use pathops utils to improve precision of cubic chopping in scan converter

BUG=skia:

Review URL: https://codereview.chromium.org/1113963002
diff --git a/src/core/SkEdgeClipper.cpp b/src/core/SkEdgeClipper.cpp
index 32277bc..87bfbb9 100644
--- a/src/core/SkEdgeClipper.cpp
+++ b/src/core/SkEdgeClipper.cpp
@@ -225,6 +225,7 @@
 
 ///////////////////////////////////////////////////////////////////////////////
 
+#ifdef SK_SUPPORT_LEGACY_CUBIC_CHOPPER
 static SkScalar eval_cubic_coeff(SkScalar A, SkScalar B, SkScalar C,
                                  SkScalar D, SkScalar t) {
     return SkScalarMulAdd(SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C), t, D);
@@ -274,23 +275,29 @@
 static bool chopMonoCubicAtX(SkPoint pts[4], SkScalar x, SkScalar* t) {
     return chopMonoCubicAt(pts[0].fX, pts[1].fX, pts[2].fX, pts[3].fX, x, t);
 }
+#endif
 
 // Modify pts[] in place so that it is clipped in Y to the clip rect
 static void chop_cubic_in_Y(SkPoint pts[4], const SkRect& clip) {
 
     // are we partially above
     if (pts[0].fY < clip.fTop) {
+        SkPoint tmp[7];
+#ifdef SK_SUPPORT_LEGACY_CUBIC_CHOPPER
         SkScalar t;
         if (chopMonoCubicAtY(pts, clip.fTop, &t)) {
-            SkPoint tmp[7];
             SkChopCubicAt(pts, tmp, t);
-
-            // tmp[3, 4, 5].fY should all be to the below clip.fTop.
+#else
+        if (SkChopMonoCubicAtY(pts, clip.fTop, tmp)) {
+#endif
+            // tmp[3, 4].fY should all be to the below clip.fTop.
             // Since we can't trust the numerics of
             // the chopper, we force those conditions now
             tmp[3].fY = clip.fTop;
             clamp_ge(tmp[4].fY, clip.fTop);
+#ifdef SK_SUPPORT_LEGACY_CUBIC_CHOPPER
             clamp_ge(tmp[5].fY, clip.fTop);
+#endif
 
             pts[0] = tmp[3];
             pts[1] = tmp[4];
@@ -306,10 +313,14 @@
 
     // are we partially below
     if (pts[3].fY > clip.fBottom) {
+        SkPoint tmp[7];
+#ifdef SK_SUPPORT_LEGACY_CUBIC_CHOPPER
         SkScalar t;
         if (chopMonoCubicAtY(pts, clip.fBottom, &t)) {
-            SkPoint tmp[7];
             SkChopCubicAt(pts, tmp, t);
+#else
+        if (SkChopMonoCubicAtY(pts, clip.fBottom, tmp)) {
+#endif
             tmp[3].fY = clip.fBottom;
             clamp_le(tmp[2].fY, clip.fBottom);
 
@@ -360,18 +371,24 @@
 
     // are we partially to the left
     if (pts[0].fX < clip.fLeft) {
+        SkPoint tmp[7];
+#ifdef SK_SUPPORT_LEGACY_CUBIC_CHOPPER
         SkScalar t;
         if (chopMonoCubicAtX(pts, clip.fLeft, &t)) {
-            SkPoint tmp[7];
             SkChopCubicAt(pts, tmp, t);
+#else
+        if (SkChopMonoCubicAtX(pts, clip.fLeft, tmp)) {
+#endif
             this->appendVLine(clip.fLeft, tmp[0].fY, tmp[3].fY, reverse);
 
-            // tmp[3, 4, 5].fX should all be to the right of clip.fLeft.
+            // tmp[3, 4].fX should all be to the right of clip.fLeft.
             // Since we can't trust the numerics of
             // the chopper, we force those conditions now
             tmp[3].fX = clip.fLeft;
             clamp_ge(tmp[4].fX, clip.fLeft);
+#ifdef SK_SUPPORT_LEGACY_CUBIC_CHOPPER
             clamp_ge(tmp[5].fX, clip.fLeft);
+#endif
 
             pts[0] = tmp[3];
             pts[1] = tmp[4];
@@ -386,13 +403,19 @@
 
     // are we partially to the right
     if (pts[3].fX > clip.fRight) {
+        SkPoint tmp[7];
+#ifdef SK_SUPPORT_LEGACY_CUBIC_CHOPPER
         SkScalar t;
         if (chopMonoCubicAtX(pts, clip.fRight, &t)) {
-            SkPoint tmp[7];
             SkChopCubicAt(pts, tmp, t);
+#else
+        if (SkChopMonoCubicAtX(pts, clip.fRight, tmp)) {
+#endif
             tmp[3].fX = clip.fRight;
             clamp_le(tmp[2].fX, clip.fRight);
+#ifdef SK_SUPPORT_LEGACY_CUBIC_CHOPPER
             clamp_le(tmp[1].fX, clip.fRight);
+#endif
 
