├── .eslintrc.json ├── .github └── workflows │ └── node.js.yml ├── .gitignore ├── .npmignore ├── COPYING ├── LICENSE ├── README.md ├── package.json ├── rollup.config.js ├── src └── index.js ├── test ├── .eslintrc.json └── versor-test.js └── yarn.lock /.eslintrc.json: -------------------------------------------------------------------------------- 1 | { 2 | "extends": "eslint:recommended", 3 | "parserOptions": { 4 | "sourceType": "module", 5 | "ecmaVersion": 8 6 | } 7 | } 8 | -------------------------------------------------------------------------------- /.github/workflows/node.js.yml: -------------------------------------------------------------------------------- 1 | # https://help.github.com/actions/language-and-framework-guides/using-nodejs-with-github-actions 2 | 3 | name: Node.js CI 4 | 5 | on: 6 | push: 7 | branches: [ main ] 8 | pull_request: 9 | branches: [ main ] 10 | 11 | jobs: 12 | build: 13 | 14 | runs-on: ubuntu-latest 15 | 16 | strategy: 17 | matrix: 18 | node-version: [14.x] 19 | 20 | steps: 21 | - uses: actions/checkout@v2 22 | - name: Use Node.js ${{ matrix.node-version }} 23 | uses: actions/setup-node@v1 24 | with: 25 | node-version: ${{ matrix.node-version }} 26 | - run: yarn --frozen-lockfile 27 | - run: | 28 | echo ::add-matcher::.github/eslint.json 29 | yarn run eslint src test --format=compact 30 | - run: yarn test 31 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | .DS_Store 2 | *~ 3 | dist/ 4 | node_modules/ 5 | package-lock.json 6 | -------------------------------------------------------------------------------- /.npmignore: -------------------------------------------------------------------------------- 1 | *.sublime-* 2 | dist/*.zip 3 | img/ 4 | test/ 5 | -------------------------------------------------------------------------------- /COPYING: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Copyright 2013-2021 Mike Bostock 2 | 3 | Permission to use, copy, modify, and/or distribute this software for any purpose 4 | with or without fee is hereby granted, provided that the above copyright notice 5 | and this permission notice appear in all copies. 6 | 7 | THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH 8 | REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND 9 | FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, 10 | INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS 11 | OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER 12 | TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF 13 | THIS SOFTWARE. -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Versor 2 | 3 | Rotate the globe with the mouse. 4 | 5 | The naïve method uses `mouse.x` and `mouse.y` as proxies for longitude and latitude. It works when the rotation is small, but try to put the globe "upside-down" and suddenly moving the mouse to the left rotates the globe to the right, and vice versa. 6 | 7 | The correct solution is to track the spherical coordinates of the point that is under the mouse, and apply a rotation to the globe that will move the initial point to the current mouse position. Computing that rotation involves quaternions. 8 | 9 | This method, introduced by [Jason Davies](https://www.jasondavies.com/maps/rotate/) and Mike Bostock, is called [versor dragging](https://gist.github.com/mbostock/7ea1dde508cec6d2d95306f92642bc42). 10 | 11 | This module contains the quaternion & versor functions. For a directly usable package, see [d3-inertia](https://github.com/Fil/d3-inertia). 