Tensor-Fields Visualization Using a Fabric-like Texture Applied to Arbitrary Two-dimensional Surfaces

Summary

We present a visualization method for the exploration of three-dimensional tensor fields. The representation of the tensor field on a one-parameter family of two-dimensional surfaces as stretched, compressed and bent piece of fabric reflects the physical properties of stress and strain tensor fields. The texture parameters as the fiber density and fiber direction are controlled by tensor field. The surface family is defined as a set of isosurfaces extracted from an additional scalar field. This field can be a “connected” scalar field, for example, pressure or a scalar field representing some symmetry or inherent structure of the dataset. The texture generation consists basically of three steps. The first is the transformation of the tensor field into a positive definite metric. In the second step, we generate a spot noise texture as input for the final fabric generation. Shape and density of the spots are controlled by the eigenvalues of the tensor field. This spot image incorporates the entire information defined by the three eigenvalue fields. In the third step we use line integral convolution (LIC) to provide a contin- uous representation that enhances the visibility of the eigendirections. This method supports an intuitive distinction between positive and negative eigenvalues and supports the additional visualization of a connected scalar field.