add conics to path ops

src/pathops/SkDConicLineIntersection.cpp

+/*
+ * Copyright 2015 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 "SkPathOpsConic.h"
+#include "SkPathOpsLine.h"
+
+class LineConicIntersections {
+public:
+    enum PinTPoint {
+        kPointUninitialized,
+        kPointInitialized
+    };
+
+    LineConicIntersections(const SkDConic& c, const SkDLine& l, SkIntersections* i)
+        : fConic(c)
+        , fLine(l)
+        , fIntersections(i)
+        , fAllowNear(true) {
+        i->setMax(3);  // allow short partial coincidence plus discrete intersection
+    }
+
+    void allowNear(bool allow) {
+        fAllowNear = allow;
+    }
+
+    void checkCoincident() {
+        int last = fIntersections->used() - 1;
+        for (int index = 0; index < last; ) {
+            double conicMidT = ((*fIntersections)[0][index] + (*fIntersections)[0][index + 1]) / 2;
+            SkDPoint conicMidPt = fConic.ptAtT(conicMidT);
+            double t = fLine.nearPoint(conicMidPt, NULL);
+            if (t < 0) {
+                ++index;
+                continue;
+            }
+            if (fIntersections->isCoincident(index)) {
+                fIntersections->removeOne(index);
+                --last;
+            } else if (fIntersections->isCoincident(index + 1)) {
+                fIntersections->removeOne(index + 1);
+                --last;
+            } else {
+                fIntersections->setCoincident(index++);
+            }
+            fIntersections->setCoincident(index);
+        }
+    }
+
+#ifdef SK_DEBUG
+    static bool close_to(double a, double b, const double c[3]) {
+        double max = SkTMax(-SkTMin(SkTMin(c[0], c[1]), c[2]), SkTMax(SkTMax(c[0], c[1]), c[2]));
+        return approximately_zero_when_compared_to(a - b, max);
+    }
+#endif
+
+    int horizontalIntersect(double axisIntercept, double left, double right, bool flipped) {
+        this->addExactHorizontalEndPoints(left, right, axisIntercept);
+        if (fAllowNear) {
+            this->addNearHorizontalEndPoints(left, right, axisIntercept);
+        }
+        double roots[2];
+        double conicVals[] = { fConic[0].fY, fConic[1].fY, fConic[2].fY };
+        int count = this->validT(conicVals, axisIntercept, roots);
+        for (int index = 0; index < count; ++index) {
+            double conicT = roots[index];
+            SkDPoint pt = fConic.ptAtT(conicT);
+            SkASSERT(close_to(pt.fY, axisIntercept, conicVals));
+            double lineT = (pt.fX - left) / (right - left);
+            if (this->pinTs(&conicT, &lineT, &pt, kPointInitialized)
+                    && this->uniqueAnswer(conicT, pt)) {
+                fIntersections->insert(conicT, lineT, pt);
+            }
+        }
+        if (flipped) {
+            fIntersections->flip();
+        }
+        this->checkCoincident();
+        return fIntersections->used();
+    }
+
+    int intersect() {
+        this->addExactEndPoints();
+        if (fAllowNear) {
+            this->addNearEndPoints();
+        }
+        double rootVals[2];
+        int roots = this->intersectRay(rootVals);
+        for (int index = 0; index < roots; ++index) {
+            double conicT = rootVals[index];
+            double lineT = this->findLineT(conicT);
+            SkDEBUGCODE(SkDPoint conicPt = fConic.ptAtT(conicT));
+            SkDEBUGCODE(SkDPoint linePt = fLine.ptAtT(lineT));
+            SkASSERT(conicPt.approximatelyEqual(linePt));
+            SkDPoint pt;
+            if (this->pinTs(&conicT, &lineT, &pt, kPointUninitialized)
+                    && this->uniqueAnswer(conicT, pt)) {
+                fIntersections->insert(conicT, lineT, pt);
+            }
+        }
+        this->checkCoincident();
+        return fIntersections->used();
+    }
+
+    int intersectRay(double roots[2]) {
+        double adj = fLine[1].fX - fLine[0].fX;
+        double opp = fLine[1].fY - fLine[0].fY;
+        double r[3];
+        for (int n = 0; n < 3; ++n) {
+            r[n] = (fConic[n].fY - fLine[0].fY) * adj - (fConic[n].fX - fLine[0].fX) * opp;
+        }
+        return this->validT(r, 0, roots);
+    }
+
+    int validT(double r[3], double axisIntercept, double roots[2]) {
+        double A = r[2];
