mirror of
https://github.com/scratchfoundation/paper.js.git
synced 2025-01-10 06:41:59 -05:00
531 lines
13 KiB
JavaScript
531 lines
13 KiB
JavaScript
/*
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* Paper.js
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*
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* This file is part of Paper.js, a JavaScript Vector Graphics Library,
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* based on Scriptographer.org and designed to be largely API compatible.
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* http://paperjs.org/
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* http://scriptographer.org/
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*
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* Distributed under the MIT license. See LICENSE file for details.
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*
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* Copyright (c) 2011, Juerg Lehni & Jonathan Puckey
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* http://lehni.org/ & http://jonathanpuckey.com/
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*
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* All rights reserved.
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*/
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var Curve = this.Curve = Base.extend({
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/** @lends Curve# */
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beans: true,
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/**
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* Creates a new curve object.
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*
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* @name Curve
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* @constructor
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* @param {Segment} segment1
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* @param {Segment} segment2
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*
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* @class The Curve object represents...
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*/
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initialize: function(arg0, arg1, arg2, arg3) {
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var count = arguments.length;
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if (count == 0) {
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this._segment1 = new Segment();
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this._segment2 = new Segment();
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} else if (count == 1) {
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// TODO: If beans are not activated, this won't copy from
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// an existing segment. OK?
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this._segment1 = new Segment(arg0.segment1);
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this._segment2 = new Segment(arg0.segment2);
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} else if (count == 2) {
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this._segment1 = new Segment(arg0);
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this._segment2 = new Segment(arg1);
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} else if (count == 4) {
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this._segment1 = new Segment(arg0, null, arg1);
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this._segment2 = new Segment(arg3, arg2, null);
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}
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},
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_changed: function() {
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// Clear cached values.
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delete this._length;
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},
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/**
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* The first anchor point of the curve.
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*
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* @type Point
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* @bean
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*/
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getPoint1: function() {
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return this._segment1._point;
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},
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setPoint1: function(point) {
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point = Point.read(arguments);
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this._segment1._point.set(point.x, point.y);
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},
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/**
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* The second anchor point of the curve.
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*
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* @type Point
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* @bean
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*/
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getPoint2: function() {
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return this._segment2._point;
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},
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setPoint2: function(point) {
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point = Point.read(arguments);
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this._segment2._point.set(point.x, point.y);
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},
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/**
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* The handle point that describes the tangent in the first anchor point.
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*
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* @type Point
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* @bean
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*/
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getHandle1: function() {
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return this._segment1._handleOut;
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},
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setHandle1: function(point) {
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point = Point.read(arguments);
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this._segment1._handleOut.set(point.x, point.y);
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},
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/**
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* The handle point that describes the tangent in the second anchor point.
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*
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* @type Point
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* @bean
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*/
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getHandle2: function() {
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return this._segment2._handleIn;
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},
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setHandle2: function(point) {
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point = Point.read(arguments);
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this._segment2._handleIn.set(point.x, point.y);
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},
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/**
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* The first segment of the curve.
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*
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* @type Segment
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* @bean
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*/
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getSegment1: function() {
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return this._segment1;
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},
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/**
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* The second segment of the curve.
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*
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* @type Segment
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* @bean
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*/
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getSegment2: function() {
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return this._segment2;
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},
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/**
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* The path that the curve belongs to.
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*
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* @type Path
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* @bean
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*/
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getPath: function() {
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return this._path;
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},
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/**
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* The index of the curve in the {@link Path#curves} array.
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*
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* @type number
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* @bean
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*/
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getIndex: function() {
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return this._segment1._index;
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},
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/**
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* The next curve in the {@link Path#curves} array that the curve
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* belongs to.
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*
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* @type Curve
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* @bean
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*/
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getNext: function() {
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var curves = this._path && this._path._curves;
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return curves && (curves[this._segment1._index + 1]
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|| this._path._closed && curves[0]) || null;
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},
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/**
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* The previous curve in the {@link Path#curves} array that the curve
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* belongs to.
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*
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* @type Curve
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* @bean
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*/
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getPrevious: function() {
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var curves = this._path && this._path._curves;
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return curves && (curves[this._segment1._index - 1]
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|| this._path._closed && curves[curves.length - 1]) || null;
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},
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/**
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* Specifies whether the handles of the curve are selected.
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*
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* @type boolean
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* @bean
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*/
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isSelected: function() {
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return this.getHandle1().isSelected() && this.getHandle2().isSelected();
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},
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setSelected: function(selected) {
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this.getHandle1().setSelected(selected);
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this.getHandle2().setSelected(selected);
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},
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getCurveValues: function() {
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var p1 = this._segment1._point,
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h1 = this._segment1._handleOut,
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h2 = this._segment2._handleIn,
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p2 = this._segment2._point;
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return [
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p1.x, p1.y,
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p1.x + h1.x, p1.y + h1.y,
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p2.x + h2.x, p2.y + h2.y,
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p2.x, p2.y
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];
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},
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// DOCS: document Curve#getLength(from, to)
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/**
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* The approximated length of the curve in points.
