particles/geometric-paradox.html at main · danlex/particles · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Geometric Paradox — Particles</title>
  <meta name="description" content="Morphing between impossible shapes: Penrose triangle, Necker cube, and Mobius strip.">
  <meta name="author" content="Alexandru DAN">
  <meta name="theme-color" content="#050505">
  <link rel="canonical" href="https://particles.alexandrudan.com/geometric-paradox.html">
  <link rel="icon" type="image/svg+xml" href="favicon.svg">

  <!-- Open Graph -->
  <meta property="og:type" content="website">
  <meta property="og:url" content="https://particles.alexandrudan.com/geometric-paradox.html">
  <meta property="og:title" content="Geometric Paradox — Particles">
  <meta property="og:description" content="Morphing between impossible shapes: Penrose triangle, Necker cube, and Mobius strip.">
  <meta property="og:image" content="https://particles.alexandrudan.com/og-image.svg">
  <meta property="og:site_name" content="Particles">

  <!-- Twitter -->
  <meta name="twitter:card" content="summary_large_image">
  <meta name="twitter:title" content="Geometric Paradox — Particles">
  <meta name="twitter:description" content="Morphing between impossible shapes: Penrose triangle, Necker cube, and Mobius strip.">
  <meta name="twitter:image" content="https://particles.alexandrudan.com/og-image.svg">
  <style>
    * { margin: 0; padding: 0; box-sizing: border-box; }
    body { background: #000; overflow: hidden; font-family: 'Courier New', monospace; }
    canvas { display: block; }
    #controls {
      position: fixed;
      bottom: 24px;
      left: 50%;
      transform: translateX(-50%);
      display: flex;
      gap: 20px;
      background: rgba(0,0,0,0.6);
      backdrop-filter: blur(12px);
      border: 1px solid rgba(255,255,255,0.08);
      border-radius: 12px;
      padding: 14px 28px;
      z-index: 10;
      align-items: center;
    }
    .ctrl-group {
      display: flex; flex-direction: column; align-items: center; gap: 4px;
    }
    .ctrl-group label {
      color: rgba(255,255,255,0.4); font-size: 9px;
      text-transform: uppercase; letter-spacing: 1.5px;
    }
    .ctrl-group input[type="range"] {
      -webkit-appearance: none; width: 100px; height: 3px;
      background: rgba(255,255,255,0.15); border-radius: 2px; outline: none;
    }
    .ctrl-group input[type="range"]::-webkit-slider-thumb {
      -webkit-appearance: none; width: 12px; height: 12px;
      border-radius: 50%; background: #fff; cursor: pointer;
    }
    #info {
      position: fixed; top: 24px; left: 28px; z-index: 10;
    }
    #info h1 {
      color: rgba(255,255,255,0.7); font-size: 14px; font-weight: 400;
      letter-spacing: 3px; text-transform: uppercase;
    }
    #info p {
      color: rgba(255,255,255,0.25); font-size: 10px;
      margin-top: 6px; letter-spacing: 1px;
    }
    #fps {
      position: fixed; top: 24px; right: 28px;
      color: rgba(255,255,255,0.2); font-size: 10px;
      letter-spacing: 1px; z-index: 10;
    }
    #back {
      position: fixed; top: 24px; left: 50%; transform: translateX(-50%);
      z-index: 10;
    }
    #back a {
      color: rgba(255,255,255,0.2); font-size: 9px; text-decoration: none;
      letter-spacing: 2px; text-transform: uppercase;
      transition: color 0.3s;
    }
    #back a:hover { color: rgba(255,255,255,0.5); }
      .zoom-btn {
      width: 32px; height: 32px; border-radius: 50%;
      background: rgba(255,255,255,0.06); border: 1px solid rgba(255,255,255,0.12);
      color: rgba(255,255,255,0.5); font-size: 18px; cursor: pointer;
      display: flex; align-items: center; justify-content: center;
      transition: background 0.2s;
      font-family: monospace;
    }
    .zoom-btn:hover { background: rgba(255,255,255,0.12); }
  </style>
</head>
<body>
  <div id="info">
    <h1>Geometric Paradox</h1>
    <p id="particle-count"></p>
  </div>
  <div id="fps"></div>
  <div id="back"><a href="index.html">Gallery</a></div>
  <div id="controls">
    <div class="ctrl-group">
      <input type="range" id="speed" min="0.1" max="5" step="0.1" value="1">
      <label>Speed</label>
    </div>
    <div class="ctrl-group">
      <input type="range" id="bloom" min="0" max="3" step="0.1" value="0.4">
      <label>Bloom</label>
    </div>
    <div class="ctrl-group">
      <input type="range" id="size" min="0.5" max="4" step="0.1" value="1.0">
      <label>Size</label>
    </div>
    <div class="ctrl-group">
      <input type="range" id="hueShift" min="0" max="1" step="0.01" value="0">
      <label>Hue</label>
    </div>
    <button class="zoom-btn" id="zoomOut">−</button>
    <button class="zoom-btn" id="zoomIn">+</button>
  </div>

