src/pathops/SkOpAngle.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 "SkIntersections.h"
#include "SkOpAngle.h"
#include "SkOpSegment.h"
#include "SkPathOpsCurve.h"
#include "SkTSort.h"

#if DEBUG_ANGLE
#include "SkString.h"

static const char funcName[] = "SkOpSegment::operator<";
static const int bugChar = strlen(funcName) + 1;
#endif

/* Angles are sorted counterclockwise. The smallest angle has a positive x and the smallest
   positive y. The largest angle has a positive x and a zero y. */

#if DEBUG_ANGLE
    static bool CompareResult(SkString* bugOut, const char* append, bool compare) {
        bugOut->appendf("%s", append);
        bugOut->writable_str()[bugChar] = "><"[compare];
        SkDebugf("%s\n", bugOut->c_str());
        return compare;
    }

    #define COMPARE_RESULT(append, compare) CompareResult(&bugOut, append, compare)
#else
    #define COMPARE_RESULT(append, compare) compare
#endif

bool SkOpAngle::calcSlop(double x, double y, double rx, double ry, bool* result) const{
    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);
    SkPath::Verb verb = fSegment->verb();
    SkASSERT(verb == SkPath::kQuad_Verb || verb == SkPath::kCubic_Verb);
    // FIXME: the quad and cubic factors are made up ; determine actual values
    double slop = verb == SkPath::kQuad_Verb ? 4 * epsilon : 512 * epsilon;
    double xSlop = slop;
    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;
    *result = x_ry1 < rx_y1;
    double x2 = x + xSlop;
    double y2 = y - ySlop;
    double x_ry2 = x2 * ry;
    double rx_y2 = rx * y2;
    bool less2 = x_ry2 < rx_y2;
    return *result == less2;
}

/*
for quads and cubics, set up a parameterized line (e.g. LineParameters )
for points [0] to [1]. See if point [2] is on that line, or on one side
or the other. If it both quads' end points are on the same side, choose
the shorter tangent. If the tangents are equal, choose the better second
tangent angle

