Visualização de campos tensoriais utilizando simulação lagrangeana de fluidos

Abstract

Analysis and visualization of symmetric second order tensor fields are challenging since they generally represent multivariate data. Works in this area use different approaches to enhance desired properties of the field. Those properties are, for example, colinear and coplanar structures. In some cases, such as tensor fields obtained by magnetic resonance imaging of organic tissues, highlighting those structures can be useful for studies in neu roscience and diagnostics, for example. A specific technique of visualization consists in observing particles’ trajectories along the field. But, most of those methods are static and does not present interaction between particles. This work proposes a method that induces the human perceptual system to visualize more intuitively those structures, using fluid dynamics. Modifications in a specific implementation of Navier-Stokes equations, called Smoothed Particle Hydrodynamics (SPH) were proposed. Different from other ap proaches, interactions between particles are used to enhance the perception of underlying structures in a tensor field. It was also proposed an external force to keep particles around areas of interest and a distortion in the kernel functions, both based on tensors’ informa tion.The distortion forces particles to align according to consecutive colinear and coplanar structures of a field, showing continuities and connectivities.