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Projective Line
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| { | |
| "uuid": "6ef68984-26c6-4eb9-aa94-326c901bf8be", | |
| "description": "Projective Line", | |
| "dependencies": { | |
| "DomReady": "latest", | |
| "davinci-mathbox": "1.0.14" | |
| } | |
| } |
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| <!doctype html> | |
| <html> | |
| <head> | |
| <meta charset="utf-8"> | |
| <title>MathBox - Empty Example.</title> | |
| <!-- STYLE-MARKER --> | |
| <!-- SCRIPTS-MARKER --> | |
| </head> | |
| <body> | |
| <div id="info"></div> | |
| <script type='text/javascript'> | |
| try { | |
| <!-- CODE-MARKER --> | |
| } | |
| catch(e) { | |
| console.log(e); | |
| } | |
| </script> | |
| </body> | |
| </html> |
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| DomReady.ready(function() { | |
| ThreeBox.preload(['../shaders/MathBox.glsl.html'], init); | |
| }); | |
| function init() { | |
| // MathBox boilerplate | |
| var mathbox = window['mathbox'] = mathBox({ | |
| cameraControls: true, | |
| cursor: true, | |
| controlClass: ThreeBox.OrbitControls, | |
| elementResize: true, | |
| fullscreen: true, | |
| screenshot: true, | |
| stats: false, | |
| scale: 1, | |
| }); | |
| var stage = mathbox.start(); | |
| // Viewport camera/setup | |
| stage | |
| // Polar viewport | |
| .viewport({ | |
| type: 'polar', | |
| range: [[-π, π], [-1, 1], [-4, 4]], | |
| scale: [.8, .8, .8], | |
| polar: 1, | |
| rotation: [τ/4, 0, 0], | |
| }) | |
| .camera({ | |
| orbit: 3.5, | |
| phi: τ/4+.5, | |
| theta: 0.1, | |
| }) | |
| .transition(300) | |
| // Animated curve | |
| .curve({ | |
| domain: [-1, 1], | |
| n: 256, | |
| expression: rationalFunc, | |
| lineWidth: 1, | |
| }) | |
| // Manual conical grid lines | |
| .curve({ | |
| n: 2, | |
| domain: [-1, 1], | |
| data: [[0, 0, -4], [0, .5, 4]], | |
| color: 0xa0a0a0, | |
| lineWidth: 1, | |
| }) | |
| .curve({ | |
| n: 2, | |
| domain: [-1, 1], | |
| data: [[0, 0, -4], [.25*π, .5, 4]], | |
| color: 0xa0a0a0, | |
| lineWidth: 1, | |
| }) | |
| .curve({ | |
| n: 2, | |
| domain: [-1, 1], | |
| data: [[0, 0, -4], [.5*π, .5, 4]], | |
| color: 0xa0a0a0, | |
| lineWidth: 1, | |
| }) | |
| .curve({ | |
| n: 2, | |
| domain: [-1, 1], | |
| data: [[0, 0, -4], [.75*π, .5, 4]], | |
| color: 0xa0a0a0, | |
| lineWidth: 1, | |
| }) | |
| .curve({ | |
| n: 2, | |
| domain: [-1, 1], | |
| data: [[0, 0, -4], [π, .5, 4]], | |
| color: 0xa0a0a0, | |
| lineWidth: 1, | |
| }) | |
| .curve({ | |
| n: 2, | |
| domain: [-1, 1], | |
| data: [[0, 0, -4], [1.25*π, .5, 4]], | |
| color: 0xa0a0a0, | |
| lineWidth: 1, | |
| }) | |
| .curve({ | |
| n: 2, | |
| domain: [-1, 1], | |
| data: [[0, 0, -4], [1.5*π, .5, 4]], | |
| color: 0xa0a0a0, | |
| lineWidth: 1, | |
| }) | |
| .curve({ | |
| n: 2, | |
| domain: [-1, 1], | |
| data: [[0, 0, -4], [1.75*π, .5, 4]], | |
| color: 0xa0a0a0, | |
| lineWidth: 1, | |
| }) | |
| .curve({ | |
| n: 48, | |
| domain: [-π, π], | |
| expression: function (x) { return [x, .5, 4]; }, | |
| color: 0xa0a0a0, | |
| lineWidth: 1, | |
| }); | |
| // Rotate camera continuously | |