FIXME: maybe I could set up LineParameters lazily
*/
bool SkOpAngle::operator<(const SkOpAngle& rh) const {  // this/lh: left-hand; rh: right-hand
    double y = dy();
    double ry = rh.dy();
#if DEBUG_ANGLE
    SkString bugOut;
    bugOut.printf("%s _ id=%d segId=%d tStart=%1.9g tEnd=%1.9g"
        " | id=%d segId=%d tStart=%1.9g tEnd=%1.9g ", funcName,
        fID, fSegment->debugID(), fSegment->t(fStart), fSegment->t(fEnd),
        rh.fID, rh.fSegment->debugID(), rh.fSegment->t(rh.fStart), rh.fSegment->t(rh.fEnd));
#endif
    double y_ry = y * ry;
    if (y_ry < 0) {  // if y's are opposite signs, we can do a quick return
        return COMPARE_RESULT("1 y * ry < 0", y < 0);
    }
    // at this point, both y's must be the same sign, or one (or both) is zero
    double x = dx();
    double rx = rh.dx();
    if (x * rx < 0) {  // if x's are opposite signs, use y to determine first or second half
        if (y < 0 && ry < 0) {  // if y's are negative, lh x is smaller if positive
            return COMPARE_RESULT("2 x_rx < 0 && y < 0 ...", x > 0);
        }
        if (y >= 0 && ry >= 0) {  // if y's are zero or positive, lh x is smaller if negative
            return COMPARE_RESULT("3 x_rx < 0 && y >= 0 ...", x < 0);
        }
        SkASSERT((y == 0) ^ (ry == 0));  // if one y is zero and one is negative, neg y is smaller
        return COMPARE_RESULT("4 x_rx < 0 && y == 0 ...", y < 0);
    }
    // at this point, both x's must be the same sign, or one (or both) is zero
    if (y_ry == 0) { // if either y is zero
        if (y + ry < 0) { // if the other y is less than zero, it must be smaller
            return COMPARE_RESULT("5 y_ry == 0 && y + ry < 0", y < 0);
        }
        if (y + ry > 0) { // if a y is greater than zero and an x is positive,  non zero is smaller
            return COMPARE_RESULT("6 y_ry == 0 && y + ry > 0", (x + rx > 0) ^ (y == 0));
        }
        // at this point, both y's are zero, so lines are coincident or one is degenerate
        SkASSERT(x * rx != 0);  // and a degenerate line should haven't gotten this far
    }
    // see if either curve can be lengthened before trying the tangent
    if (fSegment->other(fEnd) != rh.fSegment  // tangents not absolutely identical
            && rh.fSegment->other(rh.fEnd) != fSegment) {  // and not intersecting
        SkOpAngle longer = *this;
        SkOpAngle rhLonger = rh;
        if ((longer.lengthen(rh) | rhLonger.lengthen(*this))  // lengthen both
                && (fUnorderable || !longer.fUnorderable)
                && (rh.fUnorderable || !rhLonger.fUnorderable)) {
#if DEBUG_ANGLE
            bugOut.prepend("  ");
#endif
            return COMPARE_RESULT("10 longer.lengthen(rh) ...", longer < rhLonger);
        }
    }
    SkPath::Verb verb = fSegment->verb();
    SkPath::Verb rVerb = rh.fSegment->verb();
    if (y_ry != 0) { // if they aren't coincident, look for a stable cross product
        // at this point, y's are the same sign, neither is zero
        //   and x's are the same sign, or one (or both) is zero
        double x_ry = x * ry;
        double rx_y = rx * y;
        if (!fComputed && !rh.fComputed) {
            if (!SkDLine::NearRay(x, y, rx, ry) && x_ry != rx_y) {
                return COMPARE_RESULT("7 !fComputed && !rh.fComputed", x_ry < rx_y);
            }
            if (fSide2 == 0 && rh.fSide2 == 0) {
                return COMPARE_RESULT("7a !fComputed && !rh.fComputed", x_ry < rx_y);
            }
        } else {
            // if the vector was a result of subdividing a curve, see if it is stable
            bool sloppy1 = x_ry < rx_y;
            bool sloppy2 = !sloppy1;
            if ((!fComputed || calcSlop(x, y, rx, ry, &sloppy1))
                    && (!rh.fComputed || rh.calcSlop(rx, ry, x, y, &sloppy2))
                    && sloppy1 != sloppy2) {
                return COMPARE_RESULT("8 CalcSlop(x, y ...", sloppy1);
            }
        }
    }
    if (fSide2 * rh.fSide2 == 0) {  // one is zero
#if DEBUG_ANGLE
        if (fSide2 == rh.fSide2 && y_ry) {  // both is zero; coincidence was undetected
            SkDebugf("%s coincidence!\n", __FUNCTION__);
        }
#endif
        return COMPARE_RESULT("9a fSide2 * rh.fSide2 == 0 ...", fSide2 < rh.fSide2);
