Clifford Algebra in Vector Field Visualization

Abstract

The visualization of vector fields is still based on piecewise linear approximation. This is fast and good enough in large areas but has drawbacks if the non-linear behavior of a field has local topological implications like close simple critical points or higher order singularities. This article introduces the concept of Clifford algebra into the visualization of vector fields to deal with these difficulties. It derives a close relationship between the description of some polynomial 2D vector fields in Clifford algebra and their topology, especially the index and the position of critical points. This is used to develop an algorithm for vector field visualization without the problems of conventional methods.