The Visualization of Second Order Tensor Fields

The field of scientific visualization covers the study of visual representations of sci- entific data. These data often consist of continuous scalar, vector, or second-order tensor fields extending across a n-dimensional space, with n less than 1. While research efforts aimed at developing efficient representations of scalar and vector data have led to important achievements, this dissertation is the first extensive study of visualization techniques for second-order tensor fields. Tensor fields are multivariate; they can embed as much information as n squared scalar fields, or equivalently, n vector fields. Visualizing continuous tensor data is, therefore, difficult mainly because the underlying continuity must be rendered while visual clutter has to be avoided. We develop a theoretical ground work for the visualization of symmetric tensor fields by studying their geometry and their topological structure, and by designing at each step appropriate icons to represent the information. We