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*
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* @type number
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* @bean
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*/
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getLength: function(/* from, to */) {
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var from = arguments[0],
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to = arguments[1];
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fullLength = arguments.length == 0 || from == 0 && to == 1;
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if (fullLength && this._length != null)
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return this._length;
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// Hide parameters from Bootstrap so it injects bean too
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var args = this.getCurveValues();
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if (!fullLength)
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args.push(from, to);
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var length = Curve.getLength.apply(Curve, args);
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if (fullLength)
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this._length = length;
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return length;
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},
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/**
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* Checks if this curve is linear, meaning it does not define any curve
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* handle.
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* @return {boolean} true if the curve is linear, false otherwise.
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*/
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isLinear: function() {
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return this._segment1._handleOut.isZero()
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&& this._segment2._handleIn.isZero();
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},
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// PORT: Add support for start parameter to Sg
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// DOCS: document Curve#getParameter(length, start)
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/**
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* @param {number} length
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* @param {number} [start]
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* @return {boolean} true if the curve is linear, false otherwise.
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*/
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getParameter: function(length, start) {
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var args = this.getCurveValues();
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args.push(length, start !== undefined ? start : length < 0 ? 1 : 0);
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return Curve.getParameter.apply(Curve, args);
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},
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// TODO: getParameter(point, precision)
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// TODO: getLocation
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// TODO: getIntersections
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// TODO: adjustThroughPoint
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// DOCS: document Curve#transform(matrix)
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/**
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* @param {Matrix} matrix
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* @return {Curve}
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*/
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transform: function(matrix) {
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return new Curve(
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matrix._transformPoint(this._segment1._point),
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matrix._transformPoint(this._segment1._handleOut),
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matrix._transformPoint(this._segment2._handleIn),
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matrix._transformPoint(this._segment2._point));
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},
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/**
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* Returns a reversed version of the curve, without modifying the curve
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* itself.
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*
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* @return {Curve} a reversed version of the curve
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*/
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reverse: function() {
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return new Curve(this._segment2.reverse(), this._segment1.reverse());
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},
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// TODO: divide
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// TODO: split
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/**
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* Returns a copy of the curve.
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*
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* @return {Curve}
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*/
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clone: function() {
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return new Curve(this._segment1, this._segment2);
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},
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/**
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* @return {string} A string representation of the curve.
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*/
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toString: function() {
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var parts = [ 'point1: ' + this._segment1._point ];
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if (!this._segment1._handleOut.isZero())
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parts.push('handle1: ' + this._segment1._handleOut);
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if (!this._segment2._handleIn.isZero())
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parts.push('handle2: ' + this._segment2._handleIn);
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parts.push('point2: ' + this._segment2._point);
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return '{ ' + parts.join(', ') + ' }';
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},
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statics: {
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create: function(path, segment1, segment2) {
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var curve = new Curve(Curve.dont);
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curve._path = path;
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curve._segment1 = segment1;
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curve._segment2 = segment2;
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return curve;
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}
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}
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}, new function() {
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function evaluate(that, t, type) {
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// Calculate the polynomial coefficients. caution: handles are relative
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// to points
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var point1 = that._segment1._point,
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handle1 = that._segment1._handleOut,
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handle2 = that._segment2._handleIn,
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point2 = that._segment2._point,
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x, y;
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// Handle special case at beginning / end of curve
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// PORT: Change in Sg too, so 0.000000000001 won't be
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// required anymore
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if (t == 0 || t == 1) {
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var point;
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switch (type) {
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case 0: // point
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point = t == 0 ? point1 : point2;
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break;
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case 1: // tangent
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case 2: // normal
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point = t == 0
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? handle1.isZero()
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? handle2.isZero()
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? point2.subtract(point1)
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: point2.add(handle2).subtract(point1)
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: handle1
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: handle2.isZero() // t == 1
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? handle1.isZero()
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? point1.subtract(point2)
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: point1.add(handle1).subtract(point2)
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: handle2;
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break;
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}
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x = point.x;
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y = point.y;
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} else {
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var dx = point2.x - point1.x,
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cx = 3 * handle1.x,
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bx = 3 * (dx + handle2.x - handle1.x) - cx,
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ax = dx - cx - bx,
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dy = point2.y - point1.y,
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cy = 3 * handle1.y,
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by = 3 * (dy + handle2.y - handle1.y) - cy,
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ay = dy - cy - by;
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switch (type) {
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case 0: // point
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x = ((ax * t + bx) * t + cx) * t + point1.x;
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y = ((ay * t + by) * t + cy) * t + point1.y;
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break;
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case 1: // tangent
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case 2: // normal
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// Simply use the derivation of the bezier function for both
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// the x and y coordinates:
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x = (3 * ax * t + 2 * bx) * t + cx;
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y = (3 * ay * t + 2 * by) * t + cy;
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break;
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}
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}
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// The normal is simply the rotated tangent:
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// TODO: Rotate normals the other way in Scriptographer too?
