Researching the operation of GeoCAS.Multivector.
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September 20, 2016 14:36
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EIGHT with GeoCAS Multivector
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| /** | |
| * Displays an exception by writing it to a <pre> element. | |
| */ | |
| export default function displayError(e: any) { | |
| const stderr = <HTMLPreElement>document.getElementById('error') | |
| stderr.style.color = "#FF0000" | |
| stderr.innerHTML = `${e}` | |
| } |
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| /** | |
| * The Field Adapter for a number field. | |
| */ | |
| const fa = new GeoCAS.NumberFieldAdapter(); | |
| /** | |
| * Setting the metric parameter to the number of dimensions | |
| * is equivalent to specifying a [1, 1, 1] diagonal metric. | |
| */ | |
| const dimensions = 3; | |
| /** | |
| * A (diagonal) Euclidean metric for a 3D vector space. | |
| */ | |
| const diag = [1, 1, 1]; | |
| const metric = dimensions; | |
| export const one = GeoCAS.getScalar(1, metric, fa); | |
| export const e1 = GeoCAS.getBasisVector(0, metric, fa); | |
| export const e2 = GeoCAS.getBasisVector(1, metric, fa); | |
| export const e3 = GeoCAS.getBasisVector(2, metric, fa); | |
| /** | |
| * Updates a mutable SpinorE3 from a Multivector<number>. | |
| */ | |
| export function setSpinorE3(target: EIGHT.SpinorE3, source: GeoCAS.Multivector<number>): void { | |
| target.a = source.scp(one); | |
| target.zx = source.scp(e1 ^ e3) | |
| target.xy = source.scp(e2 ^ e1) | |
| target.yz = source.scp(e3 ^ e2) | |
| } | |
| /** | |
| * Updates a mutable VectorE3 from a Multivector<number>. | |
| */ | |
| export function setVectorE3(target: EIGHT.VectorE3, source: GeoCAS.Multivector<number>): void { | |
| target.x = source.scp(e1) | |
| target.y = source.scp(e2) | |
| target.z = source.scp(e3) | |
| } | |
| /** | |
| * Universal exponential function for more natural notation. | |
| */ | |
| export function exp<T extends {exp: ()=>T}>(arg: T): T { | |
| return arg.exp() | |
| } |
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| <!doctype html> | |
| <html> | |
| <head> | |
| <!-- STYLES-MARKER --> | |
| <style> | |
| /* STYLE-MARKER */ | |
| </style> | |
| <script src='https://jspm.io/[email protected]'></script> | |
| <!-- SHADERS-MARKER --> | |
| <!-- SCRIPTS-MARKER --> | |
| </head> | |
| <body> | |
| <canvas id='canvas'></canvas> | |
| <pre id='error'></pre> | |
| <script> | |
| // CODE-MARKER | |
| </script> | |
| <script> | |
| System.import('./index.js') | |
| </script> | |
| </body> | |
| </html> |
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| import {one, e1, e2, e3} from './e3ga'; | |
| import {setSpinorE3, setVectorE3} from './e3ga'; | |
| import {exp} from './e3ga'; | |
| // Comment out the following line to use the standard window.requestAnimationFrame | |
| import requestAnimationFrame from './requestAnimationFrame'; | |
| import WireCube from './WireCube'; | |
| /** | |
| * Wrapper around the WebGLRenderingContext providing the ContextManager interface. | |
| */ | |
| const engine = new EIGHT.Engine('canvas') | |
| .size(500, 500) | |
| .clearColor(0.1, 0.1, 0.1, 1.0) | |
| .enable(EIGHT.Capability.DEPTH_TEST) | |
| /** | |
| * A collection of objects that can be rendered with a single draw method call. | |
| */ | |
| const scene = new EIGHT.Scene(engine) | |
| /** | |
| * Rendering information that applies to all objects. | |
| */ | |
| const ambients: EIGHT.Facet[] = [] | |
| /** | |
| * Provides the viewing point and perspective transformation. | |
| */ | |
| const camera = new EIGHT.PerspectiveCamera() | |
| setVectorE3(camera.eye, 3 * e3) | |
| ambients.push(camera) | |
| /** | |
| * Provides a light color and direction for Lambert shading. | |
| */ | |
| const dirLight = new EIGHT.DirectionalLight() | |
| ambients.push(dirLight) | |
| /** | |
| * Controls the camera by accumulating mouse movements then moving and rotating the camera. | |
| */ | |
| const trackball = new EIGHT.TrackballControls(camera, window) | |
| trackball.subscribe(engine.canvas) | |
| trackball.noPan = true; | |
| // Create drawables such as Arrow, Box, Curve, Grid, Sphere, Cylinder. | |
| // Add them to the scene here... | |
| const box = new EIGHT.Box({color: EIGHT.Color.green}) | |
| box.width = 0.6 | |
| box.height = 0.6 | |
| box.depth = 0.6 | |
| scene.add(box) | |
| const geometry = new WireCube(engine) | |
