Particle Physics
Apply forces, fields, and constraints to create dynamic particle motion.
Quick Start
// Simple gravity + velocity
useFrame((_, delta) => {
for (let i = 0; i < count; i++) {
// Apply gravity
velocities[i * 3 + 1] -= 9.8 * delta;
// Update position
positions[i * 3] += velocities[i * 3] * delta;
positions[i * 3 + 1] += velocities[i * 3 + 1] * delta;
positions[i * 3 + 2] += velocities[i * 3 + 2] * delta;
}
geometry.attributes.position.needsUpdate = true;
});
Force Types
Gravity (Constant Force)
function applyGravity(
velocities: Float32Array,
count: number,
gravity: THREE.Vector3,
delta: number
) {
for (let i = 0; i < count; i++) {
velocities[i * 3] += gravity.x * delta;
velocities[i * 3 + 1] += gravity.y * delta;
velocities[i * 3 + 2] += gravity.z * delta;
}
}
// Usage
const gravity = new THREE.Vector3(0, -9.8, 0);
applyGravity(velocities, count, gravity, delta);
Wind (Directional + Noise)
function applyWind(
velocities: Float32Array,
positions: Float32Array,
count: number,
direction: THREE.Vector3,
strength: number,
turbulence: number,
time: number,
delta: number
) {
for (let i = 0; i < count; i++) {
const x = positions[i * 3];
const y = positions[i * 3 + 1];
const z = positions[i * 3 + 2];
// Base wind
let wx = direction.x * strength;
let wy = direction.y * strength;
let wz = direction.z * strength;
// Add turbulence (using simple noise approximation)
const noise = Math.sin(x * 0.5 + time) * Math.cos(z * 0.5 + time);
wx += noise * turbulence;
wy += Math.sin(y * 0.3 + time * 1.3) * turbulence * 0.5;
wz += Math.cos(x * 0.4 + time * 0.7) * turbulence;
velocities[i * 3] += wx * delta;
velocities[i * 3 + 1] += wy * delta;
velocities[i * 3 + 2] += wz * delta;
}
}
Drag (Velocity Damping)
function applyDrag(
velocities: Float32Array,
count: number,
drag: number, // 0-1, higher = more drag
delta: number
) {
const factor = 1 - drag * delta;
for (let i = 0; i < count; i++) {
velocities[i * 3] *= factor;
velocities[i * 3 + 1] *= factor;
velocities[i * 3 + 2] *= factor;
}
}
// Quadratic drag (more realistic)
function applyQuadraticDrag(
velocities: Float32Array,
count: number,
coefficient: number,
delta: number
) {
for (let i = 0; i < count; i++) {
const vx = velocities[i * 3];
const vy = velocities[i * 3 + 1];
const vz = velocities[i * 3 + 2];
const speed = Math.sqrt(vx * vx + vy * vy + vz * vz);
if (speed > 0) {
const dragForce = coefficient * speed * speed;
const factor = Math.max(0, 1 - (dragForce * delta) / speed);
velocities[i * 3] *= factor;
velocities[i * 3 + 1] *= factor;
velocities[i * 3 + 2] *= factor;
}
}
}
Attractors & Repulsors
Point Attractor
function applyAttractor(
velocities: Float32Array,
positions: Float32Array,
count: number,
attractorPos: THREE.Vector3,
strength: number, // Positive = attract, negative = repel
delta: number
) {
for (let i = 0; i < count; i++) {
const dx = attractorPos.x - positions[i * 3];
const dy = attractorPos.y - positions[i * 3 + 1];
const dz = attractorPos.z - positions[i * 3 + 2];
const distSq = dx * dx + dy * dy + dz * dz;
const dist = Math.sqrt(distSq);
if (dist > 0.1) { // Avoid division by zero
// Inverse square falloff
const force = strength / distSq;
velocities[i * 3] += (dx / dist) * force * delta;
velocities[i * 3 + 1] += (dy / dist) * force * delta;
velocities[i * 3 + 2] += (dz / dist) * force * delta;
}
}
}
Orbit Attractor
function applyOrbitAttractor(
velocities: Float32Array,
positions: Float32Array,
count: number,
center: THREE.Vector3,
orbitStrength: number,
pullStrength: number,
delta: number
) {
for (let i = 0; i < count; i++) {
const dx = positions[i * 3] - center.x;
const dy = positions[i * 3 + 1] - center.y;
const dz = positions[i * 3 + 2] - center.z;
const dist = Math.sqrt(dx * dx + dy * dy + dz * dz);
if (dist > 0.1) {
// Tangential force (orbit)
const tx = -dz / dist;
const tz = dx / dist;
velocities[i * 3] += tx * orbitStrength * delta;
velocities[i * 3 + 2] += tz * orbitStrength * delta;
// Radial force (pull toward center)
velocities[i * 3] -= (dx / dist) * pullStrength * delta;
velocities[i * 3 + 1] -= (dy / dist) * pullStrength * delta;
velocities[i * 3 + 2] -= (dz / dist) * pullStrength * delta;
}
}
}
Multiple Attractors