    }
    // at this point, the initial tangent line is nearly coincident
    // see if edges curl away from each other
    if (fSide * rh.fSide < 0 && (!approximately_zero(fSide) || !approximately_zero(rh.fSide))) {
        return COMPARE_RESULT("9b fSide * rh.fSide < 0 ...", fSide < rh.fSide);
    }
    if (fUnsortable || rh.fUnsortable) {
        // even with no solution, return a stable sort
        return COMPARE_RESULT("11 fUnsortable || rh.fUnsortable", this < &rh);
    }
    if ((verb == SkPath::kLine_Verb && approximately_zero(y) && approximately_zero(x))
            || (rVerb == SkPath::kLine_Verb
            && approximately_zero(ry) && approximately_zero(rx))) {
        // See general unsortable comment below. This case can happen when
        // one line has a non-zero change in t but no change in x and y.
        fUnsortable = true;
        return COMPARE_RESULT("12 verb == SkPath::kLine_Verb ...", this < &rh);
    }
    if (fSegment->isTiny(this) || rh.fSegment->isTiny(&rh)) {
        fUnsortable = true;
        return COMPARE_RESULT("13 verb == fSegment->isTiny(this) ...", this < &rh);
    }
    SkASSERT(verb >= SkPath::kQuad_Verb);
    SkASSERT(rVerb >= SkPath::kQuad_Verb);
    // FIXME: until I can think of something better, project a ray from the
    // end of the shorter tangent to midway between the end points
    // through both curves and use the resulting angle to sort
    // FIXME: some of this setup can be moved to set() if it works, or cached if it's expensive
    double len = fTangentPart.normalSquared();
    double rlen = rh.fTangentPart.normalSquared();
    SkDLine ray;
    SkIntersections i, ri;
    int roots, rroots;
    bool flip = false;
    bool useThis;
    bool leftLessThanRight = fSide > 0;
    do {
        useThis = (len < rlen) ^ flip;
        const SkDCubic& part = useThis ? fCurvePart : rh.fCurvePart;
        SkPath::Verb partVerb = useThis ? verb : rVerb;
        ray[0] = partVerb == SkPath::kCubic_Verb && part[0].approximatelyEqual(part[1]) ?
            part[2] : part[1];
        ray[1] = SkDPoint::Mid(part[0], part[SkPathOpsVerbToPoints(partVerb)]);
        SkASSERT(ray[0] != ray[1]);
        roots = (i.*CurveRay[SkPathOpsVerbToPoints(verb)])(fSegment->pts(), ray);
        rroots = (ri.*CurveRay[SkPathOpsVerbToPoints(rVerb)])(rh.fSegment->pts(), ray);
    } while ((roots == 0 || rroots == 0) && (flip ^= true));
    if (roots == 0 || rroots == 0) {
        // FIXME: we don't have a solution in this case. The interim solution
        // is to mark the edges as unsortable, exclude them from this and
        // future computations, and allow the returned path to be fragmented
        fUnsortable = true;
        return COMPARE_RESULT("roots == 0 || rroots == 0", this < &rh);
    }
    SkASSERT(fSide != 0 && rh.fSide != 0);
    SkASSERT(fSide * rh.fSide > 0); // both are the same sign
    SkDPoint lLoc;
    double best = SK_ScalarInfinity;
#if DEBUG_SORT
    SkDebugf("lh=%d rh=%d use-lh=%d ray={{%1.9g,%1.9g}, {%1.9g,%1.9g}} %c\n",
            fSegment->debugID(), rh.fSegment->debugID(), useThis, ray[0].fX, ray[0].fY,
            ray[1].fX, ray[1].fY, "-+"[fSide > 0]);
#endif
    for (int index = 0; index < roots; ++index) {
        SkDPoint loc = i.pt(index);
        SkDVector dxy = loc - ray[0];
        double dist = dxy.lengthSquared();
#if DEBUG_SORT
        SkDebugf("best=%1.9g dist=%1.9g loc={%1.9g,%1.9g} dxy={%1.9g,%1.9g}\n",
                best, dist, loc.fX, loc.fY, dxy.fX, dxy.fY);
#endif
        if (best > dist) {
            lLoc = loc;
            best = dist;
        }
    }
    flip = false;
    SkDPoint rLoc;
    for (int index = 0; index < rroots; ++index) {
        rLoc = ri.pt(index);
        SkDVector dxy = rLoc - ray[0];
        double dist = dxy.lengthSquared();
#if DEBUG_SORT
        SkDebugf("best=%1.9g dist=%1.9g %c=(fSide < 0) rLoc={%1.9g,%1.9g} dxy={%1.9g,%1.9g}\n",
                best, dist, "><"[fSide < 0], rLoc.fX, rLoc.fY, dxy.fX, dxy.fY);
#endif
        if (best > dist) {
            flip = true;
            break;
        }
    }
    if (flip) {
        leftLessThanRight = !leftLessThanRight;
    }
    return COMPARE_RESULT("14 leftLessThanRight", leftLessThanRight);
}