12 | 13 | 14 | In Node: 15 | 16 | ```js 17 | const versor = require("versor"); 18 | 19 | // interpolate angles (slerp), see https://observablehq.com/@d3/world-tour 20 | versor.interpolate(rotation0, rotation1); // function of (t) 21 | 22 | // quaternion to rotate between p0 and p1, see d3-inertia 23 | const p0 = [0, 0], 24 | p1 = [90, 0], 25 | c0 = versor.cartesian(p0), 26 | c1 = versor.cartesian(p1); 27 | versor.delta(c0, c1); // [0.7071, 0.7071, 0, 0] 28 | 29 | // tweening: quaternion to rotate halfway between p0 and p1 30 | versor.delta(c0, c1, 0.5); // [0.9239, 0.3827, 0, 0] 31 | 32 | 33 | // utilities 34 | 35 | // get cartesian coordinates [x, y, z] given spherical coordinates [λ, φ]. 36 | versor.cartesian = function(e) { 37 | var l = e[0] * radians, p = e[1] * radians, cp = cos(p); 38 | return [cp * cos(l), cp * sin(l), sin(p)]; 39 | }; 40 | 41 | // create a quaternion from Euler angles 42 | const q0 = versor([90,0,0]); // [0.7071068, 0.7071068, 0, 0] 43 | const q1 = versor([0,90,0]); // [0.7071068, 0, 0.7071068, 0] 44 | 45 | // the quaternion that represents q0 * q1. 46 | q01 = versor.multiply(q0, q1); // [0.5, 0.5, 0.5, 0.5] 47 | 48 | // Euler rotation angles [λ, φ, γ] for the given quaternion. 49 | versor.rotation(q01); // [90, 0, 90] 50 | 51 | 52 | 53 | ``` 54 | 55 | If you use npm, `npm install versor`. You can also download the [latest release on GitHub](https://github.com/d3/versor/releases/latest). For vanilla HTML in modern browsers, import versor from Skypack: 56 | 57 | ```html 58 | 62 | ``` 63 | 64 | For legacy environments, you can load versor’s UMD bundle from an npm-based CDN such as jsDelivr; a `versor` global is exported: 65 | 66 | ```html 67 | 68 | 73 | ``` 74 | -------------------------------------------------------------------------------- /package.json: -------------------------------------------------------------------------------- 1 | { 2 | "name": "versor", 3 | "version": "0.2.0", 4 | "description": "Versor", 5 | "homepage": "https://github.com/Fil/versor", 6 | "repository": { 7 | "type": "git", 8 | "url": "https://github.com/Fil/versor.git" 9 | }, 10 | "keywords": [ 11 | "d3", 12 | "d3-module", 13 | "d3-geo", 14 | "versor" 15 | ], 16 | "license": "ISC", 17 | "author": { 18 | "name": "Mike Bostock", 19 | "url": "https://github.com/mbostock" 20 | }, 21 | "type": "module", 22 | "module": "src/index.js", 23 | "main": "src/index.js", 24 | "jsdelivr": "dist/versor.min.js", 25 | "unpkg": "dist/versor.min.js", 26 | "exports": { 27 | "umd": "./dist/versor.min.js", 28 | "default": "./src/index.js" 29 | }, 30 | "dependencies": {}, 31 | "devDependencies": { 32 | "eslint": "7", 33 | "mocha": "8", 34 | "rollup": "2", 35 | "rollup-plugin-terser": "5" 36 | }, 37 | "scripts": { 38 | "test": "mocha 'test/**/*-test.js' && eslint src test", 39 | "prepublishOnly": "rm -rf dist && yarn test && rollup -c" 40 | }, 41 | "engines": { 42 | "node": ">=12" 43 | }, 44 | "jsnext:main": "src/index.js" 45 | } 46 | -------------------------------------------------------------------------------- /rollup.config.js: -------------------------------------------------------------------------------- 1 | import {terser} from "rollup-plugin-terser"; 2 | import * as meta from "./package.json"; 3 | 4 | const config = { 5 | input: "src/index.js", 6 | external: Object.keys(meta.dependencies || {}), //.filter(key => /^d3-/.test(key)), 7 | output: { 8 | file: `dist/${meta.name}.js`, 9 | name: "versor", 10 | format: "umd", 11 | indent: false, 12 | extend: true, 13 | banner: `// ${meta.homepage} v${meta.version} Copyright ${(new Date).getFullYear()} ${meta.author.name}`, 14 | globals: Object.assign({}, ...Object.keys(meta.dependencies || {})) //.filter(key => /^d3-/.test(key)).map(key => ({[key]: "d3"}))) 15 | }, 16 | plugins: [] 17 | }; 18 | 19 | export default [ 20 | config, 21 | { 22 | ...config, 23 | output: { 24 | ...config.output, 25 | file: `dist/${meta.name}.min.js` 26 | }, 27 | plugins: [ 28 | ...config.plugins, 