallel at the point of intersection, and check
// for that.
}
}
SkASSERT(coStart[0] == -1);
t2Start = t2;
}
t1Start = t1;
}
i.downDepth();
}
#define LINE_FRACTION 0.1
// intersect the end of the cubic with the other. Try lines from the end to control and opposite
// end to determine range of t on opposite cubic.
static void intersectEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2,
const SkDRect& bounds2, SkIntersections& i) {
SkDLine line;
int t1Index = start ? 0 : 3;
// don't bother if the two cubics are connnected
#if 1
SkTDArray<double> tVals; // OPTIMIZE: replace with hard-sized array
line[0] = cubic1[t1Index];
// this variant looks for intersections with the end point and lines parallel to other points
for (int index = 0; index < 4; ++index) {
if (index == t1Index) {
continue;
}
SkDVector dxy1 = cubic1[index] - line[0];
dxy1 /= SkDCubic::gPrecisionUnit;
line[1] = line[0] + dxy1;
SkDRect lineBounds;
lineBounds.setBounds(line);
if (!bounds2.intersects(&lineBounds)) {
continue;
}
SkIntersections local;
if (!local.intersect(cubic2, line)) {
continue;
}
for (int idx2 = 0; idx2 < local.used(); ++idx2) {
double foundT = local[0][idx2];
if (approximately_less_than_zero(foundT)
|| approximately_greater_than_one(foundT)) {
continue;
}
if (local.pt(idx2).approximatelyEqual(line[0])) {
if (i.swapped()) { // FIXME: insert should respect swap
i.insert(foundT, start ? 0 : 1, line[0]);
} else {
i.insert(start ? 0 : 1, foundT, line[0]);
}
} else {
*tVals.append() = foundT;
}
}
}
if (tVals.count() == 0) {
return;
}
SkTQSort<double>(tVals.begin(), tVals.end() - 1);
double tMin1 = start ? 0 : 1 - LINE_FRACTION;
double tMax1 = start ? LINE_FRACTION : 1;
int tIdx = 0;
do {
int tLast = tIdx;
while (tLast + 1 < tVals.count() && roughly_equal(tVals[tLast + 1], tVals[tIdx])) {
++tLast;
}
double tMin2 = SkTMax(tVals[tIdx] - LINE_FRACTION, 0.0);
double tMax2 = SkTMin(tVals[tLast] + LINE_FRACTION, 1.0);
int lastUsed = i.used();
intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i);
if (lastUsed == i.used()) {
tMin2 = SkTMax(tVals[tIdx] - (1.0 / SkDCubic::gPrecisionUnit), 0.0);
tMax2 = SkTMin(tVals[tLast] + (1.0 / SkDCubic::gPrecisionUnit), 1.0);
intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i);
}
tIdx = tLast + 1;
} while (tIdx < tVals.count());
#else
const SkDPoint& endPt = cubic1[t1Index];
if (!bounds2.contains(endPt)) {
return;
}
// this variant looks for intersections within an 'x' of the endpoint
double delta = SkTMax(bounds2.width(), bounds2.height());
for (int index = 0; index < 2; ++index) {
if (index == 0) {
line[0].fY = line[1].fY = endPt.fY;
line[0].fX = endPt.fX - delta;
line[1].fX = endPt.fX + delta;
} else {
line[0].fX = line[1].fX = cubic1[t1Index].fX;
line[0].fY = endPt.fY - delta;
line[1].fY = endPt.fY + delta;
}
SkIntersections local;
local.intersectRay(cubic2, line); // OPTIMIZE: special for horizontal/vertical lines
int used = local.used();
for (int index = 0; index < used; ++index) {
double foundT = local[0][index];
if (approximately_less_than_zero(foundT) || approximately_greater_than_one(foundT)) {
continue;
}
if (!local.pt(index).approximatelyEqual(endPt)) {
continue;
}
if (i.swapped()) { // FIXME: insert should respect swap
i.insert(foundT, start ? 0 : 1, endPt);
} else {
i.insert(start ? 0 : 1, foundT, endPt);
}
return;
}
}
// the above doesn't catch when the end of the cubic missed the other cubic because the quad
// approximation moved too far away, so something like the below is still needed. The enabled
// code above tries to avoid this heavy lifting unless the convex hull intersected the cubic.