bool SkOpAngle::isHorizontal() const {
    return dy() == 0 && fSegment->verb() == SkPath::kLine_Verb;
}

// lengthen cannot cross opposite angle
bool SkOpAngle::lengthen(const SkOpAngle& opp) {
    if (fSegment->other(fEnd) == opp.fSegment) {
        return false;
    }
    // FIXME: make this a while loop instead and make it as large as possible?
    int newEnd = fEnd;
    if (fStart < fEnd ? ++newEnd < fSegment->count() : --newEnd >= 0) {
        fEnd = newEnd;
        setSpans();
        return true;
    }
    return false;
}

void SkOpAngle::set(const SkOpSegment* segment, int start, int end) {
    fSegment = segment;
    fStart = start;
    fEnd = end;
    setSpans();
}

void SkOpAngle::setSpans() {
    fUnorderable = fSegment->isTiny(this);
    fLastMarked = NULL;
    fUnsortable = false;
    const SkPoint* pts = fSegment->pts();
    if (fSegment->verb() != SkPath::kLine_Verb) {
        fComputed = fSegment->subDivide(fStart, fEnd, &fCurvePart);
        fSegment->subDivide(fStart, fStart < fEnd ? fSegment->count() - 1 : 0, &fCurveHalf);
    }
    // FIXME: slight errors in subdivision cause sort trouble later on. As an experiment, try
    // rounding the curve part to float precision here
    // fCurvePart.round(fSegment->verb());
    switch (fSegment->verb()) {
    case SkPath::kLine_Verb: {
        SkASSERT(fStart != fEnd);
        fCurvePart[0].set(pts[fStart > fEnd]);
        fCurvePart[1].set(pts[fStart < fEnd]);
        fComputed = false;
        // OPTIMIZATION: for pure line compares, we never need fTangentPart.c
        fTangentPart.lineEndPoints(*SkTCast<SkDLine*>(&fCurvePart));
        fSide = 0;
        fSide2 = 0;
        } break;
    case SkPath::kQuad_Verb: {
        fSide2 = -fTangentHalf.quadPart(*SkTCast<SkDQuad*>(&fCurveHalf));
        SkDQuad& quad = *SkTCast<SkDQuad*>(&fCurvePart);
        fTangentPart.quadEndPoints(quad);
        fSide = -fTangentPart.pointDistance(fCurvePart[2]);  // not normalized -- compare sign only
        if (fComputed && dx() > 0 && approximately_zero(dy())) {
            SkDCubic origCurve; // can't use segment's curve in place since it may be flipped
            int last = fSegment->count() - 1;
            fSegment->subDivide(fStart < fEnd ? 0 : last, fStart < fEnd ? last : 0, &origCurve);
            SkLineParameters origTan;
            origTan.quadEndPoints(*SkTCast<SkDQuad*>(&origCurve));
            if (origTan.dx() <= 0
                    || (dy() != origTan.dy() && dy() * origTan.dy() <= 0)) { // signs match?
                fUnorderable = true;
                return;
            }
        }
        } break;
    case SkPath::kCubic_Verb: {
        double startT = fSegment->t(fStart);
        fSide2 = -fTangentHalf.cubicPart(fCurveHalf);
        fTangentPart.cubicEndPoints(fCurvePart);
        double testTs[4];
        // OPTIMIZATION: keep inflections precomputed with cubic segment?
        int testCount = SkDCubic::FindInflections(pts, testTs);
        double endT = fSegment->t(fEnd);
        double limitT = endT;
        int index;
        for (index = 0; index < testCount; ++index) {
            if (!between(startT, testTs[index], limitT)) {
                testTs[index] = -1;
            }
        }
        testTs[testCount++] = startT;
        testTs[testCount++] = endT;
        SkTQSort<double>(testTs, &testTs[testCount - 1]);
        double bestSide = 0;
        int testCases = (testCount << 1) - 1;
        index = 0;
        while (testTs[index] < 0) {
