tiled_projection.js

tiledProjection(points, quantizationBits) {
    const q = quantizationBits;
    const qRange = Math.pow(2, q);
    const sqrtQRange = Math.floor(Math.sqrt(qRange));
    const maxTiledCoord = Math.max(sqrtQRange * qRange + qRange - 1, 1);
    
    // Create new projected points array
    const projectedPoints = new Float32Array(points.length);
    
    for (let i = 0; i < points.length; i += 3) {
        const x = points[i];
        const y = points[i + 1];
        const z = points[i + 2];
        
        // Convert normalized coordinates [-1,1] to discrete grid [0, qRange-1]
        const discreteX = Math.max(0, Math.min(qRange - 1, Math.floor((x + 1) / 2 * qRange)));
        const discreteY = Math.max(0, Math.min(qRange - 1, Math.floor((y + 1) / 2 * qRange)));
        const discreteZ = Math.max(0, Math.min(qRange - 1, Math.floor((z + 1) / 2 * qRange)));
        
        // Apply tiling formula: (col, row) = (z % sqrt(2^q), floor(z / sqrt(2^q)))
        const col = discreteZ % sqrtQRange;
        const row = Math.floor(discreteZ / sqrtQRange);
        
        // Calculate tiled coordinates: col * 2^q + x, row * 2^q + y
        const tiledX = col * qRange + discreteX;
        const tiledY = row * qRange + discreteY;
        
        // Normalize back for display (scale to fit in reasonable viewing area)
        projectedPoints[i] = (tiledX / maxTiledCoord) * 2 - 1;
        projectedPoints[i + 1] = (tiledY / maxTiledCoord) * 2 - 1;
        projectedPoints[i + 2] = 0; // Flatten to z=0 plane
    }
    
    return projectedPoints;
}