From d5c25dbc52ba26f9a5c98226c7a1d96e63c9e4a2 Mon Sep 17 00:00:00 2001
From: Peter Vanbroekhoven <peter@xaop.com>
Date: Sun, 22 Feb 2015 20:05:06 +0100
Subject: [PATCH] Change PathFitter to constrain newly found control points.

See https://github.com/paperjs/paper.js/issues/414 .
---
 src/path/PathFitter.js | 35 ++++++++++++++++++++++++++++-------
 1 file changed, 28 insertions(+), 7 deletions(-)

diff --git a/src/path/PathFitter.js b/src/path/PathFitter.js
index 0abe478f..6780c2f6 100644
--- a/src/path/PathFitter.js
+++ b/src/path/PathFitter.js
@@ -80,13 +80,14 @@ var PathFitter = Base.extend({
         // Parameterize points, and attempt to fit curve
         var uPrime = this.chordLengthParameterize(first, last),
             maxError = Math.max(this.error, this.error * this.error),
-            split;
+            split,
+            parametersInOrder = true;
         // Try 4 iterations
         for (var i = 0; i <= 4; i++) {
             var curve = this.generateBezier(first, last, uPrime, tan1, tan2);
             //  Find max deviation of points to fitted curve
             var max = this.findMaxError(first, last, curve, uPrime);
-            if (max.error < this.error) {
+            if (max.error < this.error && parametersInOrder) {
                 this.addCurve(curve);
                 return;
             }
@@ -94,7 +95,7 @@ var PathFitter = Base.extend({
             // If error not too large, try reparameterization and iteration
             if (max.error >= maxError)
                 break;
-            this.reparameterize(first, last, uPrime, curve);
+            parametersInOrder = this.reparameterize(first, last, uPrime, curve);
             maxError = max.error;
         }
         // Fitting failed -- split at max error point and fit recursively
@@ -178,12 +179,23 @@ var PathFitter = Base.extend({
             alpha1 = alpha2 = segLength / 3;
         }
 
+        // Check if the found control points are in the right order when
+        // projected onto the line through pt1 and pt2.
+        var line = pt2.subtract(pt1),
+            // Control points 1 and 2 are positioned an alpha distance out
+            // on the tangent vectors, left and right, respectively
+            cp1Delta = tan1.normalize(alpha1),
+            cp2Delta = tan2.normalize(alpha2);
+        if (cp1Delta.dot(line) - cp2Delta.dot(line) > segLength * segLength) {
+            // Fall back to the Wu/Barsky heuristic above.
+            alpha1 = alpha2 = segLength / 3;
+            cp1Delta = tan1.normalize(alpha1);
+            cp2Delta = tan2.normalize(alpha2);
+        }
+
         // First and last control points of the Bezier curve are
         // positioned exactly at the first and last data points
-        // Control points 1 and 2 are positioned an alpha distance out
-        // on the tangent vectors, left and right, respectively
-        return [pt1, pt1.add(tan1.normalize(alpha1)),
-                pt2.add(tan2.normalize(alpha2)), pt2];
+        return [pt1, pt1.add(cp1Delta), pt2.add(cp2Delta), pt2];
     },
 
     // Given set of points and their parameterization, try to find
@@ -192,6 +204,15 @@ var PathFitter = Base.extend({
         for (var i = first; i <= last; i++) {
             u[i - first] = this.findRoot(curve, this.points[i], u[i - first]);
         }
+        // Detect if the new parameterization has reordered the points.
+        // In that case, we would fit the points of the path in the
+        // wrong order.
+        for (var j = 1, jLen = u.length; j < jLen; j++) {
+            if (u[j] <= u[j - 1]) {
+              return false;
+            }
+        }
+        return true;
     },
 
     // Use Newton-Raphson iteration to find better root.