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drewyoungrendrewyoungren
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Add implicit sampling
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‎media/src/Story.svelte‎

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import Blank from './stories/Blank.svelte';
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import ArcLength from './stories/ArcLength.svelte';
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import Linear from './stories/Linear.svelte';
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import Lagrange from './stories/Lagrange.svelte';
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import PathIntegral from './stories/PathIntegral.svelte';
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import SurfaceArea from './stories/SurfaceArea.svelte';
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import FluxIntegral from './stories/FluxIntegral.svelte';
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<option value={Blank}>Select Story...</option>
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<option value={ArcLength}>Arc Length</option>
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<option value={Linear}>Linearization</option>
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<option value={Lagrange}>Lagrange</option>
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<option value={PathIntegral}>Path Integrals</option>
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<option value={SurfaceArea}>Surface Area</option>
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<option value={FluxIntegral}>Flux Integrals</option>

‎media/src/stories/Lagrange.svelte‎

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<script>
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import * as THREE from 'three';
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import { all, create, xor } from 'mathjs';
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import M from '../M.svelte';
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import {
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ShardsEdgesGeometry,
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ShardsGeometry,
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filterBang,
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gaussLegendre,
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sampleImplicitSurface,
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} from '../utils';
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import { mathToJSFunction } from '../objects/mathutils';
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import { onMount, onDestroy, untrack } from 'svelte';
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import { demoObjects } from '../states.svelte';
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let { scene, render } = $props();
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const config = {};
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const math = create(all, config);
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let sampleParam = $state(0);
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let backupObjects = $state(
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demoObjects.map((obj) => {
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obj.selected = false;
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return obj;
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}),
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);
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let standardExamples = $state([
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{
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uuid: 'lag-story-example-001-',
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kind: 'level',
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title: 'Sphere',
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params: {
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a: '-2',
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b: '2',
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c: '-2',
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d: '2',
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e: '-2',
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f: '2',
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g: 'x^2 + y^2 - 1',
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},
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color: '#44CB44',
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},
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]);
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const whiteLineMaterial = new THREE.LineBasicMaterial({
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color: 0xffffff,
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linewidth: 2,
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depthTest: true,
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});
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let currentSurface = $state(
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backupObjects.find((o) => o.kind === 'level') ?? standardExamples[0],
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);
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// $inspect(currentSurface);
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onMount(() => {
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render();
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});
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onDestroy(() => {
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for (let index = 0; index < boxes.children.length; index++) {
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const element = boxes.children[index];
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element.geometry?.dispose();
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element.material?.dispose();
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}
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scene.remove(boxes);
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demoObjects.length = 0;
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demoObjects.push(...backupObjects);
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render();
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});
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let geo = $state();
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let edgesUp = $state();
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const plusMaterial = new THREE.MeshStandardMaterial({
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color: 0xccddff,
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side: THREE.DoubleSide,
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roughness: 0.4,
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metalness: 0.8,
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});
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const boxes = new THREE.Object3D();
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// boxes.add(new THREE.Mesh(undefined, plusMaterial)); // pos boxes
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// boxes.add(new THREE.LineSegments(undefined, whiteLineMaterial)); // pos edges
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// boxes.add(new THREE.Mesh(undefined, minusMaterial)); // neg boxes
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// boxes.add(new THREE.LineSegments(undefined, whiteLineMaterial)); // neg edges
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scene.add(boxes);
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let boxesVisible = $state(true);
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$effect(() => {
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boxes.visible = boxesVisible;
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});
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let nBoxes = $state(10);
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let boxing = false;
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let x0 = $derived(math.parse(currentSurface.params.a).evaluate());
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let x1 = $derived(math.parse(currentSurface.params.b).evaluate());
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let y0 = $derived(math.parse(currentSurface.params.c).evaluate());
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let y1 = $derived(math.parse(currentSurface.params.d).evaluate());
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let z0 = $derived(math.parse(currentSurface.params.e).evaluate());
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let z1 = $derived(math.parse(currentSurface.params.f).evaluate());
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let g = $derived(
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mathToJSFunction(currentSurface.params.g, ['x', 'y', 'z']),
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);
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let pts = $derived(
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sampleImplicitSurface(g, [
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[x0, x1],
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[y0, y1],
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[z0, z1],
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nBoxes,
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nBoxes,
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nBoxes,
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]),
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);
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$inspect(pts);
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const sphereGeo = new THREE.SphereGeometry(0.01, 14, 14);
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$effect(() => {
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untrack(() => {
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for (let index = boxes.children.length - 1; index >= 0; index--) {
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const element = boxes.children[index];
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// element.geometry?.dispose();
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// element.material?.dispose();
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boxes.remove(element);
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}
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});
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for (const p of pts) {
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const box = new THREE.Mesh(sphereGeo, plusMaterial);
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box.position.set(...p);
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boxes.add(box);
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}
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console.log('effecttt', boxes);
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render();
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});
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$effect(() => {
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// console.log('demobj maintenance');
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if (currentSurface)
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untrack(() => {
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demoObjects[0] = currentSurface;
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demoObjects.length = 1;
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// filterBang(
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// (o) => o === currentField || o === currentSurface,
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// demoObjects,
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// );
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// if (demoObjects.findIndex((o) => o === currentField) < 0)
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// demoObjects.push(currentField);
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// if (demoObjects.findIndex((o) => o === currentSurface) < 0)
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// demoObjects.push(currentSurface);
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});
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});
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</script>
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<div>
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<p>Hello</p>
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<input
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type="range"
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name=""
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id=""
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min="1"
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bind:value={nBoxes}
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step="1"
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max="20"
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/>
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</div>
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<style>
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/* .demos-obj-select {
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border-bottom-right-radius: 0;
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border-top-right-radius: 0;
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} */
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/* .blue-button {
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background-color: red;
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} */
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</style>

