Out-of-Core Particle Tracing for Monte Carlo Rendering of Finite-Time Lyapunov Exponents

Abstract

The motion in time-dependent fluid flows is governed by Lagrangian coherent structures (LCS). One common approach to visualize hyperbolic LCS is to extract and visualize the finite-time Lyapunov exponent. Its visualization on large time-dependent fluid flow is challenging for two reasons. First, the time steps needed for particle tracing do not necessarily fit at once into memory. And second, conventional ray marching exhibits artifacts when the FTLE ridges are sharp, which instead requires Monte Carlo volume rendering techniques to produce unbiased results. So far, these two problems have only been looked at in isolation. In this paper, we implement the first out-of-core Monte Carlo FTLE tracer, which is able to visualize the finitetime Lyapunov exponent field of time-dependent fluid flows that do not fit into main memory at once. To achieve this, we designed a data processing pipeline that alternates between two phases: a photon tracing phase and a particle tracing phase. We demonstrate and evaluate the approach on several large time-dependent vector fields.