Update wmts-hidpi, add nicer-api-docs
This commit is contained in:
Andreas Hocevar
311
nicer-api-docs/closure-library/closure/goog/math/bezier.js
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311
nicer-api-docs/closure-library/closure/goog/math/bezier.js
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// Copyright 2007 The Closure Library Authors. All Rights Reserved.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS-IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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/**
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* @fileoverview Represents a cubic Bezier curve.
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*
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* Uses the deCasteljau algorithm to compute points on the curve.
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* http://en.wikipedia.org/wiki/De_Casteljau's_algorithm
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*
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* Currently it uses an unrolled version of the algorithm for speed. Eventually
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* it may be useful to use the loop form of the algorithm in order to support
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* curves of arbitrary degree.
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*
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* @author robbyw@google.com (Robby Walker)
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* @author wcrosby@google.com (Wayne Crosby)
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*/
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goog.provide('goog.math.Bezier');
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goog.require('goog.math');
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goog.require('goog.math.Coordinate');
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/**
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* Object representing a cubic bezier curve.
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* @param {number} x0 X coordinate of the start point.
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* @param {number} y0 Y coordinate of the start point.
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* @param {number} x1 X coordinate of the first control point.
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* @param {number} y1 Y coordinate of the first control point.
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* @param {number} x2 X coordinate of the second control point.
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* @param {number} y2 Y coordinate of the second control point.
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* @param {number} x3 X coordinate of the end point.
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* @param {number} y3 Y coordinate of the end point.
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* @constructor
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*/
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goog.math.Bezier = function(x0, y0, x1, y1, x2, y2, x3, y3) {
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/**
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* X coordinate of the first point.
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* @type {number}
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*/
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this.x0 = x0;
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/**
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* Y coordinate of the first point.
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* @type {number}
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*/
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this.y0 = y0;
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/**
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* X coordinate of the first control point.
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* @type {number}
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*/
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this.x1 = x1;
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/**
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* Y coordinate of the first control point.
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* @type {number}
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*/
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this.y1 = y1;
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/**
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* X coordinate of the second control point.
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* @type {number}
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*/
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this.x2 = x2;
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/**
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* Y coordinate of the second control point.
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* @type {number}
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*/
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this.y2 = y2;
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/**
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* X coordinate of the end point.
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* @type {number}
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*/
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this.x3 = x3;
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/**
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* Y coordinate of the end point.
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* @type {number}
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*/
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this.y3 = y3;
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};
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/**
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* Constant used to approximate ellipses.
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* See: http://canvaspaint.org/blog/2006/12/ellipse/
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* @type {number}
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*/
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goog.math.Bezier.KAPPA = 4 * (Math.sqrt(2) - 1) / 3;
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/**
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* @return {!goog.math.Bezier} A copy of this curve.
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*/
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goog.math.Bezier.prototype.clone = function() {
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return new goog.math.Bezier(this.x0, this.y0, this.x1, this.y1, this.x2,
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this.y2, this.x3, this.y3);
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};
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/**
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* Test if the given curve is exactly the same as this one.
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* @param {goog.math.Bezier} other The other curve.
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* @return {boolean} Whether the given curve is the same as this one.
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*/
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goog.math.Bezier.prototype.equals = function(other) {
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return this.x0 == other.x0 && this.y0 == other.y0 && this.x1 == other.x1 &&
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this.y1 == other.y1 && this.x2 == other.x2 && this.y2 == other.y2 &&
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this.x3 == other.x3 && this.y3 == other.y3;
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};
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/**
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* Modifies the curve in place to progress in the opposite direction.
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*/
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goog.math.Bezier.prototype.flip = function() {
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var temp = this.x0;
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this.x0 = this.x3;
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this.x3 = temp;
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temp = this.y0;
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this.y0 = this.y3;
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this.y3 = temp;
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temp = this.x1;
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this.x1 = this.x2;
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this.x2 = temp;
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temp = this.y1;
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this.y1 = this.y2;
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this.y2 = temp;
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};
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/**
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* Computes the curve at a point between 0 and 1.
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* @param {number} t The point on the curve to find.
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* @return {!goog.math.Coordinate} The computed coordinate.
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*/
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goog.math.Bezier.prototype.getPoint = function(t) {
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// Special case start and end
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if (t == 0) {
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return new goog.math.Coordinate(this.x0, this.y0);
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} else if (t == 1) {
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return new goog.math.Coordinate(this.x3, this.y3);
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}
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// Step one - from 4 points to 3
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var ix0 = goog.math.lerp(this.x0, this.x1, t);
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var iy0 = goog.math.lerp(this.y0, this.y1, t);
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var ix1 = goog.math.lerp(this.x1, this.x2, t);
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var iy1 = goog.math.lerp(this.y1, this.y2, t);
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var ix2 = goog.math.lerp(this.x2, this.x3, t);
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var iy2 = goog.math.lerp(this.y2, this.y3, t);
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// Step two - from 3 points to 2
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ix0 = goog.math.lerp(ix0, ix1, t);
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iy0 = goog.math.lerp(iy0, iy1, t);
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ix1 = goog.math.lerp(ix1, ix2, t);
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iy1 = goog.math.lerp(iy1, iy2, t);
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// Final step - last point
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return new goog.math.Coordinate(goog.math.lerp(ix0, ix1, t),
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goog.math.lerp(iy0, iy1, t));
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};
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/**
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* Changes this curve in place to be the portion of itself from [t, 1].