| stage.world().loop().hookPreRender(function () { | |
| stage.set('camera', { phi: +new Date() * .0003 }); | |
| }); | |
| } | |
| // Clock that starts as soon as it is first called (per id). | |
| var clocks: {[key:number]:number} = {}; | |
| function clock(id: number): number { | |
| if (!clocks[id]) clocks[id] = Date.now(); | |
| return (Date.now() - clocks[id]) * .001; | |
| } | |
| // Map the real numbers onto a finite range | |
| function map(x: number): number { | |
| if (Math.abs(x) < 1) return x; | |
| if (x > 1) return 2 - 1/x; | |
| return -2 - 1/x; | |
| } | |
| // Rational function with moving poles, squished into a cone | |
| function rationalFunc(x: number): number[] { | |
| var poles: number[] = []; | |
| var t = clock(1); | |
| poles.push(Math.sin(t*.36+3) + 3); | |
| poles.push(Math.sin(t*.71+5) + 2); | |
| poles.push(Math.sin(t*1.13-8) - 1); | |
| poles.push(Math.sin(t*0.87+1) - 3); | |
| var y = 5, i = x*4; | |
| // The underscore library is coming from the MathBox bundle, version 1.3.3 | |
| // That's a problem, because 1.8.3 dous not have loop. | |
| window['_'].each(poles, function (z) { y /= (i - z) }); | |
| return [π/2*map(y) + t, x*.25 + .25, i]; | |
| } |
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| html, body { height: 100%; } | |
| body { margin: 0; padding: 0 } | |
| canvas { display: block } | |
| #info { | |
| position: absolute; | |
| left: 50%; | |
| bottom: 50px; | |
| z-index: 20; | |
| width: 300px; | |
| margin-left: -150px; | |
| padding: 25px; | |
| background: rgba(0, 0, 0, .5); | |
| color: #fff; | |
| font-family: "Lucida Grande", sans-serif; | |
| font-size: 16px; | |
| text-align: center; | |
| border-radius: 3px; | |
| text-shadow: 0px 1px 0px rgba(0, 0, 0, .4); | |
| opacity: 0; | |
| } | |
| #info.transition { | |
| -webkit-transition: opacity 300ms ease-in-out; | |
| -moz-transition: opacity 300ms ease-in-out; | |
| transition: opacity 300ms ease-in-out; | |
| } | |
| #info kbd { | |
| background: #aaa; | |
| box-shadow: 0px 1px 1px rgba(0, 0, 0, .3); | |
| border-radius: 3px; | |
| padding: 3px; | |
| margin: 3px; | |
| font-family: inherit; | |
| } | |
| .mathbox-label { | |
| font-family: 'klavika-web', sans-serif; | |
| font-weight: normal; | |
| font-style: normal; | |
| text-shadow: | |
| 3px 0px 1px rgb(255, 255, 255), | |
| -3px 0px 1px rgb(255, 255, 255), | |
| 0px -3px 1px rgb(255, 255, 255), | |
| 0px 3px 1px rgb(255, 255, 255), | |
| 2px 2px 1px rgb(255, 255, 255), | |
| -2px 2px 1px rgb(255, 255, 255), | |
| 2px -2px 1px rgb(255, 255, 255), | |
| -2px -2px 1px rgb(255, 255, 255), | |
| 3px 2px 1px rgb(255, 255, 255), | |
| -3px 2px 1px rgb(255, 255, 255), | |
| 3px -2px 1px rgb(255, 255, 255), | |
| -3px -2px 1px rgb(255, 255, 255), | |
| 1px 3px 1px rgb(255, 255, 255), | |
| -1px 3px 1px rgb(255, 255, 255), | |
| 1px -3px 1px rgb(255, 255, 255), | |
| -1px -3px 1px rgb(255, 255, 255), | |
| -1px -1px 1px rgb(255, 255, 255), | |
| -1px 1px 1px rgb(255, 255, 255), | |
| 1px -1px 1px rgb(255, 255, 255), | |
| 1px 1px 1px rgb(255, 255, 255); | |
| } |
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