Accelerated Monte Carlo Rendering of Finite-Time Lyapunov Exponents

Time-dependent fluid flows often contain numerous hyperbolic Lagrangian coherent structures, which act as transport barriers that guide the advection. The finite-time Lyapunov exponent is a commonly-used approximation to locate these repelling or attracting structures. Especially on large numerical simulations, the FTLE ridges can become arbitrarily sharp and very complex. Thus, the discrete sampling onto a grid for a subsequent direct volume rendering is likely to miss sharp ridges in the visualization. For this reason, an unbiased Monte Carlo-based rendering approach was recently proposed that treats the FTLE field as participating medium with single scattering. This method constructs a ground truth rendering without discretization, but it is prohibitively slow with render times in the order of days or weeks for a single image. In this paper, we accelerate the rendering process significantly, which allows us to compute video sequence of high-resolution FTLE animations in a much more reasonable time frame. For this, we follow two orthogonal approaches to improve on the rendering process: the volumetric light path integration in gradient domain and an acceleration of the transmittance estimation. We analyze the convergence and performance of the proposed method and demonstrate the approach by rendering complex FTLE fields in several 3D vector fields.