Topological vector field visualization with Clifford algebra

Visualization is the discipline in Computer Science dealing with the representation of data by computer generated images. “It transforms the symbolic into the geometric, enabling researchers to observe their simulations and computations,” [MD87, p. 2]. One major area visualizes vector fields. In applied mathematics, the study of gas dynamics, combustion and fluid flow leads to vector fields describing velocity, vorticity, and gradients of pressure, density and temperature. In engineering, computational fluid dynamics (CFD) and finite element analysis (FEA) produce large data sets. They are central for aeronautics, automotive design, construction, meteorology and geology. Methods based on topology have been used successfully because of their ability to concentrate information related to important properties. In fluid flows, important features like vortices and separation lines can be detected automatically by extracting topology [HH91]. Conventional approaches are based on piecewise linear or bilinear interpolation. Drawbacks of these methods are attacked in this thesis. • The detection and analysis of higher order critical points is not possible. • The role of the grid in the field topology is not recognized. • There is no continous derivative over grid edges.