Adaptive particle relaxation for time surfaces

Time surfaces are a versatile tool to visualise advection and deformation in flow fields. Due to complex flow behaviours involving stretching, shearing, and folding, straightforward mesh-based representations of these surfaces can develop artefacts and degenerate quickly. Common counter-measures rely on refinement and adaptive insertion of new particles which lead to an unpredictable increase in memory requirements. We propose a novel time surface extraction technique that keeps the number of required flow particles constant, while providing a high level of fidelity and enabling straightforward load balancing. Our solution implements a 2D particle relaxation procedure that makes use of local surface metric tensors to model surface deformations. We combine this with an accurate bicubic surface representation to provide an artefact-free surface visualisation. We demonstrate and evaluate benefits of the proposed method with respect to surface accuracy and computational efficiency.