  <script type="importmap">
  {
    "imports": {
      "three": "https://cdn.jsdelivr.net/npm/three@0.160.0/build/three.module.js",
      "three/addons/": "https://cdn.jsdelivr.net/npm/three@0.160.0/examples/jsm/"
    }
  }
  </script>
  <script type="module">
    import * as THREE from 'three';
    import { OrbitControls } from 'three/addons/controls/OrbitControls.js';
    import { EffectComposer } from 'three/addons/postprocessing/EffectComposer.js';
    import { RenderPass } from 'three/addons/postprocessing/RenderPass.js';
    import { UnrealBloomPass } from 'three/addons/postprocessing/UnrealBloomPass.js';
    import { GPUComputationRenderer } from 'three/addons/misc/GPUComputationRenderer.js';

    const WIDTH = 256;
    const PARTICLE_COUNT = WIDTH * WIDTH;

    // Scene
    const scene = new THREE.Scene();
    const camera = new THREE.PerspectiveCamera(60, innerWidth / innerHeight, 0.1, 2000);
    camera.position.set(0, 0, 28);

    const renderer = new THREE.WebGLRenderer({ antialias: false, powerPreference: 'high-performance' });
    renderer.setSize(innerWidth, innerHeight);
    renderer.setPixelRatio(1);
    document.body.appendChild(renderer.domElement);

    const orbitControls = new OrbitControls(camera, renderer.domElement);
    orbitControls.enableDamping = true;
    orbitControls.dampingFactor = 0.05;
    orbitControls.autoRotate = true;
    orbitControls.autoRotateSpeed = 0.5;

    // Post-processing
    const composer = new EffectComposer(renderer);
    composer.addPass(new RenderPass(scene, camera));
    const bloomPass = new UnrealBloomPass(
      new THREE.Vector2(innerWidth / 2, innerHeight / 2),
      0.4, 0.3, 0.85
    );
    composer.addPass(bloomPass);

    // GPU Computation
    const gpuCompute = new GPUComputationRenderer(WIDTH, WIDTH, renderer);
    const posTex0 = gpuCompute.createTexture();

    // Seed initial positions for the geometric shapes
    function seedTexture(tex) {
      const data = tex.image.data;
      for (let i = 0; i < PARTICLE_COUNT; i++) {
        const t = i / PARTICLE_COUNT;
        const idx = i * 4;

        // Start with Penrose triangle shape
        const segment = t * 3.0;
        const segIdx = Math.floor(segment);
        const segT = segment - segIdx;

        const S = 6.0;
        const ang0 = segIdx * 2.0944;
        const ang1 = (segIdx + 1) * 2.0944;
        const thickness = 0.8;
        const barAngle = Math.atan2(Math.sin(ang1) - Math.sin(ang0), Math.cos(ang1) - Math.cos(ang0));
        const perpX = -Math.sin(barAngle) * thickness * (((i * 0.001) % 1) - 0.5);
        const perpY = Math.cos(barAngle) * thickness * (((i * 0.002) % 1) - 0.5);

        const x = (S * Math.cos(ang0) * (1 - segT) + S * Math.cos(ang1) * segT) + perpX;
        const y = (S * Math.sin(ang0) * (1 - segT) + S * Math.sin(ang1) * segT) + perpY;
        const z = Math.sin(segIdx * 2.094 + segT * 2.094) * 2.0;

        data[idx]     = x;
        data[idx + 1] = y;
        data[idx + 2] = z;
        data[idx + 3] = 0;
      }
    }

    seedTexture(posTex0);

    const positionShader = `
      uniform float uTime;
      uniform float uSpeed;

      void main() {
        vec2 uv = gl_FragCoord.xy / resolution.xy;

        float idx = gl_FragCoord.y * resolution.x + gl_FragCoord.x;
        float total = resolution.x * resolution.y;
        float t = idx / total;

