Anchor Flow Maps: Efficient Sampling and Approximation of the Entire Flow Map

Flow maps are a fundamental concept for the visualization and analysis of time‐dependent flows. A common approach is to apply sampling and reconstruction – which comes with a number of problems: flow maps are high‐dimensional functions with locally large gradients which makes approximations very challenging. In general, one must apply large sampling resolutions and more advanced methods to achieve sufficiently good results. Existing methods for efficient, high‐quality sampling and approximation restrict to subsets of flow maps, e.g., with fixed start and end times, or at least fixed differences. In this paper, we propose the first method to handle the entire flow map by decreasing the dimensionality of the space‐time‐time domain. Essentially, it is a framework which splits the high‐dimensional flow map into few lower‐dimensional functions. This enables to achieve much larger resolutions than traditional sampling with the same memory consumption. We use our method in established applications and show that it can significantly decrease errors in the reconstruction by using these larger resolutions.