A phase field model for continuous clustering on vector fields

摘要

A new method for the simplification of flow fields is presented.nIt is based on continuous clustering. A well-known physical clusteringnmodel, the Cahn-Hilliard (1958) model, which describes phase separation,nis modified to reflect the properties of the data to be visualized.nClusters are defined implicitly as connected components of thenpositivity set of a density function. An evolution equation for thisnfunction is obtained as a suitable gradient flow of an underlyingnanisotropic energy functional, where time serves as the scale parameter.nThe evolution is characterized by a successive coarsening of patterns,nduring which the underlying simulation data specifies preferable patternnboundaries. We introduce specific physical quantities in the simulationnto control the shape, orientation and distribution of the clusters as anfunction of the underlying flow field. In addition, the model isnexpanded, involving elastic effects. In the early stages of thenevolution, a shear-layer-type representation of the flow field cannthereby be generated, whereas, for later stages, the distribution ofnclusters can be influenced. Furthermore, we incorporate upwind ideas tongive the clusters an oriented drop-shaped appearance. We discuss thenapplicability of this new type of approach mainly for flow fields, wherenthe cluster energy penalizes cross-streamline boundaries. However, thenmethod also carries provisions for other fields as well. The clustersncan be displayed directly as a flow texture. Alternatively, the clustersncan be visualized by iconic representations, which are positioned bynusing a skeletonization algorithm