Vector Coupled Map Lattice PRNG for Monte Carlo Rendering

• Published in: Periodica polytechnica. Electrical engineering and computer science Vol. 69; no. 3; pp. 334 - 345
• Main Authors: Kárpáti, Attila, Kárpáti, Viktória, Szécsi, László
• Format: Journal Article
• Language: English
• Published: Budapest Periodica Polytechnica, Budapest University of Technology and Economics 18.09.2025
• Subjects: Anisotropy; Cellular automata; Distribution functions; Importance sampling; Normal distribution; Probability density functions; Pseudorandom; Random numbers; Spheres; Statistical analysis; Vectors (mathematics)
• ISSN: 2064-5260; 2064-5279; 2064-5279
• DOI: 10.3311/PPee.40410

In this paper we propose a straightforward method to generate random points uniformly distributed on the unit sphere or following a 3D Gaussian distribution. For that, we use a small Coupled Map Lattice (CML), which is similar to a cellular automaton but with cells containing arbitrary variables in place of states from a finite set. Our lattice variables are 3D unit vectors. We use this setup to solve the otherwise challenging task of generating uniformly distributed direction vectors on the unit sphere without resorting to rejection sampling. We also generate samples of a 3D Gaussian distribution with sufficient accuracy by summing several of the above random vectors. To showcase the possible uses of this method, we introduce a new Bidirectional Reflection Distribution Function (BRDF) model that is physically plausible and features: perfect importance sampling, only needing a few intuitive parameters, not rejecting samples, and supporting anisotropy. The sampling process is generalized by projecting 3D Gaussian samples to 2D direction space. The resulting probability density function over directions is obtained in a closed form. We also demonstrate the capabilities of our lattice Pseudo-Random Number Generators (PRNG) by creating an especially fast Lambertian path tracer and a volumetric scattering effect.