add conics to path ops

src/pathops/SkPathOpsConic.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 "SkLineParameters.h"
+#include "SkPathOpsConic.h"
+#include "SkPathOpsCubic.h"
+#include "SkPathOpsQuad.h"
+
+// cribbed from the float version in SkGeometry.cpp
+static void conic_deriv_coeff(const double src[],
+                              SkScalar w,
+                              double coeff[3]) {
+    const double P20 = src[4] - src[0];
+    const double P10 = src[2] - src[0];
+    const double wP10 = w * P10;
+    coeff[0] = w * P20 - P20;
+    coeff[1] = P20 - 2 * wP10;
+    coeff[2] = wP10;
+}
+
+static double conic_eval_tan(const double coord[], SkScalar w, double t) {
+    double coeff[3];
+    conic_deriv_coeff(coord, w, coeff);
+    return t * (t * coeff[0] + coeff[1]) + coeff[2];
+}
+
+int SkDConic::FindExtrema(const double src[], SkScalar w, double t[1]) {
+    double coeff[3];
+    conic_deriv_coeff(src, w, coeff);
+
+    double tValues[2];
+    int roots = SkDQuad::RootsValidT(coeff[0], coeff[1], coeff[2], tValues);
+    SkASSERT(0 == roots || 1 == roots);
+
+    if (1 == roots) {
+        t[0] = tValues[0];
+        return 1;
+    }
+    return 0;
+}
+
+SkDVector SkDConic::dxdyAtT(double t) const {
+    SkDVector result = {
+        conic_eval_tan(&fPts[0].fX, fWeight, t),
+        conic_eval_tan(&fPts[0].fY, fWeight, t)
+    };
+    return result;
+}
+
+static double conic_eval_numerator(const double src[], SkScalar w, double t) {
+    SkASSERT(src);
+    SkASSERT(t >= 0 && t <= 1);
+    double src2w = src[2] * w;
+    double C = src[0];
+    double A = src[4] - 2 * src2w + C;
+    double B = 2 * (src2w - C);
+    return (A * t + B) * t + C;
+}
+
+
+static double conic_eval_denominator(SkScalar w, double t) {
+    double B = 2 * (w - 1);
+    double C = 1;
+    double A = -B;
+    return (A * t + B) * t + C;
+}
+
+bool SkDConic::hullIntersects(const SkDCubic& cubic, bool* isLinear) const {
+    return cubic.hullIntersects(*this, isLinear);
+}
+
+SkDPoint SkDConic::ptAtT(double t) const {
+    double denominator = conic_eval_denominator(fWeight, t);
+    SkDPoint result = {
+        conic_eval_numerator(&fPts[0].fX, fWeight, t) / denominator,
+        conic_eval_numerator(&fPts[0].fY, fWeight, t) / denominator
+    };
+    return result;
+}
+
+SkDPoint SkDConic::top(double startT, double endT) const {
+    SkDConic sub = subDivide(startT, endT);
+    SkDPoint topPt = sub[0];
+    if (topPt.fY > sub[2].fY || (topPt.fY == sub[2].fY && topPt.fX > sub[2].fX)) {
+        topPt = sub[2];
+    }
+    if (!between(sub[0].fY, sub[1].fY, sub[2].fY)) {
+        double extremeT;
+        if (FindExtrema(&sub[0].fY, sub.fWeight, &extremeT)) {
+            extremeT = startT + (endT - startT) * extremeT;
+            SkDPoint test = ptAtT(extremeT);
+            if (topPt.fY > test.fY || (topPt.fY == test.fY && topPt.fX > test.fX)) {
+                topPt = test;
+            }
+        }
+    }
+    return topPt;
+}
+
+/* see quad subdivide for rationale */
+SkDConic SkDConic::subDivide(double t1, double t2) const {
+    double ax = conic_eval_numerator(&fPts[0].fX, fWeight, t1);
+    double ay = conic_eval_numerator(&fPts[0].fY, fWeight, t1);
+    double az = conic_eval_denominator(fWeight, t1);
+    double midT = (t1 + t2) / 2;
+    double dx = conic_eval_numerator(&fPts[0].fX, fWeight, midT);
+    double dy = conic_eval_numerator(&fPts[0].fY, fWeight, midT);
+    double dz = conic_eval_denominator(fWeight, midT);
+    double cx = conic_eval_numerator(&fPts[0].fX, fWeight, t2);
+    double cy = conic_eval_numerator(&fPts[0].fY, fWeight, t2);
+    double cz = conic_eval_denominator(fWeight, t2);
+    double bx = 2 * dx - (ax + cx) / 2;
+    double by = 2 * dy - (ay + cy) / 2;
+    double bz = 2 * dz - (az + cz) / 2;
+    double dt = t2 - t1;
+    double dt_1 = 1 - dt;
+    SkScalar w = SkDoubleToScalar((1 + dt * (fWeight - 1))
+            / sqrt(dt * dt + 2 * dt * dt_1 * fWeight + dt_1 * dt_1));
+    SkDConic dst = {{{{ax / az, ay / az}, {bx / bz, by / bz}, {cx / cz, cy / cz}}}, w };
+    return dst;
+}
+
+SkDPoint SkDConic::subDivide(const SkDPoint& a, const SkDPoint& c, double t1, double t2,
+        SkScalar* weight) const {
+    SkDConic chopped = this->subDivide(t1, t2);
+    *weight = chopped.fWeight;
+    return chopped[1];
+}