‎media/src/utils.js‎

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@@ -2876,3 +2876,88 @@ export {
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scaleExp,
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filterBang,
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};
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/**
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* Sample roughly evenly spaced points on an implicit surface g(x, y, z) = 0
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* within a cuboid defined by [xmin, xmax], [ymin, ymax], [zmin, zmax].
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*
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* @param {Function} g - scalar field function g(x, y, z)
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* @param {Array} bounds - [[xmin, xmax], [ymin, ymax], [zmin, zmax]]
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* @param {number} nx - grid resolution in x
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* @param {number} ny - grid resolution in y
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* @param {number} nz - grid resolution in z
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* @returns {Array<[number, number, number]>} sampled points
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*/
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export function sampleImplicitSurface(g, bounds, nx = 40, ny = 40, nz = 40) {
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const [[xmin, xmax], [ymin, ymax], [zmin, zmax]] = bounds;
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const dx = (xmax - xmin) / (nx - 1);
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const dy = (ymax - ymin) / (ny - 1);
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const dz = (zmax - zmin) / (nz - 1);
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// Precompute scalar field on the grid
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const grid = Array.from({ length: nx }, () =>
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Array.from({ length: ny }, () => new Array(nz))
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);
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for (let i = 0; i < nx; i++) {
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const x = xmin + i * dx;
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for (let j = 0; j < ny; j++) {
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const y = ymin + j * dy;
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for (let k = 0; k < nz; k++) {
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const z = zmin + k * dz;
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grid[i][j][k] = g(x, y, z);
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}
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}
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}
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const points = [];
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// Check each cube in the grid for sign changes (surface crossings)
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for (let i = 0; i < nx - 1; i++) {
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for (let j = 0; j < ny - 1; j++) {
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for (let k = 0; k < nz - 1; k++) {
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// The cube's 8 corner values
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const corners = [
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[i, j, k],
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[i + 1, j, k],
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[i + 1, j + 1, k],
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[i, j + 1, k],
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[i, j, k + 1],
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[i + 1, j, k + 1],
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[i + 1, j + 1, k + 1],
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[i, j + 1, k + 1]
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].map(([ii, jj, kk]) => grid[ii][jj][kk]);
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const minVal = Math.min(...corners);
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const maxVal = Math.max(...corners);
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if (minVal * maxVal > 0) continue; // No sign change → skip
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// Find approximate intersection point (weighted average)
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let sumWeights = 0;
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let px = 0, py = 0, pz = 0;
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for (let ii = 0; ii <= 1; ii++) {
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for (let jj = 0; jj <= 1; jj++) {
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for (let kk = 0; kk <= 1; kk++) {
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const val = grid[i + ii][j + jj][k + kk];
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const weight = 1 / (Math.abs(val) + 1e-6);
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const x = xmin + (i + ii) * dx;
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const y = ymin + (j + jj) * dy;
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const z = zmin + (k + kk) * dz;
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px += weight * x;
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py += weight * y;
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pz += weight * z;
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sumWeights += weight;
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}
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}
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}
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points.push([px / sumWeights, py / sumWeights, pz / sumWeights]);
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}
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}
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}
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return points;
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}

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