From fb5f8c011501a7b55ba2dd0e4c6abd1e288eb23e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?J=C3=BCrg=20Lehni?= <juerg@scratchdisk.com>
Date: Sat, 12 Sep 2015 10:35:47 +0200
Subject: [PATCH] Introduce GEOMETRIC_EPSILON, for isOrthogonal(),
 isCollinear() and overlap checks.

Relates to #777
---
 src/basic/Line.js     |  4 +---
 src/basic/Point.js    | 10 ++--------
 src/path/Curve.js     |  2 +-
 src/path/Path.js      |  3 +--
 src/util/Numerical.js |  1 +
 5 files changed, 6 insertions(+), 14 deletions(-)

diff --git a/src/basic/Line.js b/src/basic/Line.js
index 28c6883c..a31b2f28 100644
--- a/src/basic/Line.js
+++ b/src/basic/Line.js
@@ -113,10 +113,8 @@ var Line = Base.extend(/** @lends Line# */{
     },
 
     isCollinear: function(line) {
-        // TODO: Tests showed that 1e-10 might work well here, but we want to
-        // keep it in sync with Point#isCollinear()
         return this._vx * line._vy - this._vy * line._vx
-                < /*#=*/Numerical.TOLERANCE;
+                < /*#=*/Numerical.GEOMETRIC_EPSILON;
     },
 
     statics: /** @lends Line */{
diff --git a/src/basic/Point.js b/src/basic/Point.js
index d96e08e8..e2cd6b43 100644
--- a/src/basic/Point.js
+++ b/src/basic/Point.js
@@ -702,10 +702,7 @@ var Point = Base.extend(/** @lends Point# */{
      * @return {Boolean} {@true it is collinear}
      */
     isCollinear: function(point) {
-        // NOTE: Numerical.EPSILON is too small, breaking shape-path-shape
-        // conversion test. But tolerance is probably too large?
-        // TODO: Tests showed that 1e-10 might work well here.
-        return Math.abs(this.cross(point)) < /*#=*/Numerical.TOLERANCE;
+        return Math.abs(this.cross(point)) < /*#=*/Numerical.GEOMETRIC_EPSILON;
     },
 
     // TODO: Remove version with typo after a while (deprecated June 2015)
@@ -719,10 +716,7 @@ var Point = Base.extend(/** @lends Point# */{
      * @return {Boolean} {@true it is orthogonal}
      */
     isOrthogonal: function(point) {
-        // NOTE: Numerical.EPSILON is too small, breaking shape-path-shape
-        // conversion test.
-        // TODO: Test if 1e-10 works here too? See #isCollinear()
-        return Math.abs(this.dot(point)) < /*#=*/Numerical.TOLERANCE;
+        return Math.abs(this.dot(point)) < /*#=*/Numerical.GEOMETRIC_EPSILON;
     },
 
     /**
diff --git a/src/path/Curve.js b/src/path/Curve.js
index b9bbea51..cd4c76e3 100644
--- a/src/path/Curve.js
+++ b/src/path/Curve.js
@@ -1614,7 +1614,7 @@ new function() { // Scope for intersection using bezier fat-line clipping
             var line1 = new Line(v1[0], v1[1], v1[6], v1[7]),
                 line2 = new Line(v2[0], v2[1], v2[6], v2[7]);
             if (!line1.isCollinear(line2) || line1.getDistance(line2.getPoint())
-                    > /*#=*/Numerical.GEOMETRY_TOLERANCE)
+                    > /*#=*/Numerical.GEOMETRIC_EPSILON)
                 return false;
         } else if (straight1 ^ straight2) {
             // If one curve is straight, the other curve must be straight, too,
diff --git a/src/path/Path.js b/src/path/Path.js
index 0bc06d55..e56137a5 100644
--- a/src/path/Path.js
+++ b/src/path/Path.js
@@ -2502,7 +2502,6 @@ new function() { // PostScript-style drawing commands
                     x = pt.x,
                     y = pt.y,
                     abs = Math.abs,
-                    epsilon = /*#=*/Numerical.EPSILON,
                     rx = abs(radius.width),
                     ry = abs(radius.height),
                     rxSq = rx * rx,
@@ -2519,7 +2518,7 @@ new function() { // PostScript-style drawing commands
                 }
                 factor = (rxSq * rySq - rxSq * ySq - rySq * xSq) /
                         (rxSq * ySq + rySq * xSq);
-                if (abs(factor) < epsilon)
+                if (abs(factor) < /*#=*/Numerical.EPSILON)
                     factor = 0;
                 if (factor < 0)
                     throw new Error(
diff --git a/src/util/Numerical.js b/src/util/Numerical.js
index ed5cc1eb..8bfbc0a5 100644
--- a/src/util/Numerical.js
+++ b/src/util/Numerical.js
@@ -81,6 +81,7 @@ var Numerical = new function() {
          * range (see MACHINE_EPSILON).
          */
         EPSILON: EPSILON,
+        GEOMETRIC_EPSILON: 1e-9,
         /**
          * MACHINE_EPSILON for a double precision (Javascript Number) is
          * 2.220446049250313e-16. (try this in the js console)