+        double B = r[1] * fConic.fWeight - axisIntercept * fConic.fWeight + axisIntercept;
+        double C = r[0];
+        A += C - 2 * B;  // A = a + c - 2*(b*w - xCept*w + xCept)
+        B -= C;  // B = b*w - w * xCept + xCept - a
+        C -= axisIntercept;
+        return SkDQuad::RootsValidT(A, 2 * B, C, roots);
+    }
+
+    int verticalIntersect(double axisIntercept, double top, double bottom, bool flipped) {
+        this->addExactVerticalEndPoints(top, bottom, axisIntercept);
+        if (fAllowNear) {
+            this->addNearVerticalEndPoints(top, bottom, axisIntercept);
+        }
+        double roots[2];
+        double conicVals[] = { fConic[0].fX, fConic[1].fX, fConic[2].fX };
+        int count = this->validT(conicVals, axisIntercept, roots);
+        for (int index = 0; index < count; ++index) {
+            double conicT = roots[index];
+            SkDPoint pt = fConic.ptAtT(conicT);
+            SkASSERT(close_to(pt.fX, axisIntercept, conicVals));
+            double lineT = (pt.fY - top) / (bottom - top);
+            if (this->pinTs(&conicT, &lineT, &pt, kPointInitialized)
+                    && this->uniqueAnswer(conicT, pt)) {
+                fIntersections->insert(conicT, lineT, pt);
+            }
+        }
+        if (flipped) {
+            fIntersections->flip();
+        }
+        this->checkCoincident();
+        return fIntersections->used();
+    }
+
+protected:
+// OPTIMIZE: Functions of the form add .. points are indentical to the conic routines.
+    // add endpoints first to get zero and one t values exactly
+    void addExactEndPoints() {
+        for (int cIndex = 0; cIndex < SkDConic::kPointCount; cIndex += SkDConic::kPointLast) {
+            double lineT = fLine.exactPoint(fConic[cIndex]);
+            if (lineT < 0) {
+                continue;
+            }
+            double conicT = (double) (cIndex >> 1);
+            fIntersections->insert(conicT, lineT, fConic[cIndex]);
+        }
+    }
+
+    void addNearEndPoints() {
+        for (int cIndex = 0; cIndex < SkDConic::kPointCount; cIndex += SkDConic::kPointLast) {
+            double conicT = (double) (cIndex >> 1);
+            if (fIntersections->hasT(conicT)) {
+                continue;
+            }
+            double lineT = fLine.nearPoint(fConic[cIndex], NULL);
+            if (lineT < 0) {
+                continue;
+            }
+            fIntersections->insert(conicT, lineT, fConic[cIndex]);
+        }
+        // FIXME: see if line end is nearly on conic
+    }
+
+    void addExactHorizontalEndPoints(double left, double right, double y) {
+        for (int cIndex = 0; cIndex < SkDConic::kPointCount; cIndex += SkDConic::kPointLast) {
+            double lineT = SkDLine::ExactPointH(fConic[cIndex], left, right, y);
+            if (lineT < 0) {
+                continue;
+            }
+            double conicT = (double) (cIndex >> 1);
+            fIntersections->insert(conicT, lineT, fConic[cIndex]);
+        }
+    }
+
+    void addNearHorizontalEndPoints(double left, double right, double y) {
+        for (int cIndex = 0; cIndex < SkDConic::kPointCount; cIndex += SkDConic::kPointLast) {
+            double conicT = (double) (cIndex >> 1);
+            if (fIntersections->hasT(conicT)) {
+                continue;
+            }
+            double lineT = SkDLine::NearPointH(fConic[cIndex], left, right, y);
+            if (lineT < 0) {
+                continue;
+            }
+            fIntersections->insert(conicT, lineT, fConic[cIndex]);
+        }
+        // FIXME: see if line end is nearly on conic
+    }
+
+    void addExactVerticalEndPoints(double top, double bottom, double x) {
+        for (int cIndex = 0; cIndex < SkDConic::kPointCount; cIndex += SkDConic::kPointLast) {
+            double lineT = SkDLine::ExactPointV(fConic[cIndex], top, bottom, x);
+            if (lineT < 0) {
+                continue;
+            }
+            double conicT = (double) (cIndex >> 1);
+            fIntersections->insert(conicT, lineT, fConic[cIndex]);
+        }
+    }
+
+    void addNearVerticalEndPoints(double top, double bottom, double x) {
+        for (int cIndex = 0; cIndex < SkDConic::kPointCount; cIndex += SkDConic::kPointLast) {