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// (Depending on orientation, I guess?)
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return type == 2 ? new Point(y, -x) : new Point(x, y);
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}
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function getLengthIntegrand(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y) {
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// Calculate the coefficients of a Bezier derivative.
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var ax = 9 * (c1x - c2x) + 3 * (p2x - p1x),
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bx = 6 * (p1x + c2x) - 12 * c1x,
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cx = 3 * (c1x - p1x),
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ay = 9 * (c1y - c2y) + 3 * (p2y - p1y),
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by = 6 * (p1y + c2y) - 12 * c1y,
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cy = 3 * (c1y - p1y);
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return function(t) {
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// Calculate quadratic equations of derivatives for x and y
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var dx = (ax * t + bx) * t + cx,
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dy = (ay * t + by) * t + cy;
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return Math.sqrt(dx * dx + dy * dy);
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};
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}
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// Amount of integral evaluations for the interval 0 <= a < b <= 1
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function getIterations(a, b) {
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// Guess required precision based and size of range...
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// TODO: There should be much better educated guesses for
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// this. Also, what does this depend on? Required precision?
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return Math.max(2, Math.min(16, Math.ceil(Math.abs(b - a) * 32)));
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}
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return {
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/** @lends Curve# */
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/**
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* Returns the point on the curve at the specified position.
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*
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* @param {number} parameter the position at which to find the point as
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* a value between 0 and 1.
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* @return {Point}
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*/
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getPoint: function(parameter) {
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return evaluate(this, parameter, 0);
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},
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/**
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* Returns the tangent point on the curve at the specified position.
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*
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* @param {number} parameter the position at which to find the tangent
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* point as a value between 0 and 1.
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*/
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getTangent: function(parameter) {
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return evaluate(this, parameter, 1);
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},
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/**
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* Returns the normal point on the curve at the specified position.
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*
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* @param {number} parameter the position at which to find the normal
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* point as a value between 0 and 1.
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*/
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getNormal: function(parameter) {
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return evaluate(this, parameter, 2);
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},
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statics: {
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getLength: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, a, b) {
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if (a === undefined)
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a = 0;
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if (b === undefined)
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b = 1;
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if (p1x == c1x && p1y == c1y && p2x == c2x && p2y == c2y) {
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// Straight line
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var dx = p2x - p1x,
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dy = p2y - p1y;
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return (b - a) * Math.sqrt(dx * dx + dy * dy);
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}
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var ds = getLengthIntegrand(
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p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y);
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return Numerical.integrate(ds, a, b, getIterations(a, b));
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},
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getParameter: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y,
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length, start) {
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if (length == 0)
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return start;
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// See if we're going forward or backward, and handle cases
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// differently
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var forward = length > 0,
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a = forward ? start : 0,
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b = forward ? 1 : start,
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length = Math.abs(length),
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// Use integrand to calculate both range length and part
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// lengths in f(t) below.
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ds = getLengthIntegrand(
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p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y),
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// Get length of total range
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rangeLength = Numerical.integrate(ds, a, b,
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getIterations(a, b));
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if (length >= rangeLength)
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return forward ? b : a;
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// Use length / rangeLength for an initial guess for t, to
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// bring us closer:
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var guess = length / rangeLength,
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len = 0;
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// Iteratively calculate curve range lengths, and add them up,
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// using integration precision depending on the size of the
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// range. This is much faster and also more precise than not
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// modifing start and calculating total length each time.
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function f(t) {
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var count = getIterations(start, t);
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if (start < t) {
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len += Numerical.integrate(ds, start, t, count);
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} else {
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len -= Numerical.integrate(ds, t, start, count);
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}
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start = t;
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return len - length;
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}
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return Numerical.findRoot(f, ds,
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forward ? a + guess : b - guess, // Initial guess for x
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a, b, 16, Numerical.TOLERANCE);
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},
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subdivide: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t) {
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var u = 1 - t,
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// Interpolate from 4 to 3 points
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p3x = u * p1x + t * c1x,
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p3y = u * p1y + t * c1y,
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p4x = u * c1x + t * c2x,
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p4y = u * c1y + t * c2y,
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p5x = u * c2x + t * p2x,
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p5y = u * c2y + t * p2y,
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// Interpolate from 3 to 2 points
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p6x = u * p3x + t * p4x,
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p6y = u * p3y + t * p4y,
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p7x = u * p4x + t * p5x,
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p7y = u * p4y + t * p5y,
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// Interpolate from 2 points to 1 point
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p8x = u * p6x + t * p7x,
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p8y = u * p6y + t * p7y;
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// We now have all the values we need to build the subcurves:
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return [
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[p1x, p1y, p3x, p3y, p6x, p6y, p8x, p8y], // left
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[p8x, p8y, p7x, p7y, p5x, p5y, p2x, p2y] // right
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];
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}
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}
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};
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});
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