├── .gitignore ├── .travis.yml ├── LICENSE ├── README.md ├── index.d.ts ├── index.js ├── package-lock.json ├── package.json └── test └── unitbezier.js /.gitignore: -------------------------------------------------------------------------------- 1 | .nyc_output 2 | -------------------------------------------------------------------------------- /.travis.yml: -------------------------------------------------------------------------------- 1 | language: node_js 2 | node_js: 3 | - node 4 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | BSD-2-Clause 2 | 3 | Copyright (C) 2008 Apple Inc. All Rights Reserved. 4 | 5 | Redistribution and use in source and binary forms, with or without 6 | modification, are permitted provided that the following conditions 7 | are met: 8 | 9 | 1. Redistributions of source code must retain the above copyright 10 | notice, this list of conditions and the following disclaimer. 11 | 2. Redistributions in binary form must reproduce the above copyright 12 | notice, this list of conditions and the following disclaimer in the 13 | documentation and/or other materials provided with the distribution. 14 | 15 | THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY 16 | EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 17 | IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 18 | PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR 19 | CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 20 | EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 21 | PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 22 | PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY 23 | OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 24 | (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 25 | OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 26 | 27 | Ported from Webkit 28 | http://svn.webkit.org/repository/webkit/trunk/Source/WebCore/platform/graphics/UnitBezier.h 29 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | [![Build Status](https://travis-ci.org/mapbox/unitbezier.svg)](https://travis-ci.org/mapbox/unitbezier) 2 | 3 | # unitbezier 4 | 5 | Unit bezier interpolation function: a port to JavaScript from Webkit: 6 | 7 | http://svn.webkit.org/repository/webkit/trunk/Source/WebCore/platform/graphics/UnitBezier.h 8 | 9 | ## api 10 | 11 | ### new UnitBezier(p1x, p1y, p2x, p2y) 12 | 13 | Initialize a new bezier curve given the points 14 | 15 | ### bezier.solve(x, epsilon) 16 | 17 | Evaluate bezier for value `x` (ranging from 0 to 1) with `epsilon` precision (1e-6 by default). 18 | -------------------------------------------------------------------------------- /index.d.ts: -------------------------------------------------------------------------------- 1 | export default class UnitBezier { 2 | constructor(p1x: number, p1y: number, p2x: number, p2y: number); 3 | sampleCurveX(t: number): number; 4 | sampleCurveY(t: number): number; 5 | sampleCurveDerivativeX(t: number): number; 6 | solveCurveX(x: number, epsilon?: number): number; 7 | solve(x: number, epsilon?: number): number; 8 | } 9 | -------------------------------------------------------------------------------- /index.js: -------------------------------------------------------------------------------- 1 | 'use strict'; 2 | 3 | module.exports = UnitBezier; 4 | 5 | function UnitBezier(p1x, p1y, p2x, p2y) { 6 | // Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1). 7 | this.cx = 3.0 * p1x; 8 | this.bx = 3.0 * (p2x - p1x) - this.cx; 9 | this.ax = 1.0 - this.cx - this.bx; 10 | 11 | this.cy = 3.0 * p1y; 12 | this.by = 3.0 * (p2y - p1y) - this.cy; 13 | this.ay = 1.0 - this.cy - this.by; 14 | 15 | this.p1x = p1x; 16 | this.p1y = p1y; 17 | this.p2x = p2x; 18 | this.p2y = p2y; 19 | } 20 | 21 | UnitBezier.prototype = { 22 | sampleCurveX: function (t) { 23 | // `ax t^3 + bx t^2 + cx t' expanded using Horner's rule. 24 | return ((this.ax * t + this.bx) * t + this.cx) * t; 25 | }, 26 | 27 | sampleCurveY: function (t) { 28 | return ((this.ay * t + this.by) * t + this.cy) * t; 29 | }, 30 | 31 | sampleCurveDerivativeX: function (t) { 32 | return (3.0 * this.ax * t + 2.0 * this.bx) * t + this.cx; 33 | }, 34 | 35 | solveCurveX: function (x, epsilon) { 36 | if (epsilon === undefined) epsilon = 1e-6; 37 | 38 | if (x < 0.0) return 0.0; 39 | if (x > 1.0) return 1.0; 40 | 41 | var t = x; 42 | 43 | // First try a few iterations of Newton's method - normally very fast. 44 | for (var i = 0; i < 8; i++) { 45 | var x2 = this.sampleCurveX(t) - x; 46 | if (Math.abs(x2) < epsilon) return t; 47 | 48 | var d2 = this.sampleCurveDerivativeX(t); 49 | if (Math.abs(d2) < 1e-6) break; 50 | 51 | t = t - x2 / d2; 52 | } 53 | 54 | // Fall back to the bisection method for reliability. 55 | var t0 = 0.0; 56 | var t1 = 1.0; 57 | t = x; 58 | 59 | for (i = 0; i < 20; i++) { 60 | x2 = this.sampleCurveX(t); 61 | if (Math.abs(x2 - x) < epsilon) break; 62 | 63 | if (x > x2) { 64 | t0 = t; 65 | } else { 66 | t1 = t; 67 | } 68 | 69 | t = (t1 - t0) * 0.5 + t0; 70 | } 71 | 72 | return t; 73 | }, 74 | 75 | solve: function (x, epsilon) { 76 | return 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"pretest": "eslint index.js test/*.js", 9 | "test": "node test/unitbezier.js" 10 | }, 11 | "files": [ 12 | "index.js", 13 | "index.d.ts" 14 | ], 15 | "repository": { 16 | "type": "git", 17 | "url": "git@github.com:mapbox/unitbezier.git" 18 | }, 19 | "keywords": [ 20 | "unit", 21 | "bezier", 22 | "interpolation", 23 | "webkit" 24 | ], 25 | "author": "", 26 | "license": "BSD-2-Clause", 27 | "bugs": { 28 | "url": "https://github.com/mapbox/unitbezier/issues" 29 | }, 30 | "homepage": "https://github.com/mapbox/unitbezier", 31 | "devDependencies": { 32 | "eslint": "^8.0.1", 33 | "eslint-config-mourner": "^2.0.3", 34 | "tape": "^5.3.1" 35 | }, 36 | "eslintConfig": { 37 | "extends": "mourner" 38 | } 39 | } 40 | -------------------------------------------------------------------------------- /test/unitbezier.js: -------------------------------------------------------------------------------- 1 | 'use strict'; 2 | 3 | var test = require('tape').test, 4 | UnitBezier = require('../'); 5 | 6 | test('unit bezier', function (t) { 7 | var u = new UnitBezier(0, 0, 1, 1); 8 | t.equal(u.sampleCurveY(1), 1, 'sampleCurveY'); 9 | t.equal(u.sampleCurveX(1), 1, 'sampleCurveX'); 10 | t.equal(u.sampleCurveDerivativeX(0.1), 0.54, 'sampleCurveDerivativeX'); 11 | t.equal(u.solveCurveX(0), 0, 'solveCurveX'); 12 | t.equal(u.solveCurveX(1), 1, 'solveCurveX'); 13 | t.equal(u.solveCurveX(1.25552, 1.e-8), 1, 'solveCurveX'); 14 | t.equal(u.solveCurveX(1, 1e-8), 1, 'solveCurveX'); 15 | t.equal(u.solveCurveX(0.5), 0.5, 'solveCurveX'); 16 | t.equal(u.solve(0.5), 0.5, 'solve'); 17 | t.end(); 18 | }); 19 | --------------------------------------------------------------------------------