        // Morph parameter cycles between shapes
        float morphTime = uTime * 0.1 * uSpeed;
        float morphPhase = mod(morphTime, 3.0);

        // === Penrose Triangle ===
        float segment = t * 3.0;
        float segIdx = floor(segment);
        float segT = fract(segment);

        float S = 6.0;
        float ang0 = segIdx * 2.0944;
        float ang1 = (segIdx + 1.0) * 2.0944;
        float thickness = 0.8;
        float barAngle = atan(sin(ang1) - sin(ang0), cos(ang1) - cos(ang0));
        float perpX = -sin(barAngle) * thickness * (fract(idx * 0.001) - 0.5);
        float perpY = cos(barAngle) * thickness * (fract(idx * 0.002) - 0.5);
        float triX = mix(S*cos(ang0), S*cos(ang1), segT) + perpX;
        float triY = mix(S*sin(ang0), S*sin(ang1), segT) + perpY;
        float triZ = sin(segIdx * 2.094 + segT * 2.094) * 2.0;

        // === Impossible Cube (Necker cube) ===
        float edge = t * 12.0;
        float edgeIdx = floor(edge);
        float edgeT = fract(edge);
        float cubeS = 4.0;
        float v0x = mod(floor(edgeIdx), 2.0) * 2.0 - 1.0;
        float v0y = mod(floor(edgeIdx / 2.0), 2.0) * 2.0 - 1.0;
        float v0z = mod(floor(edgeIdx / 4.0), 2.0) * 2.0 - 1.0;
        float v1x = mod(floor(edgeIdx + 1.0), 2.0) * 2.0 - 1.0;
        float v1y = mod(floor((edgeIdx + 1.0) / 2.0), 2.0) * 2.0 - 1.0;
        float v1z = mod(floor((edgeIdx + 1.0) / 4.0), 2.0) * 2.0 - 1.0;
        float cubeX = mix(v0x, v1x, edgeT) * cubeS;
        float cubeY = mix(v0y, v1y, edgeT) * cubeS;
        float cubeZ = mix(v0z, v1z, edgeT) * cubeS;
        cubeZ += sin(edgeT * 3.14159 + edgeIdx) * 1.5;

        // === Mobius Strip ===
        float mobiusU = t * 6.28318;
        float mobiusV = (fract(idx * 0.003) - 0.5) * 2.0;
        float halfU = mobiusU * 0.5;
        float mobiusR = 5.0;
        float mobiusX = (mobiusR + mobiusV * cos(halfU)) * cos(mobiusU);
        float mobiusY = (mobiusR + mobiusV * cos(halfU)) * sin(mobiusU);
        float mobiusZ = mobiusV * sin(halfU);

        // Smooth morph between shapes
        float w1 = smoothstep(0.0, 1.0, 1.0 - abs(morphPhase - 0.0));
        float w2 = smoothstep(0.0, 1.0, 1.0 - abs(morphPhase - 1.0));
        float w3 = smoothstep(0.0, 1.0, 1.0 - abs(morphPhase - 2.0));
        float wTotal = w1 + w2 + w3 + 0.001;

        float x = (triX * w1 + cubeX * w2 + mobiusX * w3) / wTotal;
        float y = (triY * w1 + cubeY * w2 + mobiusY * w3) / wTotal;
        float z = (triZ * w1 + cubeZ * w2 + mobiusZ * w3) / wTotal;

        float speed = w1 * 0.3 + w2 * 0.6 + w3 * 0.9;

        gl_FragColor = vec4(x, y, z, speed);
      }
    `;

    const posVar = gpuCompute.addVariable('texturePosition', positionShader, posTex0);
    gpuCompute.setVariableDependencies(posVar, [posVar]);

    posVar.material.uniforms.uTime = { value: 0.0 };
    posVar.material.uniforms.uSpeed = { value: 1.0 };

    posVar.wrapS = THREE.RepeatWrapping;
    posVar.wrapT = THREE.RepeatWrapping;

    const err = gpuCompute.init();
    if (err !== null) console.error('GPU Computation init error:', err);