29 | terser({ 30 | output: { 31 | preamble: config.output.banner 32 | } 33 | }) 34 | ] 35 | } 36 | ]; 37 | -------------------------------------------------------------------------------- /src/index.js: -------------------------------------------------------------------------------- 1 | const acos = Math.acos, 2 | asin = Math.asin, 3 | atan2 = Math.atan2, 4 | cos = Math.cos, 5 | hypot = Math.hypot, 6 | max = Math.max, 7 | min = Math.min, 8 | PI = Math.PI, 9 | sin = Math.sin, 10 | radians = PI / 180, 11 | degrees = 180 / PI; 12 | 13 | class Versor { 14 | static fromCartesian([x, y, z]) { 15 | return [0, z, -y, x]; 16 | } 17 | static fromAngles([l, p, g]) { 18 | l *= radians / 2; 19 | p *= radians / 2; 20 | g = (g||0) * radians / 2; 21 | const sl = sin(l), cl = cos(l); 22 | const sp = sin(p), cp = cos(p); 23 | const sg = sin(g), cg = cos(g); 24 | return [ 25 | cl * cp * cg + sl * sp * sg, 26 | sl * cp * cg - cl * sp * sg, 27 | cl * sp * cg + sl * cp * sg, 28 | cl * cp * sg - sl * sp * cg 29 | ]; 30 | } 31 | static toAngles([a, b, c, d]) { 32 | return [ 33 | atan2(2 * (a * b + c * d), 1 - 2 * (b * b + c * c)) * degrees, 34 | asin(max(-1, min(1, 2 * (a * c - d * b)))) * degrees, 35 | atan2(2 * (a * d + b * c), 1 - 2 * (c * c + d * d)) * degrees 36 | ]; 37 | } 38 | static interpolateAngles(a, b) { 39 | const i = Versor.interpolate(Versor.fromAngles(a), Versor.fromAngles(b)); 40 | return t => Versor.toAngles(i(t)); 41 | } 42 | static interpolateLinear([a1, b1, c1, d1], [a2, b2, c2, d2]) { 43 | a2 -= a1, b2 -= b1, c2 -= c1, d2 -= d1; 44 | const x = new Array(4); 45 | return t => { 46 | const l = hypot(x[0] = a1 + a2 * t, x[1] = b1 + b2 * t, x[2] = c1 + c2 * t, x[3] = d1 + d2 * t); 47 | x[0] /= l, x[1] /= l, x[2] /= l, x[3] /= l; 48 | return x; 49 | }; 50 | } 51 | static interpolate([a1, b1, c1, d1], [a2, b2, c2, d2]) { 52 | let dot = Versor.dot([a1, b1, c1, d1], [a2, b2, c2, d2]); 53 | if (dot < 0) a2 = -a2, b2 = -b2, c2 = -c2, d2 = -d2, dot = -dot; 54 | if (dot > 0.9995) return Versor.interpolateLinear([a1, b1, c1, d1], [a2, b2, c2, d2]); 55 | const theta0 = acos(max(-1, min(1, dot))); 56 | const x = new Array(4); 57 | const l = hypot(a2 -= a1 * dot, b2 -= b1 * dot, c2 -= c1 * dot, d2 -= d1 * dot); 58 | a2 /= l, b2 /= l, c2 /= l, d2 /= l; 59 | return t => { 60 | const theta = theta0 * t; 61 | const s = sin(theta); 62 | const c = cos(theta); 63 | x[0] = a1 * c + a2 * s; 64 | x[1] = b1 * c + b2 * s; 65 | x[2] = c1 * c + c2 * s; 66 | x[3] = d1 * c + d2 * s; 67 | return x; 68 | }; 69 | } 70 | static dot([a1, b1, c1, d1], [a2, b2, c2, d2]) { 71 | return a1 * a2 + b1 * b2 + c1 * c2 + d1 * d2; 72 | } 73 | static multiply([a1, b1, c1, d1], [a2, b2, c2, d2]) { 74 | return [ 75 | a1 * a2 - b1 * b2 - c1 * c2 - d1 * d2, 76 | a1 * b2 + b1 * a2 + c1 * d2 - d1 * c2, 77 | a1 * c2 - b1 * d2 + c1 * a2 + d1 * b2, 78 | a1 * d2 + b1 * c2 - c1 * b2 + d1 * a2 79 | ]; 80 | } 81 | } 82 | 83 | /* 84 | * Old API 85 | */ 86 | 87 | // Returns the unit quaternion for the given Euler rotation angles [λ, φ, γ]. 88 | const versor = Versor.fromAngles; 89 | 90 | // Returns the quaternion that represents q0 * q1. 91 | versor.multiply = Versor.multiply; 92 | 93 | // Returns the Euler rotation angles [λ, φ, γ] for the given quaternion. 94 | versor.rotation = Versor.toAngles; 95 | 96 | // interpolate angles 97 | versor.interpolate = Versor.interpolateAngles; 98 | 99 | // Returns Cartesian coordinates [x, y, z] given spherical coordinates [λ, φ]. 100 | versor.cartesian = function(e) { 101 | const l = e[0] * radians, p = e[1] * radians, cp = cos(p); 102 | return [cp * cos(l), cp * sin(l), sin(p)]; 103 | }; 104 | 105 | // Returns the quaternion to rotate between two cartesian points on the sphere. 