Classification and Visualization of Critical Points in 3D Vector Fields

Abstract

Classification and visualization of critical points in 3D vector fields is a challenging task. In this thesis, we have developed a full set of methods ranging from locating critical points, to classification and visualization techniques.

To achieve a good visualization of critical points, it is important that the methods for extracting and classifying them are robust. For locating critical points, we improved upon a previously developed analytic method using trilinear interpolation. The improved analytic method proved itself a viable tool for locating critical points, both in terms of effectiveness and robustness.

We have proposed a classification method for critical points based on phase planes. In a local region around a critical point, the phase planes inherit characteristic topologies that we have used in the classification of critical points. For a given critical point, these phase plane topologies are combined to yield a full 3D classification. The scheme also covers degenerate cases.

Building on the basis given by the classification scheme, we introduced a new set of seeding templates for field line visualization of critical points. The field lines are rendered using the Illuminated Field Line technique, which we have implemented to run as a vertex shader program on a graphics processor.

We have also developed and implemented a method called Tangent LIC on the GPU for computing a LIC texture of the tangential component of a 3D vector field in a slicing plane. This visualization technique was used to visualize the phase planes of critical points. We achieved a visualization in which the LIC texture of the slicing plane is updated in real-time, allowing for interactive exploration of the visualization. This visualization method was combined with Illuminated Field Lines in a hybrid visualization. The hybrid visualization managed to clearly capture both the details of the phase planes of the critical points, as well as the surrounding vector field topology.