The Parallel Eigenvectors Operator

Abstract

The parallel vectors operator is a prominent tool in visualization that has been used for line feature extraction in a variety of applications such as ridge and valley lines, separation and attachment lines, and vortex core lines. It yields all points in a 3D domain where two vector fields are parallel. We extend this concept to the space of tensor fields, by introducing the parallel eigenvectors (PEV) operator. It yields all points in 3D space where two tensor fields have real parallel eigenvectors. Similar to the parallel vectors operator, these points form structurally stable line structures. We present an algorithm for extracting these lines from piecewise linear tensor fields by finding and connecting all intersections with the cell faces of a data set. The core of the approach is a simultaneous recursive search both in space and on all possible eigenvector directions. We demonstrate the PEV operator on different analytic tensor fields and apply it to several data sets from structural mechanics simulations.