    // Particle Rendering
    const vertexShader = `
      uniform vec3 uMouseWorld;
      uniform float uMouseStrength;
      uniform sampler2D uPositionTexture;
      uniform float uHueShift;
      uniform float uPointSize;
      uniform float uScale;
      attribute vec2 aTexCoord;
      varying vec3 vColor;

      vec3 hsl2rgb(float h, float s, float l) {
        float c = (1.0 - abs(2.0 * l - 1.0)) * s;
        float h6 = h * 6.0;
        float x = c * (1.0 - abs(mod(h6, 2.0) - 1.0));
        float m = l - c * 0.5;
        vec3 rgb;
        if (h6 < 1.0) rgb = vec3(c, x, 0.0);
        else if (h6 < 2.0) rgb = vec3(x, c, 0.0);
        else if (h6 < 3.0) rgb = vec3(0.0, c, x);
        else if (h6 < 4.0) rgb = vec3(0.0, x, c);
        else if (h6 < 5.0) rgb = vec3(x, 0.0, c);
        else rgb = vec3(c, 0.0, x);
        return rgb + m;
      }

      void main() {
        vec4 posData = texture2D(uPositionTexture, aTexCoord);
        float x = posData.x;
        float y = posData.y;
        float z = posData.z;
        float speed = posData.w; // morph phase identity

        vec3 pos = vec3(x, y, z) * uScale;
        // Mouse displacement
        vec3 toM = uMouseWorld - pos;
        float mDist = length(toM);
        pos += toM * uMouseStrength * 0.5 / (mDist * mDist + 2.0);

        // Color based on shape identity: Triangle=cyan(0.5), Cube=orange(0.08), Mobius=magenta(0.83)
        float hue = fract(mix(0.5, mix(0.08, 0.83, (speed - 0.3) / 0.6), step(0.3, speed)) + uHueShift);
        // More nuanced: blend hue based on speed (which encodes morph weights)
        // speed=0.3 -> triangle (cyan ~0.5), speed=0.6 -> cube (orange ~0.08), speed=0.9 -> mobius (magenta ~0.83)
        float triWeight = smoothstep(0.15, 0.3, speed) * (1.0 - smoothstep(0.3, 0.45, speed));
        float cubeWeight = smoothstep(0.45, 0.6, speed) * (1.0 - smoothstep(0.6, 0.75, speed));
        float mobiusWeight = smoothstep(0.75, 0.9, speed);
        hue = fract(0.5 * triWeight + 0.08 * cubeWeight + 0.83 * mobiusWeight
              + 0.5 * (1.0 - triWeight - cubeWeight - mobiusWeight) + uHueShift);

        float saturation = 0.85;
        float lightness = 0.12 + speed * 0.15;

        vColor = hsl2rgb(hue, saturation, lightness);

        vec4 mvPosition = modelViewMatrix * vec4(pos, 1.0);
        gl_PointSize = uPointSize * (55.0 / -mvPosition.z);
        gl_PointSize = max(gl_PointSize, 0.3);
        gl_Position = projectionMatrix * mvPosition;
      }
    `;

    const fragmentShader = `
      varying vec3 vColor;
      void main() {
        float d = length(gl_PointCoord - 0.5) * 2.0;
        if (d > 1.0) discard;
        // Soft gaussian falloff with bright core
        float glow = exp(-d * d * 3.0);
        float core = exp(-d * d * 12.0);
        float alpha = (glow * 0.15 + core * 0.3);
        // Slight color boost at core (hotter center)
        vec3 col = vColor + core * 0.15;
        gl_FragColor = vec4(col, alpha);
      }
    `;

