A Toy Vector Field Based on Geometric Algebra

Abstract

Scheuermann et al used Geometric Algebra to demonstrate a new relationship between the topology of a 2D vector field and its analytic description. We have used the insights provided by this work to create a computer program that allows a user to design, modify and visualize a 2D vector field in real time. The vector field is polynomial over the complex field C, and is therefore more computationally efficient and stable than Polya’s rational version over C, which is the traditional approach for such work. Such “toy” vector fields are useful for instruction, understanding and topological simulation of many issues associated with all vector fields.