106 | // alpha for tweening [0,1] 107 | // see https://github.com/Fil/versor/issues/8 108 | versor.delta = function(v0, v1, alpha) { 109 | if (arguments.length == 2) alpha = 1; 110 | 111 | const sqrt = Math.sqrt; 112 | function cross(v0, v1) { 113 | return [v0[1] * v1[2] - v0[2] * v1[1], v0[2] * v1[0] - v0[0] * v1[2], v0[0] * v1[1] - v0[1] * v1[0]]; 114 | } 115 | function dot(v0, v1) { 116 | return v0[0] * v1[0] + v0[1] * v1[1] + v0[2] * v1[2]; 117 | } 118 | 119 | const w = cross(v0, v1), l = sqrt(dot(w, w)); 120 | if (!l) return [1, 0, 0, 0]; 121 | const t = alpha * acos(max(-1, min(1, dot(v0, v1)))) / 2, s = sin(t); // t = θ / 2 122 | return [cos(t), w[2] / l * s, -w[1] / l * s, w[0] / l * s]; 123 | }; 124 | 125 | export default versor; -------------------------------------------------------------------------------- /test/.eslintrc.json: -------------------------------------------------------------------------------- 1 | { 2 | "extends": "eslint:recommended", 3 | "parserOptions": { 4 | "sourceType": "module", 5 | "ecmaVersion": 8 6 | }, 7 | "env": { 8 | "mocha": true 9 | } 10 | } 11 | -------------------------------------------------------------------------------- /test/versor-test.js: -------------------------------------------------------------------------------- 1 | import assert from "assert"; 2 | import versor from "../src/index.js"; 3 | 4 | function distance2 (a,b) { 5 | return a 6 | .map(function(x,i) { return (x - b[i]) * (x - b[i]); }) 7 | .reduce(function(a,b) { return a + b; }, 0); 8 | } 9 | 10 | it("versor offers functions", () => { 11 | assert.strictEqual(typeof versor, 'function'); 12 | assert.strictEqual(typeof versor.cartesian, 'function'); 13 | assert.strictEqual(typeof versor.rotation, 'function'); 14 | assert.strictEqual(typeof versor.delta, 'function'); 15 | }); 16 | 17 | it("90° versors", () => { 18 | assert(distance2(versor([ 90, 0, 0 ]), [ Math.sqrt(2)/2, Math.sqrt(2)/2, 0, 0 ]) < 1e-8); 19 | assert(distance2(versor([ -90, 0, 0 ]), [ Math.sqrt(2)/2, -Math.sqrt(2)/2, 0, 0 ]) < 1e-8); 20 | assert(distance2(versor([ 0, 90, 0 ]), [ Math.sqrt(2)/2, 0, Math.sqrt(2)/2, 0 ]) < 1e-8); 21 | assert(distance2(versor([ 0, -90, 0 ]), [ Math.sqrt(2)/2, 0, -Math.sqrt(2)/2, 0 ]) < 1e-8); 22 | assert(distance2(versor([ 0, 0, 90 ]), [ Math.sqrt(2)/2, 0, 0, Math.sqrt(2)/2 ]) < 1e-8); 23 | assert(distance2(versor([ 0, 0, -90 ]), [ Math.sqrt(2)/2, 0, 0, -Math.sqrt(2)/2 ]) < 1e-8); 24 | }); 25 | 26 | 27 | it("delta for large angles https://github.com/Fil/versor/issues/8", function(){ 28 | assert(distance2(versor.delta([0.5963903847916048, -0.48599667744373487, -0.6388471949079623], [0.2185627727412969, 0.8848373533648707, -0.4114525154399803]), [ 0.6939654197615048, 29 | 0.45674413520077356, 30 | -0.07619840032229953, 31 | 0.551353421067883 ]) < 1e-8); 32 | }); 33 | 34 | it("delta", () => { 35 | let a = versor.cartesian([ 0, 0 ]), b = versor.cartesian([ 90, 0 ]); 36 | assert(distance2(versor.delta(a,b), [ 0.7071, 0.7071, 0, 0 ]) < 1e-8); 37 | b = versor.cartesian([ 0, 90 ]); 38 | assert(distance2(versor.delta(a,b), [ 0.7071, 0, 0.7071, 0 ]) < 1e-8); 39 | 40 | a = versor.cartesian([ 0, 0 ]), b = versor.cartesian([ 180, 0 ]); 41 | assert(distance2(versor.delta(a,b), [ 0, 1, 0, 0 ]) < 1e-8); 42 | }); 43 | 44 | it("delta tweening", () => { 45 | const a = versor.cartesian([ 0, 0 ]), b = versor.cartesian([ 90, 0 ]); 46 | assert(distance2(versor.delta(a,b,0.5), [ 0.9239, 0.3827, 0, 0 ]) < 1e-8); 47 | }); 48 | -------------------------------------------------------------------------------- /yarn.lock: -------------------------------------------------------------------------------- 1 | # THIS IS AN AUTOGENERATED FILE. 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