From a9a0857ba41f2fac0253e62103c0a77528333cc2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?J=C3=BCrg=20Lehni?= <juerg@scratchdisk.com>
Date: Tue, 9 Apr 2013 20:27:55 -0700
Subject: [PATCH] Find a better strategy to avoid duplicate solutions in
 PathItem#getIntersections().

Closes #197.
---
 src/basic/Rectangle.js |  8 ++++++++
 src/path/Curve.js      | 26 +++++++++++---------------
 src/path/PathItem.js   |  2 +-
 3 files changed, 20 insertions(+), 16 deletions(-)

diff --git a/src/basic/Rectangle.js b/src/basic/Rectangle.js
index 0c55b058..c4448de3 100644
--- a/src/basic/Rectangle.js
+++ b/src/basic/Rectangle.js
@@ -596,6 +596,14 @@ var Rectangle = this.Rectangle = Base.extend(/** @lends Rectangle# */{
 				&& rect.y < this.y + this.height;
 	},
 
+	touches: function(rect) {
+		rect = Rectangle.read(arguments);
+		return rect.x + rect.width >= this.x
+				&& rect.y + rect.height >= this.y
+				&& rect.x <= this.x + this.width
+				&& rect.y <= this.y + this.height;
+	},
+
 	/**
 	 * {@grouptitle Boolean Operations}
 	 *
diff --git a/src/path/Curve.js b/src/path/Curve.js
index 33959972..d5684640 100644
--- a/src/path/Curve.js
+++ b/src/path/Curve.js
@@ -650,15 +650,7 @@ statics: {
 			strokeWidth: 0.1
 		});
 /*#*/ }
-		// We are not using Rectangle#intersects() here, since in order to
-		// detect intersections that lie on curve bounds, we need to consider
-		// touching on one side of the tested rectangles as intersection as well
-		// If touch is condired at both sides, solutions lying on the border of
-		// bounds would turn up twice.
-		if (bounds1.x + bounds1.width >= bounds2.x
-				&& bounds1.y + bounds1.height >= bounds2.y
-				&& bounds1.x < bounds2.x + bounds2.width
-				&& bounds1.y < bounds2.y + bounds2.height) {
+		if (bounds1.touches(bounds2)) {
 			// See if both curves are flat enough to be treated as lines.
 			if (Curve.isFlatEnough(v1, /*#=*/ Numerical.TOLERANCE)
 					&& Curve.isFlatEnough(v2, /*#=*/ Numerical.TOLERANCE)) {
@@ -673,12 +665,16 @@ statics: {
 				});
 /*#*/ }
 				// See if the parametric equations of the lines interesct.
-				var point = new Line(v1[0], v1[1], v1[6], v1[7], false)
-						.intersect(new Line(v2[0], v2[1], v2[6], v2[7], false));
-				// Passing null for parameter leads to lazy determination of
-				// parameter values in CurveLocation#getParameter() only once
-				// they are requested.
-				if (point)
+				var line1 = new Line(v1[0], v1[1], v1[6], v1[7], false),
+					line2 = new Line(v2[0], v2[1], v2[6], v2[7], false),
+					point = line1.intersect(line2);
+				// Filter out beginnings of the curves, to avoid duplicate
+				// solutions where curves join.
+				if (point && !point.equals(line1.point)
+						&& !point.equals(line2.point))
+					// Passing null for parameter leads to lazy determination of
+					// parameter values in CurveLocation#getParameter() only
+					// once they are requested.
 					locations.push(new CurveLocation(curve, null, point));
 			} else {
 				// Subdivide both curves, and see if they intersect.
diff --git a/src/path/PathItem.js b/src/path/PathItem.js
index 960b664f..72b40693 100644
--- a/src/path/PathItem.js
+++ b/src/path/PathItem.js
@@ -57,7 +57,7 @@ var PathItem = this.PathItem = Item.extend(/** @lends PathItem# */{
 	getIntersections: function(path) {
 		// First check the bounds of the two paths. If they don't intersect,
 		// we don't need to iterate through their curves.
-		if (!this.getBounds().intersects(path.getBounds()))
+		if (!this.getBounds().touches(path.getBounds()))
 			return [];
 		var locations = [],
 			curves1 = this.getCurves(),