| const material = new EIGHT.HTMLScriptsMaterial(['line-vs', 'line-fs'], document, [], engine) | |
| const wireCube = new EIGHT.Mesh(geometry, material, engine) | |
| scene.add(wireCube) | |
| const stats = new Stats() | |
| document.body.appendChild(stats.dom) | |
| /** | |
| * The bivector for the rotation. | |
| */ | |
| const B = e3 ^ e1; | |
| /** | |
| * Animates the scene. | |
| */ | |
| const animate = function(timestamp: number) { | |
| stats.begin() | |
| engine.clear() | |
| trackball.update() | |
| dirLight.direction.copy(camera.look).sub(camera.eye) | |
| // Manupulate the X (Position) and R (Attitude) | |
| // properties of your scene objects here... | |
| const θ = timestamp * 0.001; | |
| setSpinorE3(box.R, exp(-B * θ / 2)); | |
| scene.draw(ambients) | |
| stats.end() | |
| requestAnimationFrame(animate) | |
| } | |
| requestAnimationFrame(animate) |
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| varying highp vec4 vColor; | |
| void main(void) { | |
| gl_FragColor = vColor; | |
| } |
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| attribute vec3 aPosition; | |
| uniform vec3 uColor; | |
| uniform float uOpacity; | |
| uniform mat4 uModel; | |
| uniform mat4 uProjection; | |
| uniform mat4 uView; | |
| varying highp vec4 vColor; | |
| void main(void) { | |
| gl_Position = uProjection * uView * uModel * vec4(aPosition, 1.0); | |
| vColor = vec4(uColor, uOpacity); | |
| } |
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| { | |
| "description": "EIGHT with GeoCAS Multivector", | |
| "dependencies": { | |
| "davinci-eight": "2.310.0", | |
| "stats.js": "0.16.0", | |
| "dat-gui": "0.5.0", | |
| "geocas": "1.0.0" | |
| }, | |
| "operatorOverloading": true, | |
| "name": "copy-of-eight-starter-template", | |
| "version": "0.1.0", | |
| "keywords": [ | |
| "EIGHT", | |
| "GeoCAS", | |
| "Multivector" | |
| ], | |
| "author": "David Geo Holmes" | |
| } |
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| import displayError from './displayError' | |
| /** | |
| * Catches exceptions thrown in the animation callback and displays them. | |
| * This function will have a slight performance impact owing to the try...catch statement. | |
| * This function may be bypassed for production use by using window.requestAnimationFrame directly. | |
| */ | |
| export default function requestAnimationFrame(callback: FrameRequestCallback): number { | |
| const wrapper: FrameRequestCallback = function(time: number) { | |
| try { | |
| callback(time) | |
| } | |
| catch(e) { | |
| displayError(e) | |
| } | |
| } | |
| return window.requestAnimationFrame(wrapper) | |
| } |
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| body { margin: 0; } | |
| canvas { width: 500px; height: 500px } | |
| #stats { position: absolute; top: 0; left: 0; } |
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| /** | |
| * A Geometry for rendering a cube made from lines. | |
| */ | |
| export default class WireCube implements EIGHT.Geometry { | |
| private buffer: WebGLBuffer; | |
| public data: Float32Array; | |
| /** | |
| * | |
| */ | |
| public invalid = true; | |
| constructor(private engine: EIGHT.Engine) { | |
| const gl = engine.gl; | |
| const size = 1; | |
| const L = size / 2; | |
| this.data = new Float32Array([ | |
| -L, -L, -L, +L, -L, -L, | |
| -L, +L, -L, +L, +L, -L, | |
| -L, -L, +L, +L, -L, +L, | |
| -L, +L, +L, +L, +L, +L, | |
| -L, +L, +L, -L, +L, -L, | |
| +L, +L, +L, +L, +L, -L, | |
| -L, -L, +L, -L, -L, -L, | |
| +L, -L, +L, +L, -L, -L, | |
| -L, -L, -L, -L, +L, -L, | |
| +L, -L, -L, +L, +L, -L, | |
| -L, -L, +L, -L, +L, +L, | |
| +L, -L, +L, +L, +L, +L | |
| ]); | |
| this.buffer = gl.createBuffer(); | |
| } | |
| bind(material: EIGHT.Material): void { | |
| const gl = this.engine.gl; | |
| gl.bindBuffer(gl.ARRAY_BUFFER, this.buffer); | |
| } | |
| unbind(material: EIGHT.Material): void { | |
| const gl = this.engine.gl; | |
| gl.bindBuffer(gl.ARRAY_BUFFER, null); | |
| } | |
| draw(material: EIGHT.Material): void { | |
| const gl = this.engine.gl; | |
| const aPosition = material.getAttribLocation('aPosition'); | |
| if (this.invalid) { | |
| gl.bufferData(gl.ARRAY_BUFFER, this.data, EIGHT.Usage.STATIC_DRAW); | |
| this.invalid = false; | |
| } | |
| gl.vertexAttribPointer(aPosition, 3, EIGHT.DataType.FLOAT, true, 0, 0); | |
| gl.enableVertexAttribArray(aPosition); | |
| gl.drawArrays(EIGHT.BeginMode.LINES, 0, 24); | |
| gl.disableVertexAttribArray(aPosition); | |
| } | |
| } |
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