Mathematical Analysis and Performance Metrics of the Wave-Particle Transport Simulation (WTS) Rendering System

This document presents a mathematical derivation and performance analysis of the Wave-Particle Trans-port Simulation (WTS) rendering system. We analyze the system’s core hybrid architecture, which couplesSigned Distance Function (SDF) ray marching with a grid-based, non-linear hyperbolic partial differentialequation (PDE) solver. We demonstrate that the WTS “relaxation” kernel functions as a programmablescreen-space wave propagator, effectively approximating global illumination phenomena such as subsurfacescattering and bloom through continuous media mechanics rather than discrete Monte Carlo integration.We compare the computational complexity (O) and visual convergence properties against State-of-the-Art(SOTA) path tracing methods.