From 6dd7cc5b6a22117afcff4b6c39f9a0ca3feed755 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?J=C3=BCrg=20Lehni?= <juerg@scratchdisk.com>
Date: Sat, 24 Sep 2016 15:39:09 -0400
Subject: [PATCH] Fix imprecision in Numerical.findRoot()

Results can be slightly outside of the range.
Close #1149
---
 src/util/Numerical.js |  9 ++++++---
 test/tests/Curve.js   | 34 ++++++++++++++++++++--------------
 2 files changed, 26 insertions(+), 17 deletions(-)

diff --git a/src/util/Numerical.js b/src/util/Numerical.js
index fe6cd0dc..fa239e06 100644
--- a/src/util/Numerical.js
+++ b/src/util/Numerical.js
@@ -216,8 +216,10 @@ var Numerical = new function() {
                     nx = x - dx;
                 // See if we can trust the Newton-Raphson result. If not we use
                 // bisection to find another candidate for Newton's method.
-                if (abs(dx) < tolerance)
-                    return nx;
+                if (abs(dx) < tolerance) {
+                    x = nx;
+                    break;
+                }
                 // Update the root-bounding interval and test for containment of
                 // the candidate. If candidate is outside the root-bounding
                 // interval, use bisection instead.
@@ -234,7 +236,8 @@ var Numerical = new function() {
             }
             // Return the best result even though we haven't gotten close
             // enough to the root... (In paper.js this never seems to happen).
-            return x;
+            // But make sure, that it actually is within the given range [a, b]
+            return clamp(x, a, b);
         },
 
         /**
diff --git a/test/tests/Curve.js b/test/tests/Curve.js
index 946941ed..81bc5aa8 100644
--- a/test/tests/Curve.js
+++ b/test/tests/Curve.js
@@ -192,6 +192,25 @@ test('Curve#getTimeAt() with straight curve', function() {
     equals(t, 0.3869631475722452);
 });
 
+test('Curve#getTimeAt() with straight curve', function() {
+    // #1000:
+    var curve = new Curve([
+        1584.4999999999998, 1053.2499999999995,
+        1584.4999999999998,1053.2499999999995,
+        1520.5,1053.2499999999995,
+        1520.5,1053.2499999999995
+    ]);
+    var offset = 63.999999999999716;
+    equals(function() { return offset < curve.length; }, true);
+    equals(function() { return curve.getTimeAt(offset); }, 1);
+});
+
+test('Curve#getTimeAt() with offset at end of curve', function() {
+    // #1149:
+    var curve = [-7500, 0, -7500, 4142.135623730952, -4142.135623730952, 7500, 0, 7500];
+    equals(Curve.getTimeAt(curve, 11782.625235553916), 1);
+});
+
 test('Curve#getLocationAt()', function() {
     var curve = new Path([
         [[0, 0], [0, 0], [100, 0]],
@@ -248,7 +267,7 @@ test('Curve#isLinear()', function() {
 });
 
 test('Curve#getTimeOf()', function() {
-    // For issue #708:
+    // #708:
     var path = new Path.Rectangle({
         center: new Point(300, 100),
         size: new Point(100, 100),
@@ -275,19 +294,6 @@ test('Curve#getTimeOf()', function() {
     }
 });
 
-test('Curve#getTimeAt() with straight curve', function() {
-    // #1000:
-    var curve = new Curve([
-        1584.4999999999998, 1053.2499999999995,
-        1584.4999999999998,1053.2499999999995,
-        1520.5,1053.2499999999995,
-        1520.5,1053.2499999999995
-    ]);
-    var offset = 63.999999999999716;
-    equals(function() { return offset < curve.length; }, true);
-    equals(function() { return curve.getTimeAt(offset); }, 1);
-});
-
 test('Curve#getPartLength() with straight curve', function() {
     var curve = new Curve([0, 0, 0, 0, 64, 0, 64, 0]);
     equals(function() { return curve.getPartLength(0.0, 0.25); }, 10);