double tMin1 = start ? 0 : 1 - LINE_FRACTION;
double tMax1 = start ? LINE_FRACTION : 1;
double tMin2 = SkTMax(foundT - LINE_FRACTION, 0.0);
double tMax2 = SkTMin(foundT + LINE_FRACTION, 1.0);
int lastUsed = i.used();
intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i);
if (lastUsed == i.used()) {
tMin2 = SkTMax(foundT - (1.0 / SkDCubic::gPrecisionUnit), 0.0);
tMax2 = SkTMin(foundT + (1.0 / SkDCubic::gPrecisionUnit), 1.0);
intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i);
}
#endif
return;
}
const double CLOSE_ENOUGH = 0.001;
static bool closeStart(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) {
if (i[cubicIndex][0] != 0 || i[cubicIndex][1] > CLOSE_ENOUGH) {
return false;
}
pt = cubic.xyAtT((i[cubicIndex][0] + i[cubicIndex][1]) / 2);
return true;
}
static bool closeEnd(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) {
int last = i.used() - 1;
if (i[cubicIndex][last] != 1 || i[cubicIndex][last - 1] < 1 - CLOSE_ENOUGH) {
return false;
}
pt = cubic.xyAtT((i[cubicIndex][last] + i[cubicIndex][last - 1]) / 2);
return true;
}
int SkIntersections::intersect(const SkDCubic& c1, const SkDCubic& c2) {
::intersect(c1, 0, 1, c2, 0, 1, 1, *this);
// FIXME: pass in cached bounds from caller
SkDRect c1Bounds, c2Bounds;
c1Bounds.setBounds(c1); // OPTIMIZE use setRawBounds ?
c2Bounds.setBounds(c2);
intersectEnd(c1, false, c2, c2Bounds, *this);
intersectEnd(c1, true, c2, c2Bounds, *this);
bool selfIntersect = &c1 == &c2;
if (!selfIntersect) {
swap();
intersectEnd(c2, false, c1, c1Bounds, *this);
intersectEnd(c2, true, c1, c1Bounds, *this);
swap();
}
// If an end point and a second point very close to the end is returned, the second
// point may have been detected because the approximate quads
// intersected at the end and close to it. Verify that the second point is valid.
if (fUsed <= 1 || coincidentUsed()) {
return fUsed;
}
SkDPoint pt[2];
if (closeStart(c1, 0, *this, pt[0]) && closeStart(c2, 1, *this, pt[1])
&& pt[0].approximatelyEqual(pt[1])) {
removeOne(1);
}
if (closeEnd(c1, 0, *this, pt[0]) && closeEnd(c2, 1, *this, pt[1])
&& pt[0].approximatelyEqual(pt[1])) {
removeOne(used() - 2);
}
return fUsed;
}
// Up promote the quad to a cubic.
// OPTIMIZATION If this is a common use case, optimize by duplicating
// the intersect 3 loop to avoid the promotion / demotion code
int SkIntersections::intersect(const SkDCubic& cubic, const SkDQuad& quad) {
SkDCubic up = quad.toCubic();
(void) intersect(cubic, up);
return used();
}
/* http://www.ag.jku.at/compass/compasssample.pdf
( Self-Intersection Problems and Approximate Implicitization by Jan B. Thomassen
Centre of Mathematics for Applications, University of Oslo http://www.cma.uio.no janbth@math.uio.no
SINTEF Applied Mathematics http://www.sintef.no )
describes a method to find the self intersection of a cubic by taking the gradient of the implicit
form dotted with the normal, and solving for the roots. My math foo is too poor to implement this.*/
int SkIntersections::intersect(const SkDCubic& c) {
// check to see if x or y end points are the extrema. Are other quick rejects possible?
if (c.endsAreExtremaInXOrY()) {
return false;
}
(void) intersect(c, c);
if (used() > 0) {
SkASSERT(used() == 1);
if (fT[0][0] > fT[1][0]) {
swapPts();
}
}
return used();
}