Public
Edited
Dec 20
mutable intervalId = null;
viewof restart.addEventListener("click", () => {
if(gridinit) {
step(startingPoint.x, startingPoint.y, .05, amplitudes);
} else {
step(0, 0, .05, amplitudes);
}
});
{
// Add lights
const ambientLight = new THREE.AmbientLight(0x404040);
scene.add(ambientLight);
const directionalLight = new THREE.DirectionalLight(0xffffff, 1);
directionalLight.position.set(5, 5, 5).normalize();
scene.add(directionalLight);
// Add axes helper
const axesHelper = new THREE.AxesHelper(5);
axesHelper.material = new THREE.LineBasicMaterial({ color: 0x000000 });
scene.add(axesHelper);
// Add labels
const loader = new FL.FontLoader();
loader.load("https://threejs.org/examples/fonts/helvetiker_regular.typeface.json", function (font) {
const xLabelGeometry = new TG.TextGeometry("x", {
font: font,
size: 0.2,
depth: 0.01,
});
const yLabelGeometry = new TG.TextGeometry("y", {
font: font,
size: 0.2,
depth: 0.01,
});
const zLabelGeometry = new TG.TextGeometry("f(x,y)", {
font: font,
size: 0.2,
depth: 0.01,
});
const labelMaterial = new THREE.MeshBasicMaterial({ color: 0x000000 });
const xLabel = new THREE.Mesh(xLabelGeometry, labelMaterial);
xLabel.position.set(5, 0, 0);
xLabel.rotateX(Math.PI / 2);
scene.add(xLabel);
const yLabel = new THREE.Mesh(yLabelGeometry, labelMaterial);
yLabel.position.set(0, 5, 0);
yLabel.rotateX(Math.PI / 2);
yLabel.rotateY(Math.PI * 1.5);
scene.add(yLabel);
const zLabel = new THREE.Mesh(zLabelGeometry, labelMaterial);
zLabel.position.set(0, 0, 5);
scene.add(zLabel);
});
}
height = 650;
scene = {
const scene = new THREE.Scene();
scene.background = new THREE.Color(0xffffff);
scene.rotateX(-Math.PI / 2);
scene.rotateZ(-Math.PI / 2);
return scene;
}
camera = {
const fov = 85;
const aspect = width / height;
const near = 1;
const far = 1000;
const camera = new THREE.PerspectiveCamera(fov, aspect, near, far);
camera.position.set(5, 5, 5);
return camera;
}
FL = import('https://unpkg.com/three@0.164.1/examples/jsm/loaders/FontLoader.js?module')
TG = import('https://unpkg.com/three@0.164.1/examples/jsm/geometries/TextGeometry.js?module')
OC = import('https://unpkg.com/three@0.164.1/examples/jsm/controls/OrbitControls.js?module')
THREE = import('https://unpkg.com/three@0.164.1/build/three.module.js?module')
mutable amplitudes = [themin, themin2, themin3, themin4, themin5, themin6]; // Adjusted for other quadrants
function f(x, y, amps) {
const means = [
{ x: 1, y: 2 }, // Global minimum
{ x: 2.5, y: 2 }, // Local minimum
{ x: -.5, y: -1 }, // Additional point
{ x: -1, y: 3 }, // Additional point
{ x: 2, y: -2 }, // Additional point
{ x: -2.5, y: -3 } // Additional point
];
const sigmas = [1.4, 1.4, 1.4, 1.4, 1.4, 1.4];
let z = 2; // Constant offset to make the function positive
for (let i = 0; i < means.length; i++) {
const mean = means[i];
const sigma = sigmas[i];
const A = amps[i];
z += A * Math.exp(-((x - mean.x) * (x - mean.x) + (y - mean.y) * (y - mean.y)) / (2 * sigma * sigma));
}
return z;
}
function df(x, y, amps) {
const means = [
{ x: 1, y: 2 },
{ x: 2.5, y: 2 },
{ x: -.5, y: -1 },
{ x: -1, y: 3 },
{ x: 2, y: -2 },
{ x: -3, y: -3 }
];
const sigmas = [1.4, 1.4, 1.4, 1.4, 1.4, 1.4];
let dx = 0;
let dy = 0;
for (let i = 0; i < means.length; i++) {
const mean = means[i];
const sigma = sigmas[i];
const A = amps[i];
const factor = A * Math.exp(-((x - mean.x) * (x - mean.x) + (y - mean.y) * (y - mean.y)) / (2 * sigma * sigma)) / (sigma * sigma);
dx += (x - mean.x) * factor;
dy += (y - mean.y) * factor;
}
return { dx: dx, dy: dy };
}
scene.add(point);
point = {// Add point for current iteration value of objective function
const pointGeometry = new THREE.SphereGeometry(0.05, 32, 32);
const pointMaterial = new THREE.MeshBasicMaterial({ color: 0xff0000 });
const point = new THREE.Mesh(pointGeometry, pointMaterial);
return point;
}
point_extrem = {
const pointGeometry = new THREE.SphereGeometry(0.05, 32, 32);
const pointMaterial = new THREE.MeshBasicMaterial({ color: "blue" });
const point = new THREE.Mesh(pointGeometry, pointMaterial);
return point;
}
function generateSurface() {
// Add surface
const geometry = new THREE.PlaneGeometry(8, 8, 60, 60);
const material = new THREE.MeshStandardMaterial({
color: 0x156289,
side: THREE.DoubleSide,
flatShading: true,
wireframe: true,
});
// Access the position attribute of the geometry
const positionAttribute = geometry.getAttribute('position');
const vertex = new THREE.Vector3();
for (let i = 0; i < positionAttribute.count; i++) {
vertex.fromBufferAttribute(positionAttribute, i);
const x = vertex.x;
const y = vertex.y;
const z = f(x, y, amplitudes);
vertex.setZ(z);
positionAttribute.setXYZ(i, vertex.x, vertex.y, vertex.z);
}
// Update the position attribute and compute vertex normals
positionAttribute.needsUpdate = true;
geometry.computeVertexNormals();
const surface = new THREE.Mesh(geometry, material);
surface.name = "thesurface";
return surface;
}
scene.children
{
// Iterate over the children of the scene
scene.children.forEach(child => {
// Check if the child has a geometry and if it is a PlaneGeometry
if (child.name == "thesurface") {
scene.remove(child);
child.geometry.dispose();
child.material.dispose();
}
});
scene.add(generateSurface())
if(gridinit) {
point.position.set(startingPoint.x, startingPoint.y, f(startingPoint.x, startingPoint.y, amplitudes));
} else {
point.position.set(0, 0, f(0, 0, amplitudes));
}
}
startingPoint = {
// Function to find the best starting point on a uniform grid
function StartingPoint(f, range, gridSize) {
let bestPoint = null;
let bestValue = Infinity;
const stepSize = (range[1] - range[0]) / (gridSize - 1);
for (let i = 0; i < gridSize; i++) {
for (let j = 0; j < gridSize; j++) {
let x = range[0] + i * stepSize;
let y = range[0] + j * stepSize;
let value = f(x, y, amplitudes);
if (value < bestValue) {
bestValue = value;
bestPoint = { x: x, y: y};
}
}
}
return bestPoint;
}
const range = [-4, 4]; // Define the range for each variable
const gridSize = 5; // gridSize x gridSize points
const bestStartingPoint = StartingPoint(f, range, gridSize);
return bestStartingPoint;
}
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