From 76ea7ef066c10434957607a2bf157a8a9dce91c4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?J=C3=BCrg=20Lehni?= <juerg@scratchdisk.com>
Date: Tue, 17 Dec 2013 15:27:55 +0100
Subject: [PATCH] Inline EPSILON and TOLERANCE for better performance in
 Numerical.

---
 src/util/Numerical.js | 36 ++++++++++++++++++------------------
 1 file changed, 18 insertions(+), 18 deletions(-)

diff --git a/src/util/Numerical.js b/src/util/Numerical.js
index 0fcf166c..822eb18c 100644
--- a/src/util/Numerical.js
+++ b/src/util/Numerical.js
@@ -56,12 +56,14 @@ var Numerical = new function() {
 		sqrt = Math.sqrt,
 		pow = Math.pow,
 		cos = Math.cos,
-		PI = Math.PI;
+		PI = Math.PI,
+		TOLERANCE = 10e-6,
+		EPSILON = 10e-12;
 
 	return {
-		TOLERANCE: 10e-6,
+		TOLERANCE: TOLERANCE,
 		// Precision when comparing against 0
-		EPSILON: 10e-12,
+		EPSILON: EPSILON,
 		// Kappa, see: http://www.whizkidtech.redprince.net/bezier/circle/kappa/
 		KAPPA: 4 * (sqrt(2) - 1) / 3,
 
@@ -70,7 +72,7 @@ var Numerical = new function() {
 		 * Numerical.EPSILON.
 		 */
 		isZero: function(val) {
-			return abs(val) <= Numerical.EPSILON;
+			return abs(val) <= EPSILON;
 		},
 
 		/**
@@ -127,10 +129,9 @@ var Numerical = new function() {
 		 * a*x^2 + b*x + c = 0
 		 */
 		solveQuadratic: function(a, b, c, roots, min, max) {
-			var epsilon = Numerical.EPSILON,
-				unbound = min === undefined,
-				minE = min - epsilon,
-				maxE = max + epsilon,
+			var unbound = min === undefined,
+				minE = min - EPSILON,
+				maxE = max + EPSILON,
 				count = 0;
 
 			function add(root) {
@@ -141,17 +142,17 @@ var Numerical = new function() {
 
 			// Code ported over and adapted from Uintah library (MIT license).
 			// If a is 0, equation is actually linear, return 0 or 1 easy roots.
-			if (abs(a) < epsilon) {
-				if (abs(b) >= epsilon)
+			if (abs(a) < EPSILON) {
+				if (abs(b) >= EPSILON)
 					return add(-c / b);
 				// If all the coefficients are 0, we have infinite solutions!
-				return abs(c) < epsilon ? -1 : 0; // Infinite or 0 solutions
+				return abs(c) < EPSILON ? -1 : 0; // Infinite or 0 solutions
 			}
 			// Convert to normal form: x^2 + px + q = 0
 			var p = b / (2 * a);
 			var q = c / a;
 			var p2 = p * p;
-			if (p2 < q - epsilon)
+			if (p2 < q - EPSILON)
 				return 0;
 			var s = p2 > q ? sqrt(p2 - q) : 0;
 			add (s - p);
@@ -167,14 +168,13 @@ var Numerical = new function() {
 		 * a*x^3 + b*x^2 + c*x + d = 0
 		 */
 		solveCubic: function(a, b, c, d, roots, min, max) {
-			var epsilon = Numerical.EPSILON;
 			// If a is 0, equation is actually quadratic.
-			if (abs(a) < epsilon)
+			if (abs(a) < EPSILON)
 				return Numerical.solveQuadratic(b, c, d, roots, min, max);
 
 			var unbound = min === undefined,
-				minE = min - epsilon,
-				maxE = max + epsilon,
+				minE = min - EPSILON,
+				maxE = max + EPSILON,
 				count = 0;
 
 			function add(root) {
@@ -197,8 +197,8 @@ var Numerical = new function() {
 				D = q * q - ppp;
 			// Substitute x = y - b/3 to eliminate quadric term: x^3 +px + q = 0
 			b /= 3;
-			if (abs(D) < epsilon) {
-				if (abs(q) < epsilon) // One triple solution.
+			if (abs(D) < EPSILON) {
+				if (abs(q) < EPSILON) // One triple solution.
 					return add(-b);
 				// One single and one double solution.
 				var sqp = sqrt(p),