Add base types for path ops

src/pathops/SkPathOpsTriangle.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 "SkPathOpsTriangle.h"
+
+// http://www.blackpawn.com/texts/pointinpoly/default.html
+bool SkDTriangle::contains(const SkDPoint& pt) const {
+// Compute vectors
+    SkDVector v0 = fPts[2] - fPts[0];
+    SkDVector v1 = fPts[1] - fPts[0];
+    SkDVector v2 = pt - fPts[0];
+
+// Compute dot products
+    double dot00 = v0.dot(v0);
+    double dot01 = v0.dot(v1);
+    double dot02 = v0.dot(v2);
+    double dot11 = v1.dot(v1);
+    double dot12 = v1.dot(v2);
+
+// Compute barycentric coordinates
+    double invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
+    double u = (dot11 * dot02 - dot01 * dot12) * invDenom;
+    double v = (dot00 * dot12 - dot01 * dot02) * invDenom;
+
+// Check if point is in triangle
+    return (u >= 0) && (v >= 0) && (u + v < 1);

[whunt, 2013/03/22 18:16:06]

should be u + v <= 1 if you want to include all three edges. (It's perfectly
reasonable for the 3rd bary to be 0)

[reed1, 2013/03/22 19:00:37]

u + v <= 1

This doesn't catch if u or v are negative. Are those still considered in the
triangle?

[whunt, 2013/03/22 19:37:28]

u and v can't be negative... you check for that

[caryclark, 2013/03/22 19:38:51]

Hmm. I am only concerned with rejecting edges that are outside the triangle.
That said, this is part of a quick reject so it's hard to see when <= vs. < is
really relevant. I'll create some test cases and investigate further.

+}