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* @param {number} t The start of the desired portion of the curve.
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*/
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goog.math.Bezier.prototype.subdivideLeft = function(t) {
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if (t == 1) {
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return;
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}
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// Step one - from 4 points to 3
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var ix0 = goog.math.lerp(this.x0, this.x1, t);
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var iy0 = goog.math.lerp(this.y0, this.y1, t);
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var ix1 = goog.math.lerp(this.x1, this.x2, t);
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var iy1 = goog.math.lerp(this.y1, this.y2, t);
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var ix2 = goog.math.lerp(this.x2, this.x3, t);
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var iy2 = goog.math.lerp(this.y2, this.y3, t);
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// Collect our new x1 and y1
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this.x1 = ix0;
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this.y1 = iy0;
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// Step two - from 3 points to 2
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ix0 = goog.math.lerp(ix0, ix1, t);
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iy0 = goog.math.lerp(iy0, iy1, t);
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ix1 = goog.math.lerp(ix1, ix2, t);
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iy1 = goog.math.lerp(iy1, iy2, t);
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// Collect our new x2 and y2
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this.x2 = ix0;
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this.y2 = iy0;
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// Final step - last point
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this.x3 = goog.math.lerp(ix0, ix1, t);
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this.y3 = goog.math.lerp(iy0, iy1, t);
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};
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/**
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* Changes this curve in place to be the portion of itself from [0, t].
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* @param {number} t The end of the desired portion of the curve.
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*/
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goog.math.Bezier.prototype.subdivideRight = function(t) {
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this.flip();
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this.subdivideLeft(1 - t);
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this.flip();
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};
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/**
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* Changes this curve in place to be the portion of itself from [s, t].
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* @param {number} s The start of the desired portion of the curve.
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* @param {number} t The end of the desired portion of the curve.
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*/
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goog.math.Bezier.prototype.subdivide = function(s, t) {
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this.subdivideRight(s);
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this.subdivideLeft((t - s) / (1 - s));
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};
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/**
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* Computes the position t of a point on the curve given its x coordinate.
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* That is, for an input xVal, finds t s.t. getPoint(t).x = xVal.
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* As such, the following should always be true up to some small epsilon:
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* t ~ solvePositionFromXValue(getPoint(t).x) for t in [0, 1].
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* @param {number} xVal The x coordinate of the point to find on the curve.
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* @return {number} The position t.
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*/
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goog.math.Bezier.prototype.solvePositionFromXValue = function(xVal) {
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// Desired precision on the computation.
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var epsilon = 1e-6;
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// Initial estimate of t using linear interpolation.
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var t = (xVal - this.x0) / (this.x3 - this.x0);
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if (t <= 0) {
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return 0;
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} else if (t >= 1) {
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return 1;
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}
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// Try gradient descent to solve for t. If it works, it is very fast.
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var tMin = 0;
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var tMax = 1;
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for (var i = 0; i < 8; i++) {
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var value = this.getPoint(t).x;
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var derivative = (this.getPoint(t + epsilon).x - value) / epsilon;
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if (Math.abs(value - xVal) < epsilon) {
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return t;
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} else if (Math.abs(derivative) < epsilon) {
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break;
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} else {
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if (value < xVal) {
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tMin = t;
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} else {
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tMax = t;
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}
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t -= (value - xVal) / derivative;
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}
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}
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// If the gradient descent got stuck in a local minimum, e.g. because
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// the derivative was close to 0, use a Dichotomy refinement instead.
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// We limit the number of interations to 8.
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for (var i = 0; Math.abs(value - xVal) > epsilon && i < 8; i++) {
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if (value < xVal) {
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tMin = t;
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t = (t + tMax) / 2;
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} else {
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tMax = t;
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t = (t + tMin) / 2;
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}
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value = this.getPoint(t).x;
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}
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return t;
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};
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/**
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* Computes the y coordinate of a point on the curve given its x coordinate.
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* @param {number} xVal The x coordinate of the point on the curve.
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* @return {number} The y coordinate of the point on the curve.
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*/
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goog.math.Bezier.prototype.solveYValueFromXValue = function(xVal) {
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return this.getPoint(this.solvePositionFromXValue(xVal)).y;
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};
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