From bf9acd4499f52158c7709e0cea4de7cb3e3c1918 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?J=C3=BCrg=20Lehni?= <juerg@scratchdisk.com>
Date: Fri, 19 Apr 2013 18:57:31 -0700
Subject: [PATCH] Correct Numerical.KAPPA value.

---
 src/item/Shape.js             | 10 +++++-----
 src/path/Path.Constructors.js |  2 +-
 src/svg/SvgExport.js          |  7 ++++---
 src/util/Numerical.js         |  2 +-
 4 files changed, 11 insertions(+), 10 deletions(-)

diff --git a/src/item/Shape.js b/src/item/Shape.js
index 6d8f7821..580c4124 100644
--- a/src/item/Shape.js
+++ b/src/item/Shape.js
@@ -43,11 +43,11 @@ var Shape = this.Shape = Item.extend(/** @lends Shape# */{
 				ctx.arc(0, 0, width, 0, Math.PI * 2, true);
 				break;
 			case 'ellipse':
-				var kappa = Numerical.KAPPA,
-					cx = width * kappa,
-					cy = height * kappa,
-					mx = width / 2,
-					my = height / 2;
+				var mx = width / 2,
+					my = height / 2,
+					kappa = Numerical.KAPPA,
+					cx = mx * kappa,
+					cy = my * kappa;
 				ctx.moveTo(0, my);
 				ctx.bezierCurveTo(0, my - cy, mx - cx, 0, mx, 0);
 				ctx.bezierCurveTo(mx + cx, 0, width, my - cy, width, my);
diff --git a/src/path/Path.Constructors.js b/src/path/Path.Constructors.js
index ce4e7dae..2a6fb34f 100644
--- a/src/path/Path.Constructors.js
+++ b/src/path/Path.Constructors.js
@@ -56,7 +56,7 @@ Path.inject({ statics: new function() {
 		return path;
 	}
 
-	var kappa = Numerical.KAPPA;
+	var kappa = Numerical.KAPPA / 2;
 
 	var ellipseSegments = [
 		new Segment([0, 0.5], [0, kappa ], [0, -kappa]),
diff --git a/src/svg/SvgExport.js b/src/svg/SvgExport.js
index 002c7349..8d9082ad 100644
--- a/src/svg/SvgExport.js
+++ b/src/svg/SvgExport.js
@@ -120,7 +120,8 @@ new function() {
 			var segment = segments[i],
 				next = segment.getNext(),
 				handle1 = segment._handleOut,
-				handle2 = next._handleIn;
+				handle2 = next._handleIn,
+				kappa = Numerical.KAPPA;
 			if (handle1.isOrthogonal(handle2)) {
 				var from = segment._point,
 					to = next._point,
@@ -129,9 +130,9 @@ new function() {
 					corner = new Line(from, handle1).intersect(
 							new Line(to, handle2));
 				return corner && Numerical.isZero(handle1.getLength() /
-						corner.subtract(from).getLength() - Numerical.KAPPA)
+						corner.subtract(from).getLength() - kappa)
 					&& Numerical.isZero(handle2.getLength() /
-						corner.subtract(to).getLength() - Numerical.KAPPA);
+						corner.subtract(to).getLength() - kappa);
 			}
 		}
 
diff --git a/src/util/Numerical.js b/src/util/Numerical.js
index 5c530064..a13f5f16 100644
--- a/src/util/Numerical.js
+++ b/src/util/Numerical.js
@@ -69,7 +69,7 @@ var Numerical = this.Numerical = new function() {
 		// TODO: Find a good value
 		EPSILON: 10e-12,
 		// Kappa, see: http://www.whizkidtech.redprince.net/bezier/circle/kappa/
-		KAPPA: 2 * (sqrt(2) - 1) / 3,
+		KAPPA: 4 * (sqrt(2) - 1) / 3,
 
 		/**
 		 * Check if the value is 0, within a tolerance defined by