klz-cables.com/components/home/hero-webgl/math.ts

import { createNoise2D } from 'simplex-noise';

// Seeded random number generator
export function LCG(seed: number) {
    return function () {
        seed = Math.imul(48271, seed) | 0 % 2147483647;
        return (seed & 2147483647) / 2147483648;
    };
}

export type Vec2 = [number, number];
export type Vec3 = [number, number, number];

export function distance2D(a: Vec2, b: Vec2) {
    const dx = a[0] - b[0];
    const dy = a[1] - b[1];
    return Math.sqrt(dx * dx + dy * dy);
}

export function distance3D(a: Vec3, b: Vec3) {
    const dx = a[0] - b[0];
    const dy = a[1] - b[1];
    const dz = a[2] - b[2];
    return Math.sqrt(dx * dx + dy * dy + dz * dz);
}

// Generate points for a hanging cable between two points (catenary/sag)
export function generateCatenaryCurve(
    p1: Vec3,
    p2: Vec3,
    sag: number,
    segments: number = 10
): Vec3[] {
    const points: Vec3[] = [];
    for (let i = 0; i <= segments; i++) {
        const t = i / segments;
        const x = p1[0] + (p2[0] - p1[0]) * t;
        const z = p1[2] + (p2[2] - p1[2]) * t;

        // Linear interpolation of height
        const baseHeight = p1[1] + (p2[1] - p1[1]) * t;

        // Add parabolic sag
        // t ranges from 0 to 1. Parabola that is 0 at ends and 1 in middle is 4 * t * (1 - t)
        const sagOffset = 4 * t * (1 - t) * sag;

        const y = baseHeight - sagOffset;
        points.push([x, y, z]);
    }
    return points;
}

// Simple terrain height function combining multiple frequencies
export function getTerrainHeight(noise2D: ReturnType<typeof createNoise2D>, x: number, z: number): number {
    // We want a gigantic, hilly planet. We'll use low frequency noise.
    const n1 = noise2D(x * 0.002, z * 0.002) * 40; // Main hills
    const n2 = noise2D(x * 0.01, z * 0.01) * 10;   // Smaller details
    return n1 + n2;
}

// Helper: Place points within a radius using rejection sampling to avoid overlap
export function generateClusteredPoints(
    rng: () => number,
    center: Vec2,
    count: number,
    radius: number,
    minDist: number
): Vec2[] {
    const points: Vec2[] = [];
    let attempts = 0;
    const maxAttempts = count * 50;

    while (points.length < count && attempts < maxAttempts) {
        attempts++;
        const angle = rng() * Math.PI * 2;
        // Square root for uniform distribution in a circle
        const r = Math.sqrt(rng()) * radius;

        const p: Vec2 = [
            center[0] + Math.cos(angle) * r,
            center[1] + Math.sin(angle) * r
        ];

        let valid = true;
        for (const other of points) {
            if (distance2D(p, other) < minDist) {
                valid = false;
                break;
            }
        }

        if (valid) {
            points.push(p);
        }
    }

    return points;
}