            ++index;
        }
        index <<= 1;
        for (; index < testCases; ++index) {
            int testIndex = index >> 1;
            double testT = testTs[testIndex];
            if (index & 1) {
                testT = (testT + testTs[testIndex + 1]) / 2;
            }
            // OPTIMIZE: could avoid call for t == startT, endT
            SkDPoint pt = dcubic_xy_at_t(pts, testT);
            double testSide = fTangentPart.pointDistance(pt);
            if (fabs(bestSide) < fabs(testSide)) {
                bestSide = testSide;
            }
        }
        fSide = -bestSide;  // compare sign only
        SkASSERT(fSide == 0 || fSide2 != 0);
        if (fComputed && dx() > 0 && approximately_zero(dy())) {
            SkDCubic origCurve; // can't use segment's curve in place since it may be flipped
            int last = fSegment->count() - 1;
            fSegment->subDivide(fStart < fEnd ? 0 : last, fStart < fEnd ? last : 0, &origCurve);
            SkDCubicPair split = origCurve.chopAt(startT);
            SkLineParameters splitTan;
            splitTan.cubicEndPoints(fStart < fEnd ? split.second() : split.first());
            if (splitTan.dx() <= 0) {
                fUnorderable = true;
                fUnsortable = fSegment->isTiny(this);
                return;
            }
            // if one is < 0 and the other is >= 0
            if (dy() * splitTan.dy() < 0) {
                fUnorderable = true;
                fUnsortable = fSegment->isTiny(this);
                return;
            }
        }
        } break;
    default:
        SkASSERT(0);
    }
    if ((fUnsortable = approximately_zero(dx()) && approximately_zero(dy()))) {
        return;
    }
    if (fSegment->verb() == SkPath::kLine_Verb) {
        return;
    }
    SkASSERT(fStart != fEnd);
    int smaller = SkMin32(fStart, fEnd);
    int larger = SkMax32(fStart, fEnd);
    while (smaller < larger && fSegment->span(smaller).fTiny) {
        ++smaller;
    }
    if (precisely_equal(fSegment->span(smaller).fT, fSegment->span(larger).fT)) {
    #if DEBUG_UNSORTABLE
        SkPoint iPt = fSegment->xyAtT(fStart);
        SkPoint ePt = fSegment->xyAtT(fEnd);
        SkDebugf("%s all tiny unsortable [%d] (%1.9g,%1.9g) [%d] (%1.9g,%1.9g)\n", __FUNCTION__,
            fStart, iPt.fX, iPt.fY, fEnd, ePt.fX, ePt.fY);
    #endif
        fUnsortable = true;
        return;
    }
    fUnsortable = fStart < fEnd ? fSegment->span(smaller).fUnsortableStart
            : fSegment->span(larger).fUnsortableEnd;
#if DEBUG_UNSORTABLE
    if (fUnsortable) {
        SkPoint iPt = fSegment->xyAtT(smaller);
        SkPoint ePt = fSegment->xyAtT(larger);
        SkDebugf("%s unsortable [%d] (%1.9g,%1.9g) [%d] (%1.9g,%1.9g)\n", __FUNCTION__,
                smaller, iPt.fX, iPt.fY, fEnd, ePt.fX, ePt.fY);
    }
#endif
    return;
}

#ifdef SK_DEBUG
void SkOpAngle::dump() const {
    const SkOpSpan& spanStart = fSegment->span(fStart);
    const SkOpSpan& spanEnd = fSegment->span(fEnd);
    const SkOpSpan& spanMin = fStart < fEnd ? spanStart : spanEnd;
    SkDebugf("id=%d (%1.9g,%1.9g) start=%d (%1.9g) end=%d (%1.9g) sumWind=",
            fSegment->debugID(), fSegment->xAtT(fStart), fSegment->yAtT(fStart),
            fStart, spanStart.fT, fEnd, spanEnd.fT);
    SkPathOpsDebug::WindingPrintf(spanMin.fWindSum);
    SkDebugf(" oppWind=");
    SkPathOpsDebug::WindingPrintf(spanMin.fOppSum),
    SkDebugf(" done=%d\n", spanMin.fDone);
}
#endif