             this->appendCubic(tmp, reverse);
             this->appendVLine(clip.fRight, tmp[3].fY, tmp[6].fY, reverse);
diff --git a/src/core/SkGeometry.cpp b/src/core/SkGeometry.cpp
index b9366f3..671a1ea 100644
--- a/src/core/SkGeometry.cpp
+++ b/src/core/SkGeometry.cpp
@@ -916,6 +916,33 @@
     return count + 1;
 }
 
+#include "../pathops/SkPathOpsCubic.h"
+
+typedef int (SkDCubic::*InterceptProc)(double intercept, double roots[3]) const;
+
+static bool cubic_dchop_at_intercept(const SkPoint src[4], SkScalar intercept, SkPoint dst[7],
+                                     InterceptProc method) {
+    SkDCubic cubic;
+    double roots[3];
+    int count = (cubic.set(src).*method)(intercept, roots);
+    if (count > 0) {
+        SkDCubicPair pair = cubic.chopAt(roots[0]);
+        for (int i = 0; i < 7; ++i) {
+            dst[i] = pair.pts[i].asSkPoint();
+        }
+        return true;
+    }
+    return false;
+}
+
+bool SkChopMonoCubicAtY(SkPoint src[4], SkScalar y, SkPoint dst[7]) {
+    return cubic_dchop_at_intercept(src, y, dst, &SkDCubic::horizontalIntersect);
+}
+
+bool SkChopMonoCubicAtX(SkPoint src[4], SkScalar x, SkPoint dst[7]) {
+    return cubic_dchop_at_intercept(src, x, dst, &SkDCubic::verticalIntersect);
+}
+
 ///////////////////////////////////////////////////////////////////////////////
 
 /*  Find t value for quadratic [a, b, c] = d.
diff --git a/src/core/SkGeometry.h b/src/core/SkGeometry.h
index 811678e..a0c13d6 100644
--- a/src/core/SkGeometry.h
+++ b/src/core/SkGeometry.h
@@ -166,6 +166,9 @@
 int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13],
                               SkScalar tValues[3] = NULL);
 
+bool SkChopMonoCubicAtX(SkPoint src[4], SkScalar y, SkPoint dst[7]);
+bool SkChopMonoCubicAtY(SkPoint src[4], SkScalar x, SkPoint dst[7]);
+
 enum SkCubicType {
     kSerpentine_SkCubicType,
     kCusp_SkCubicType,
diff --git a/src/pathops/SkDCubicLineIntersection.cpp b/src/pathops/SkDCubicLineIntersection.cpp
index f658b09..ee1e3d3 100644
--- a/src/pathops/SkDCubicLineIntersection.cpp
+++ b/src/pathops/SkDCubicLineIntersection.cpp
@@ -425,3 +425,13 @@
     }
     return fUsed;
 }
+
+// SkDCubic accessors to Intersection utilities
+
+int SkDCubic::horizontalIntersect(double yIntercept, double roots[3]) const {
+    return LineCubicIntersections::HorizontalIntersect(*this, yIntercept, roots);
+}
+
+int SkDCubic::verticalIntersect(double xIntercept, double roots[3]) const {
+    return LineCubicIntersections::VerticalIntersect(*this, xIntercept, roots);
+}
diff --git a/src/pathops/SkPathOpsCubic.h b/src/pathops/SkPathOpsCubic.h
index f9d2910..3d68151 100644
--- a/src/pathops/SkPathOpsCubic.h
+++ b/src/pathops/SkPathOpsCubic.h
@@ -97,6 +97,17 @@
     int searchRoots(double extremes[6], int extrema, double axisIntercept,
                     SearchAxis xAxis, double* validRoots) const;
 
+    /**
+     *  Return the number of valid roots (0 < root < 1) for this cubic intersecting the
+     *  specified horizontal line.
+     */
+    int horizontalIntersect(double yIntercept, double roots[3]) const;
+    /**
+     *  Return the number of valid roots (0 < root < 1) for this cubic intersecting the
+     *  specified vertical line.
+     */
+    int verticalIntersect(double xIntercept, double roots[3]) const;
+
     const SkDCubic& set(const SkPoint pts[kPointCount]) {
         fPts[0] = pts[0];
         fPts[1] = pts[1];