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Clean-up PathFitter code.
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@lehni
lehni committed Feb 9, 2016
1 parent d1b11c6 commit e5d139c
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Showing 2 changed files with 57 additions and 54 deletions.
8 changes: 4 additions & 4 deletions src/path/Path.js
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Original file line number Diff line number Diff line change
Expand Up @@ -1332,10 +1332,10 @@ var Path = PathItem.extend(/** @lends Path# */{
* }
*/
simplify: function(tolerance) {
if (this._segments.length > 2) {
var fitter = new PathFitter(this, tolerance || 2.5);
this.setSegments(fitter.fit());
}
var segments = new PathFitter(this).fit(tolerance || 2.5);
if (segments)
this.setSegments(segments);
return !!segments;
},

// NOTE: Documentation is in PathItem#smooth()
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103 changes: 53 additions & 50 deletions src/path/PathFitter.js
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Original file line number Diff line number Diff line change
Expand Up @@ -13,82 +13,82 @@
// An Algorithm for Automatically Fitting Digitized Curves
// by Philip J. Schneider
// from "Graphics Gems", Academic Press, 1990
// Modifications and optimisations of original algorithm by Juerg Lehni.
// Modifications and optimizations of original algorithm by Juerg Lehni.

/**
* @name PathFitter
* @class
* @private
*/
var PathFitter = Base.extend({
initialize: function(path, error) {
initialize: function(path) {
var points = this.points = [],
segments = path._segments,
prev;
closed = path._closed;
// Copy over points from path and filter out adjacent duplicates.
for (var i = 0, l = segments.length; i < l; i++) {
var point = segments[i].point.clone();
for (var i = 0, prev, l = segments.length; i < l; i++) {
var point = segments[i].point;
if (!prev || !prev.equals(point)) {
points.push(point);
prev = point;
points.push(prev = point.clone());
}
}

// We need to duplicate the first and last segment when simplifying a
// closed path.
if (path._closed) {
this.closed = true;
if (closed) {
points.unshift(points[points.length - 1]);
points.push(points[1]); // The point previously at index 0 is now 1.
}

this.error = error;
this.closed = closed;
},

fit: function() {
fit: function(error) {
var points = this.points,
length = points.length,
segments = this.segments = length > 0
? [new Segment(points[0])] : [];
if (length > 1)
this.fitCubic(0, length - 1,
// Left Tangent
points[1].subtract(points[0]).normalize(),
// Right Tangent
points[length - 2].subtract(points[length - 1]).normalize());

// Remove the duplicated segments for closed paths again.
if (this.closed) {
segments.shift();
segments.pop();
segments = null;
if (length > 0) {
// To support reducing paths with multiple points in the same place
// to one segment:
segments = [new Segment(points[0])];
if (length > 1) {
this.fitCubic(segments, error, 0, length - 1,
// Left Tangent
points[1].subtract(points[0]).normalize(),
// Right Tangent
points[length - 2].subtract(points[length - 1]).normalize());
// Remove the duplicated segments for closed paths again.
if (this.closed) {
segments.shift();
segments.pop();
}
}
}

return segments;
},

// Fit a Bezier curve to a (sub)set of digitized points
fitCubic: function(first, last, tan1, tan2) {
fitCubic: function(segments, error, first, last, tan1, tan2) {
var points = this.points;
// Use heuristic if region only has two points in it
if (last - first == 1) {
var pt1 = this.points[first],
pt2 = this.points[last],
if (last - first === 1) {
var pt1 = points[first],
pt2 = points[last],
dist = pt1.getDistance(pt2) / 3;
this.addCurve([pt1, pt1.add(tan1.normalize(dist)),
this.addCurve(segments, [pt1, pt1.add(tan1.normalize(dist)),
pt2.add(tan2.normalize(dist)), pt2]);
return;
}
// Parameterize points, and attempt to fit curve
var uPrime = this.chordLengthParameterize(first, last),
maxError = Math.max(this.error, this.error * this.error),
maxError = Math.max(error, error * error),
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 && parametersInOrder) {
this.addCurve(curve);
if (max.error < error && parametersInOrder) {
this.addCurve(segments, curve);
return;
}
split = max.index;
Expand All @@ -99,24 +99,25 @@ var PathFitter = Base.extend({
maxError = max.error;
}
// Fitting failed -- split at max error point and fit recursively
var tanCenter = this.points[split - 1].subtract(this.points[split + 1])
var tanCenter = points[split - 1].subtract(points[split + 1])
.normalize();
this.fitCubic(first, split, tan1, tanCenter);
this.fitCubic(split, last, tanCenter.negate(), tan2);
this.fitCubic(segments, error, first, split, tan1, tanCenter);
this.fitCubic(segments, error, split, last, tanCenter.negate(), tan2);
},

addCurve: function(curve) {
var prev = this.segments[this.segments.length - 1];
addCurve: function(segments, curve) {
var prev = segments[segments.length - 1];
prev.setHandleOut(curve[1].subtract(curve[0]));
this.segments.push(
new Segment(curve[3], curve[2].subtract(curve[3])));
segments.push(new Segment(curve[3], curve[2].subtract(curve[3])));
},

// Use least-squares method to find Bezier control points for region.
generateBezier: function(first, last, uPrime, tan1, tan2) {
var epsilon = /*#=*/Numerical.EPSILON,
pt1 = this.points[first],
pt2 = this.points[last],
abs = Math.abs,
points = this.points,
pt1 = points[first],
pt2 = points[last],
// Create the C and X matrices
C = [[0, 0], [0, 0]],
X = [0, 0];
Expand All @@ -131,7 +132,7 @@ var PathFitter = Base.extend({
b3 = u * u * u,
a1 = tan1.normalize(b1),
a2 = tan2.normalize(b2),
tmp = this.points[first + i]
tmp = points[first + i]
.subtract(pt1.multiply(b0 + b1))
.subtract(pt2.multiply(b2 + b3));
C[0][0] += a1.dot(a1);
Expand All @@ -146,7 +147,7 @@ var PathFitter = Base.extend({
// Compute the determinants of C and X
var detC0C1 = C[0][0] * C[1][1] - C[1][0] * C[0][1],
alpha1, alpha2;
if (Math.abs(detC0C1) > epsilon) {
if (abs(detC0C1) > epsilon) {
// Kramer's rule
var detC0X = C[0][0] * X[1] - C[1][0] * X[0],
detXC1 = X[0] * C[1][1] - X[1] * C[0][1];
Expand All @@ -157,9 +158,9 @@ var PathFitter = Base.extend({
// Matrix is under-determined, try assuming alpha1 == alpha2
var c0 = C[0][0] + C[0][1],
c1 = C[1][0] + C[1][1];
if (Math.abs(c0) > epsilon) {
if (abs(c0) > epsilon) {
alpha1 = alpha2 = X[0] / c0;
} else if (Math.abs(c1) > epsilon) {
} else if (abs(c1) > epsilon) {
alpha1 = alpha2 = X[1] / c1;
} else {
// Handle below
Expand Down Expand Up @@ -195,8 +196,10 @@ var PathFitter = Base.extend({

// First and last control points of the Bezier curve are
// positioned exactly at the first and last data points
return [pt1, pt1.add(handle1 || tan1.normalize(alpha1)),
pt2.add(handle2 || tan2.normalize(alpha2)), pt2];
return [pt1,
pt1.add(handle1 || tan1.normalize(alpha1)),
pt2.add(handle2 || tan2.normalize(alpha2)),
pt2];
},

// Given set of points and their parameterization, try to find
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