interface Attractor {
position: THREE.Vector3;
strength: number;
radius: number; // Influence radius
}
function applyAttractors(
velocities: Float32Array,
positions: Float32Array,
count: number,
attractors: Attractor[],
delta: number
) {
for (let i = 0; i < count; i++) {
const px = positions[i * 3];
const py = positions[i * 3 + 1];
const pz = positions[i * 3 + 2];
for (const attractor of attractors) {
const dx = attractor.position.x - px;
const dy = attractor.position.y - py;
const dz = attractor.position.z - pz;
const dist = Math.sqrt(dx * dx + dy * dy + dz * dz);
if (dist > 0.1 && dist < attractor.radius) {
// Smooth falloff within radius
const falloff = 1 - dist / attractor.radius;
const force = attractor.strength * falloff * falloff;
velocities[i * 3] += (dx / dist) * force * delta;
velocities[i * 3 + 1] += (dy / dist) * force * delta;
velocities[i * 3 + 2] += (dz / dist) * force * delta;
}
}
}
}
Velocity Fields
Curl Noise Field
// In shader (GPU)
vec3 curlNoise(vec3 p) {
const float e = 0.1;
vec3 dx = vec3(e, 0.0, 0.0);
vec3 dy = vec3(0.0, e, 0.0);
vec3 dz = vec3(0.0, 0.0, e);
float n1 = snoise(p + dy) - snoise(p - dy);
float n2 = snoise(p + dz) - snoise(p - dz);
float n3 = snoise(p + dx) - snoise(p - dx);
float n4 = snoise(p + dz) - snoise(p - dz);
float n5 = snoise(p + dx) - snoise(p - dx);
float n6 = snoise(p + dy) - snoise(p - dy);
return normalize(vec3(n1 - n2, n3 - n4, n5 - n6));
}
// Usage in vertex shader
vec3 velocity = curlNoise(position * 0.5 + uTime * 0.1);
position += velocity * delta;
Flow Field (2D/3D Grid)
class FlowField {
private field: THREE.Vector3[];
private resolution: number;
private size: number;
constructor(resolution: number, size: number) {
this.resolution = resolution;
this.size = size;
this.field = [];
for (let i = 0; i < resolution ** 3; i++) {
this.field.push(new THREE.Vector3());
}
}
// Generate field from noise
generate(time: number, scale: number) {
for (let x = 0; x < this.resolution; x++) {
for (let y = 0; y < this.resolution; y++) {
for (let z = 0; z < this.resolution; z++) {
const index = x + y * this.resolution + z * this.resolution * this.resolution;
// Use noise to generate flow direction
const wx = x / this.resolution * scale;
const wy = y / this.resolution * scale;
const wz = z / this.resolution * scale;
const angle1 = noise3D(wx, wy, wz + time) * Math.PI * 2;
const angle2 = noise3D(wx + 100, wy, wz + time) * Math.PI * 2;
this.field[index].set(
Math.cos(angle1) * Math.cos(angle2),
Math.sin(angle2),
Math.sin(angle1) * Math.cos(angle2)
);
}
}
}
}
// Sample field at position
sample(position: THREE.Vector3): THREE.Vector3 {
const halfSize = this.size / 2;
const x = Math.floor(((position.x + halfSize) / this.size) * this.resolution);
const y = Math.floor(((position.y + halfSize) / this.size) * this.resolution);
const z = Math.floor(((position.z + halfSize) / this.size) * this.resolution);
const cx = Math.max(0, Math.min(this.resolution - 1, x));
const cy = Math.max(0, Math.min(this.resolution - 1, y));
const cz = Math.max(0, Math.min(this.resolution - 1, z));
const index = cx + cy * this.resolution + cz * this.resolution * this.resolution;
return this.field[index];
}
}
Vortex Field
function applyVortex(
velocities: Float32Array,
positions: Float32Array,
count: number,
center: THREE.Vector3,
axis: THREE.Vector3, // Normalized
strength: number,
falloff: number,
delta: number
) {
for (let i = 0; i < count; i++) {
const dx = positions[i * 3] - center.x;
const dy = positions[i * 3 + 1] - center.y;
const dz = positions[i * 3 + 2] - center.z;
// Project onto plane perpendicular to axis
const dot = dx * axis.x + dy * axis.y + dz * axis.z;
const px = dx - dot * axis.x;
const py = dy - dot * axis.y;
const pz = dz - dot * axis.z;
const dist = Math.sqrt(px * px + py * py + pz * pz);
if (dist > 0.1) {
// Tangent direction (cross product with axis)
const tx = axis.y * pz - axis.z * py;
const ty = axis.z * px - axis.x * pz;
const tz = axis.x * py - axis.y * px;
const tLen = Math.sqrt(tx * tx + ty * ty + tz * tz);
const force = strength * Math.exp(-dist * falloff);
velocities[i * 3] += (tx / tLen) * force * delta;
velocities[i * 3 + 1] += (ty / tLen) * force * delta;
