Vogel disk

info.txt

The pre-computed version can be rotated via a 2x2 matrix, while the function takes the rotation angle as a parameter.

vogel.frag

vec2 VogelDiskSample(int sampleIndex, int samplesCount, float rotation)
{
    const float goldenAngle = 2.399963;
    float r = sqrt(float(sampleIndex) + 0.5) / sqrt(float(samplesCount));
    float theta = float(sampleIndex) * goldenAngle + rotation;
    return vec2(cos(theta), sin(theta)) * r;
}

vogel_disk.py

import math

def vogel_disk_sample(index, total_samples):
    golden_angle = 2.399963229728653
    
    r = math.sqrt((index + 0.5) / total_samples)
    theta = index * golden_angle
    
    x = r * math.cos(theta)
    y = r * math.sin(theta)
    
    return (x, y)

for n in [4, 8, 16]:
    print(f"\nconst vec2 VOGEL_DISK_{n}[{n}] = vec2[{n}](")
    for i in range(n):
        x, y = vogel_disk_sample(i, n)
        comma = "," if i < n - 1 else ""
        print(f"    vec2({x:.6f}, {y:.6f}){comma}")
    print(");")