+            double conicT = (double) (cIndex >> 1);
+            if (fIntersections->hasT(conicT)) {
+                continue;
+            }
+            double lineT = SkDLine::NearPointV(fConic[cIndex], top, bottom, x);
+            if (lineT < 0) {
+                continue;
+            }
+            fIntersections->insert(conicT, lineT, fConic[cIndex]);
+        }
+        // FIXME: see if line end is nearly on conic
+    }
+
+    double findLineT(double t) {
+        SkDPoint xy = fConic.ptAtT(t);
+        double dx = fLine[1].fX - fLine[0].fX;
+        double dy = fLine[1].fY - fLine[0].fY;
+        if (fabs(dx) > fabs(dy)) {
+            return (xy.fX - fLine[0].fX) / dx;
+        }
+        return (xy.fY - fLine[0].fY) / dy;
+    }
+
+    bool pinTs(double* conicT, double* lineT, SkDPoint* pt, PinTPoint ptSet) {
+        if (!approximately_one_or_less_double(*lineT)) {
+            return false;
+        }
+        if (!approximately_zero_or_more_double(*lineT)) {
+            return false;
+        }
+        double qT = *conicT = SkPinT(*conicT);
+        double lT = *lineT = SkPinT(*lineT);
+        if (lT == 0 || lT == 1 || (ptSet == kPointUninitialized && qT != 0 && qT != 1)) {
+            *pt = fLine.ptAtT(lT);
+        } else if (ptSet == kPointUninitialized) {
+            *pt = fConic.ptAtT(qT);
+        }
+        SkPoint gridPt = pt->asSkPoint();
+        if (SkDPoint::ApproximatelyEqual(gridPt, fLine[0].asSkPoint())) {
+            *pt = fLine[0];
+            *lineT = 0;
+        } else if (SkDPoint::ApproximatelyEqual(gridPt, fLine[1].asSkPoint())) {
+            *pt = fLine[1];
+            *lineT = 1;
+        }
+        if (fIntersections->used() > 0 && approximately_equal((*fIntersections)[1][0], *lineT)) {
+            return false;
+        }
+        if (gridPt == fConic[0].asSkPoint()) {
+            *pt = fConic[0];
+            *conicT = 0;
+        } else if (gridPt == fConic[2].asSkPoint()) {
+            *pt = fConic[2];
+            *conicT = 1;
+        }
+        return true;
+    }
+
+    bool uniqueAnswer(double conicT, const SkDPoint& pt) {
+        for (int inner = 0; inner < fIntersections->used(); ++inner) {
+            if (fIntersections->pt(inner) != pt) {
+                continue;
+            }
+            double existingConicT = (*fIntersections)[0][inner];
+            if (conicT == existingConicT) {
+                return false;
+            }
+            // check if midway on conic is also same point. If so, discard this
+            double conicMidT = (existingConicT + conicT) / 2;
+            SkDPoint conicMidPt = fConic.ptAtT(conicMidT);
+            if (conicMidPt.approximatelyEqual(pt)) {
+                return false;
+            }
+        }
+#if ONE_OFF_DEBUG
+        SkDPoint qPt = fConic.ptAtT(conicT);
+        SkDebugf("%s pt=(%1.9g,%1.9g) cPt=(%1.9g,%1.9g)\n", __FUNCTION__, pt.fX, pt.fY,
+                qPt.fX, qPt.fY);
+#endif
+        return true;
+    }
+
+private:
+    const SkDConic& fConic;
+    const SkDLine& fLine;
+    SkIntersections* fIntersections;
+    bool fAllowNear;
+};
+
+int SkIntersections::horizontal(const SkDConic& conic, double left, double right, double y,
+                                bool flipped) {
+    SkDLine line = {{{ left, y }, { right, y }}};
+    LineConicIntersections c(conic, line, this);
+    return c.horizontalIntersect(y, left, right, flipped);
+}
+
+int SkIntersections::vertical(const SkDConic& conic, double top, double bottom, double x,
+                              bool flipped) {
+    SkDLine line = {{{ x, top }, { x, bottom }}};
+    LineConicIntersections c(conic, line, this);
+    return c.verticalIntersect(x, top, bottom, flipped);
+}
+
+int SkIntersections::intersect(const SkDConic& conic, const SkDLine& line) {
+    LineConicIntersections c(conic, line, this);
+    c.allowNear(fAllowNear);
+    return c.intersect();
+}
+
+int SkIntersections::intersectRay(const SkDConic& conic, const SkDLine& line) {
+    LineConicIntersections c(conic, line, this);
+    fUsed = c.intersectRay(fT[0]);
+    for (int index = 0; index < fUsed; ++index) {
+        fPt[index] = conic.ptAtT(fT[0][index]);
+    }
+    return fUsed;
+}