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Monte Carlo Methods for 2D Flow Visualization

Xingze Tian and Tobias Günther

Eurographics Conference on Visualization Short Papers, 2025

Abstract

In this paper, we investigate how recent advances from the computer graphics literature can be applied to improve the visualization of two-dimensional vector fields. To this end, we propose two different approaches that both start from a set of evenly-spaced streamlines. The first approach avoids the need for contrast normalization, which is usually required for LIC approaches. For this, the image synthesis is phrased as a diffusion problem by placing double-sided Dirichlet boundary conditions along the streamlines. The diffusion problem is formally modeled as a linear elliptic partial differential equation, which is solved stochastically using a variant of the walk-on-spheres algorithm in order to achieve anti-aliased results. The second approach leverages human's perception of shape to convey flow patterns. For this, we lift the streamlines into the third dimension and generate visual contrast among adjacent streamlines by means of ambient occlusion. To synthesize the images, we apply a physically-based material model and employ a Monte Carlo renderer to simulate the light transport.

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