Tensor-fields Visualization using a Fabric like Texture on Arbitrary two-dimensional Surfaces

We present a visualization method that for three-dimensional tensor fields based on the idea of a stretched or compressed piece of fabric used as a “texture” for a two-dimensional surfaces. The texture parameters as the fabric density reflect the physical properties of the tensor field. This method is especially appropriate for the visualization of stress and strain tensor fields that play an important role in many application areas including mechanics and solid state physics. To allow an investigation of a three-dimensional field we use a scalar field that defines a one-parameter family of iso-surfaces controlled by their iso-value. This scalar-field can be a “connected” scalar field, for example, pressure or an additional scalar field representing some symmetry or inherent structure of the dataset. Texture generation consists basically of three steps. The first is the transformation of the tensor field into a positive definite metric. The second step is the generation of an input for the final texture generation using line integral convolution (LIC). This input image consists of “bubbles” whose shape and density are controlled by the eigenvalues of the tensor field. This spot image incorporates the entire information content defined by the three eigenvalue fields. Convolving this input texture in direction of the eigenvector fields provides a continuous representation. This method supports an intuitive distinction between positive and negative eigenvalues and supports the additional visualization of a connected scalar field.