Comparison of Tessellated Icosahedron, Generalized Spiral, and Fibonacci Spiral Ray-Spawning Algorithms for Shooting-and-Bouncing-Ray Propagation Modeling

This study evaluates the uniformity and doublecounting behavior of three ray-spawning algorithms - tessellated icosahedron, generalized spiral, and Fibonacci spiral - used for shooting-and-bouncing-ray propagation modeling. Angular separations between neighboring ray pairs were analyzed, and spatial distribution maps of the separation angles were presented. The tessellated icosahedron demonstrated superior uniformity, as indicated by lower maximum-to-minimum separation ratios. Monte Carlo simulations were conducted to estimate the probability of double-counting, using a reception sphere radius defined by the largest separation angle. Results show that the tessellated icosahedron also yields the lowest double-counting probability (? 41 %), followed by the Fibonacci spiral excluding separation outliers (? 55 %), the generalized spiral (? 56 %), and the Fibonacci spiral with separation outliers (? 71 %). These findings support the use of the tessellated icosahedron for applications requiring high uniformity, with the generalized spiral or the Fibonacci spiral (excluding separation outliers) serving as a favorable alternative when arbitrary ray counts are needed. © 2025 IEEE.