compute split conic endpoints exactly

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"
@@ skipping 56 matching lines @@
     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 {
+    if (t == 0) {
+        return fPts[0];
+    }
+    if (t == 1) {
+        return fPts[2];
+    }
     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;
 }
 
 /* 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 ax, ay, az;
+    if (t1 == 0) {
+        ax = fPts[0].fX;
+        ay = fPts[0].fY;
+        az = 1;
+    } else if (t1 != 1) {
+        ax = conic_eval_numerator(&fPts[0].fX, fWeight, t1);
+        ay = conic_eval_numerator(&fPts[0].fY, fWeight, t1);
+        az = conic_eval_denominator(fWeight, t1);
+    } else {
+        ax = fPts[2].fX;
+        ay = fPts[2].fY;
+        az = 1;
+    }
     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 cx, cy, cz;
+    if (t2 == 1) {
+        cx = fPts[2].fX;
+        cy = fPts[2].fY;
+        cz = 1;
+    } else if (t2 != 0) {
+        cx = conic_eval_numerator(&fPts[0].fX, fWeight, t2);
+        cy = conic_eval_numerator(&fPts[0].fY, fWeight, t2);
+        cz = conic_eval_denominator(fWeight, t2);
+    } else {
+        cx = fPts[0].fX;
+        cy = fPts[0].fY;
+        cz = 1;
+    }
     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];
 }