velocities[i * 3 + 2] += (tz / tLen) * force * delta;
}
}
}
Turbulence
Simplex-Based Turbulence
// GPU turbulence in vertex shader
vec3 turbulence(vec3 p, float time, float scale, int octaves) {
vec3 result = vec3(0.0);
float amplitude = 1.0;
float frequency = scale;
for (int i = 0; i < octaves; i++) {
vec3 samplePos = p * frequency + time;
result.x += snoise(samplePos) * amplitude;
result.y += snoise(samplePos + vec3(100.0)) * amplitude;
result.z += snoise(samplePos + vec3(200.0)) * amplitude;
frequency *= 2.0;
amplitude *= 0.5;
}
return result;
}
CPU Turbulence
function applyTurbulence(
velocities: Float32Array,
positions: Float32Array,
count: number,
strength: number,
scale: number,
time: number,
delta: number
) {
for (let i = 0; i < count; i++) {
const x = positions[i * 3] * scale;
const y = positions[i * 3 + 1] * scale;
const z = positions[i * 3 + 2] * scale;
// Simple noise approximation
const nx = Math.sin(x + time) * Math.cos(z + time * 0.7);
const ny = Math.sin(y + time * 1.3) * Math.cos(x + time * 0.5);
const nz = Math.sin(z + time * 0.9) * Math.cos(y + time * 1.1);
velocities[i * 3] += nx * strength * delta;
velocities[i * 3 + 1] += ny * strength * delta;
velocities[i * 3 + 2] += nz * strength * delta;
}
}
Collision
Plane Collision
function collidePlane(
positions: Float32Array,
velocities: Float32Array,
count: number,
planeY: number,
bounce: number // 0-1
) {
for (let i = 0; i < count; i++) {
if (positions[i * 3 + 1] < planeY) {
positions[i * 3 + 1] = planeY;
velocities[i * 3 + 1] *= -bounce;
}
}
}
Sphere Collision
function collideSphere(
positions: Float32Array,
velocities: Float32Array,
count: number,
center: THREE.Vector3,
radius: number,
bounce: number,
inside: boolean // true = contain inside, false = repel from outside
) {
for (let i = 0; i < count; i++) {
const dx = positions[i * 3] - center.x;
const dy = positions[i * 3 + 1] - center.y;
const dz = positions[i * 3 + 2] - center.z;
const dist = Math.sqrt(dx * dx + dy * dy + dz * dz);
const collision = inside ? dist > radius : dist < radius;
if (collision && dist > 0) {
const nx = dx / dist;
const ny = dy / dist;
const nz = dz / dist;
// Move to surface
const targetDist = inside ? radius : radius;
positions[i * 3] = center.x + nx * targetDist;
positions[i * 3 + 1] = center.y + ny * targetDist;
positions[i * 3 + 2] = center.z + nz * targetDist;
// Reflect velocity
const dot = velocities[i * 3] * nx + velocities[i * 3 + 1] * ny + velocities[i * 3 + 2] * nz;
velocities[i * 3] = (velocities[i * 3] - 2 * dot * nx) * bounce;
velocities[i * 3 + 1] = (velocities[i * 3 + 1] - 2 * dot * ny) * bounce;
velocities[i * 3 + 2] = (velocities[i * 3 + 2] - 2 * dot * nz) * bounce;
}
}
}
Integration Methods
Euler (Simple)
// Fastest, least accurate
position += velocity * delta;
velocity += acceleration * delta;
Verlet (Better for constraints)
// Store previous position
const newPos = position * 2 - prevPosition + acceleration * delta * delta;
prevPosition = position;
position = newPos;
RK4 (Most accurate)
// Runge-Kutta 4th order (for high precision)
function rk4(position: number, velocity: number, acceleration: (p: number, v: number) => number, dt: number) {
const k1v = acceleration(position, velocity);
const k1x = velocity;
const k2v = acceleration(position + k1x * dt/2, velocity + k1v * dt/2);
const k2x = velocity + k1v * dt/2;
const k3v = acceleration(position + k2x * dt/2, velocity + k2v * dt/2);
const k3x = velocity + k2v * dt/2;
const k4v = acceleration(position + k3x * dt, velocity + k3v * dt);
const k4x = velocity + k3v * dt;
return {
position: position + (k1x + 2*k2x + 2*k3x + k4x) * dt / 6,
velocity: velocity + (k1v + 2*k2v + 2*k3v + k4v) * dt / 6
};
}
File Structure
particles-physics/
├── SKILL.md
├── references/
│ ├── forces.md # All force types
│ └── integration.md # Integration methods comparison
└── scripts/
├── forces/
│ ├── gravity.ts # Gravity implementations
│ ├── attractors.ts # Point/orbit attractors
│ └── fields.ts # Flow/velocity fields
└── collision/
├── planes.ts # Plane collision
└── shapes.ts # Sphere, box collision
Reference
references/forces.md— Complete force implementationsreferences/integration.md— When to use which integration method