Tensor Field Visualization Using a Metric Interpretation

Introduction Since the physical interpretation of mathematical features of tensor fields is highly application-specific it is important that visualization techniques are closely driven by the special application. In this chapter, we focus on symmetric tensor fields of second order that are similar to stress strain tensor fields, or the symmetrical part of the gradient tensor. These tensor fields are characterized by the property that they have positive and negative eigenvalues. The sign of the eigenvalues indicates regions of expansion and compression, and it is therefore of special interest. To understand the field behavior, it is important to express these features in an intuitive way. The underlying idea of our visualization method is to transform the tensor field into a metric. This metric is represented using a texture that is aligned to the eigenvector fields, similarly to line integral convolution (LIC) [CL93, SH95]. The eigenvalues are included using the free parameters in th