Add base types for path ops

Paths contain lines, quads, and cubics, which are
collectively curves.

To work with path intersections, intermediary curves
are constructed. For now, those intermediates use
doubles to guarantee sufficient precision.

The DVector, DPoint, DLine, DQuad, and DCubic
structs encapsulate these intermediate curves.

The DRect and DTriangle structs are created to
describe intersectable areas of interest.

The Bounds struct inherits from SkRect to create
a SkScalar-based rectangle that intersects shared
edges.

This also includes common math equalities and
debugging that the remainder of path ops builds on,
as well as a temporary top-level interface in
include/pathops/SkPathOps.h.
Review URL: https://codereview.chromium.org/12827020

git-svn-id: http://skia.googlecode.com/svn/trunk@8551 2bbb7eff-a529-9590-31e7-b0007b416f81

1 files changed, 110 insertions, 0 deletions

diff --git a/src/pathops/SkLineParameters.h b/src/pathops/SkLineParameters.h
new file mode 100644
index 0000000000..5139c6c6cf
--- /dev/null
+++ b/src/pathops/SkLineParameters.h
@@ -0,0 +1,110 @@
+/*
+ * 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;
+};