A phase field model for continuous clustering on vector fields

A new method for the simplification of flow fields is presented. It is base d on continuous clustering. A well-known physical clustering model, the Cah n Hilliard model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitl y as connected components of the positivity set of a density function. An e volution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the s cale parameter. The evolution is characterized by a successive coarsening o f patterns-the actual clustering-during which the underlying simulation dat a specifies preferable pattern boundaries. We introduce specific physical q uantities in the simulation to control the shape, orientation and distribut ion of the clusters as a function of the underlying flow field. In addition , the model is expanded, involving elastic effects. In the early stages of the evolution shear layer type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the cluster s an oriented drop-shaped appearance. Here, we discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries. However, the method also carries pr ovisions for other fields as well. The clusters can be displayed directly a s a flow texture. Alternatively, the clusters can be visualized by iconic r epresentations, which are positioned by using a skeletonization algorithm.