Visualization of second order tensor fields and matrix data

Abstract

The visualization of 3-D second-order tensor fields and matrix data is studied. The general problem of visualizing unsymmetric real or complex Hermitian second-order tensor fields can be reduced to the simultaneous visualization of a real and symmetric second-order tensor field and a real vector field. The emphasis is on exploiting the mathematical properties of tensor fields in order to facilitate their visualization and to produce a continuous representation of the data. The focus is on interactively sensing and exploring real and symmetric second-order tensor data by generalizing the vector notion of streamline to the tensor concept of hyperstreamline. The importance of a structural analysis of the data field analogous to the techniques of vector field topology extraction in order to obtain a unique and objective representation of second-order tensor fields is stressed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>