    const geometry = new THREE.BufferGeometry();
    const texCoords = new Float32Array(PARTICLE_COUNT * 2);
    for (let j = 0; j < WIDTH; j++) {
      for (let i = 0; i < WIDTH; i++) {
        const idx = (j * WIDTH + i) * 2;
        texCoords[idx]     = (i + 0.5) / WIDTH;
        texCoords[idx + 1] = (j + 0.5) / WIDTH;
      }
    }
    const dummyPositions = new Float32Array(PARTICLE_COUNT * 3);
    geometry.setAttribute('position', new THREE.BufferAttribute(dummyPositions, 3));
    geometry.setAttribute('aTexCoord', new THREE.BufferAttribute(texCoords, 2));

    const material = new THREE.ShaderMaterial({
      vertexShader,
      fragmentShader,
      uniforms: {
        uMouseWorld: { value: new THREE.Vector3(0, 0, -1000) },
        uMouseStrength: { value: 0.0 },
        uPositionTexture: { value: null },
        uHueShift: { value: 0.0 },
        uPointSize: { value: 1.0 },
        uScale: { value: 1.6 },
      },
      transparent: true,
      blending: THREE.AdditiveBlending,
      depthWrite: false,
    });

    const points = new THREE.Points(geometry, material);
    const pivot = new THREE.Group(); pivot.add(points); scene.add(pivot);

    // UI
    document.getElementById('particle-count').textContent =
      `${PARTICLE_COUNT.toLocaleString()} particles — fully GPU computed`;

    const speedSlider = document.getElementById('speed');
    const bloomSlider = document.getElementById('bloom');
    const sizeSlider = document.getElementById('size');
    const hueSlider = document.getElementById('hueShift');
    const fpsEl = document.getElementById('fps');

    document.getElementById('zoomIn').addEventListener('click', () => {
      material.uniforms.uScale.value *= 1.15;
    });
    document.getElementById('zoomOut').addEventListener('click', () => {
      material.uniforms.uScale.value *= 0.85;
    });

    // Animation Loop
    // Mouse interaction
    const mouse = new THREE.Vector2();
    const mouse3D = new THREE.Vector3();
    const raycaster = new THREE.Raycaster();
    let mouseActive = false;

    renderer.domElement.addEventListener('mousemove', (e) => {
      mouse.x = (e.clientX / innerWidth) * 2 - 1;
      mouse.y = -(e.clientY / innerHeight) * 2 + 1;
      mouseActive = true;
      raycaster.setFromCamera(mouse, camera);
      mouse3D.copy(raycaster.ray.direction).multiplyScalar(15).add(camera.position);
    });
    renderer.domElement.addEventListener('mouseleave', () => { mouseActive = false; });

    let lastTime = performance.now();
    let frameCount = 0;

    function animate(now) {
      requestAnimationFrame(animate);

      frameCount++;
      if (now - lastTime >= 1000) {
        fpsEl.textContent = `${frameCount} FPS`;
        frameCount = 0;
        lastTime = now;
      }

      posVar.material.uniforms.uSpeed.value = parseFloat(speedSlider.value);
      posVar.material.uniforms.uTime.value += 0.016;
      bloomPass.strength = parseFloat(bloomSlider.value);
      material.uniforms.uHueShift.value = parseFloat(hueSlider.value);
      material.uniforms.uPointSize.value = parseFloat(sizeSlider.value);

      // Update mouse uniforms
      if (mouseActive) {
        material.uniforms.uMouseWorld.value.copy(mouse3D);
        material.uniforms.uMouseStrength.value = 1.0;
      } else {
        material.uniforms.uMouseStrength.value *= 0.95;
      }


      gpuCompute.compute();

      material.uniforms.uPositionTexture.value =
        gpuCompute.getCurrentRenderTarget(posVar).texture;

      pivot.rotation.x += 0.0008;
      orbitControls.update();
      composer.render();
    }

    animate(performance.now());

    // Resize
    window.addEventListener('resize', () => {
      camera.aspect = innerWidth / innerHeight;
      camera.updateProjectionMatrix();
      renderer.setSize(innerWidth, innerHeight);
      composer.setSize(innerWidth, innerHeight);
    });
  </script>
<script src="shared-ui.js"></script>
</body>
</html>