Add intersections for path ops

src/pathops/SkLineParameters.h

+/*
+ * 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 "SkPathOpsCubic.h"
+#include "SkPathOpsLine.h"
+#include "SkPathOpsQuad.h"
+
+// Sources
+// computer-aided design - volume 22 number 9 november 1990 pp 538 - 549
+// online at http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf
+
+// This turns a line segment into a parameterized line, of the form
+// ax + by + c = 0
+// When a^2 + b^2 == 1, the line is normalized.
+// The distance to the line for (x, y) is d(x,y) = ax + by + c
+//
+// Note that the distances below are not necessarily normalized. To get the true
+// distance, it's necessary to either call normalize() after xxxEndPoints(), or
+// divide the result of xxxDistance() by sqrt(normalSquared())
+
+class SkLineParameters {
+public:
+    void cubicEndPoints(const SkDCubic& pts) {
+        cubicEndPoints(pts, 0, 3);
+    }
+
+    void cubicEndPoints(const SkDCubic& pts, int s, int e) {
+        a = approximately_pin(pts[s].fY - pts[e].fY);
+        b = approximately_pin(pts[e].fX - pts[s].fX);
+        c = pts[s].fX * pts[e].fY - pts[e].fX * pts[s].fY;
+    }
+
+    void lineEndPoints(const SkDLine& pts) {
+        a = approximately_pin(pts[0].fY - pts[1].fY);
+        b = approximately_pin(pts[1].fX - pts[0].fX);
+        c = pts[0].fX * pts[1].fY - pts[1].fX * pts[0].fY;
+    }
+
+    void quadEndPoints(const SkDQuad& pts) {
+        quadEndPoints(pts, 0, 2);
+    }
+
+    void quadEndPoints(const SkDQuad& pts, int s, int e) {
+        a = approximately_pin(pts[s].fY - pts[e].fY);
+        b = approximately_pin(pts[e].fX - pts[s].fX);
+        c = pts[s].fX * pts[e].fY - pts[e].fX * pts[s].fY;
+    }
+
+    double normalSquared() const {
+        return a * a + b * b;
+    }
+
+    bool normalize() {
+        double normal = sqrt(normalSquared());
+        if (approximately_zero(normal)) {
+            a = b = c = 0;
+            return false;
+        }
+        double reciprocal = 1 / normal;
+        a *= reciprocal;
+        b *= reciprocal;
+        c *= reciprocal;
+        return true;
+    }
+
+    void cubicDistanceY(const SkDCubic& pts, SkDCubic& distance) const {
+        double oneThird = 1 / 3.0;
+        for (int index = 0; index < 4; ++index) {
+            distance[index].fX = index * oneThird;
+            distance[index].fY = a * pts[index].fX + b * pts[index].fY + c;
+        }
+    }
+
+    void quadDistanceY(const SkDQuad& pts, SkDQuad& distance) const {
+        double oneHalf = 1 / 2.0;
+        for (int index = 0; index < 3; ++index) {
+            distance[index].fX = index * oneHalf;
+            distance[index].fY = a * pts[index].fX + b * pts[index].fY + c;
+        }
+    }
+
+    double controlPtDistance(const SkDCubic& pts, int index) const {
+        SkASSERT(index == 1 || index == 2);
+        return a * pts[index].fX + b * pts[index].fY + c;
+    }
+
+    double controlPtDistance(const SkDQuad& pts) const {
+        return a * pts[1].fX + b * pts[1].fY + c;
+    }
+
+    double pointDistance(const SkDPoint& pt) const {
+        return a * pt.fX + b * pt.fY + c;
+    }
+
+    double dx() const {
+        return b;
+    }
+
+    double dy() const {
+        return -a;
+    }
+
+private:
+    double a;
+    double b;
+    double c;
+};