Function createKleinBottle

geometry.js:264–299

(i, count)

}

function createKleinBottle(i, count) {
    // Klein Bottle parameters
    const a = 15;          // Main radius
    const b = 4;           // Tube radius
    const scale = 2.5;     // Overall scale
    
    // Use uniform distribution across the surface
    const lengthSteps = Math.ceil(Math.sqrt(count * 0.5));
    const circSteps = Math.ceil(count / lengthSteps);
    
    // Calculate position in the parametric space
    const lengthIndex = i % lengthSteps;
    const circIndex = Math.floor(i / lengthSteps) % circSteps;
    
    // Normalize to appropriate ranges
    const u = (lengthIndex / lengthSteps) * Math.PI * 2;  // 0 to 2π
    const v = (circIndex / circSteps) * Math.PI * 2;      // 0 to 2π
    
    // Klein Bottle parametric equation
    let x, y, z;
    
    // The Klein Bottle has different regions with different parametric equations
    if (u < Math.PI) {
        // First half (handle and transition region)
        x = scale * (a * (1 - Math.cos(u) / 2) * Math.cos(v) - b * Math.sin(u) / 2);
        y = scale * (a * (1 - Math.cos(u) / 2) * Math.sin(v));
        z = scale * (a * Math.sin(u) / 2 + b * Math.sin(u) * Math.cos(v));
    } else {
        // Second half (main bottle body)
        x = scale * (a * (1 + Math.cos(u) / 2) * Math.cos(v) + b * Math.sin(u) / 2);
        y = scale * (a * (1 + Math.cos(u) / 2) * Math.sin(v));
        z = scale * (-a * Math.sin(u) / 2 + b * Math.sin(u) * Math.cos(v));
    }
    
    return new THREE.Vector3(x, y, z);
}

function createFlower(i, count) {
    // Flower/Dandelion parameters