Tensor-fields Visualization using a Fabric like Texture on Arbitrary two-dimensional Surfaces Ingrid Hotz 1 , Louis Feng 1 , Bernd Hamann 1 , and Kenneth Joy 1 Institute for Data Analysis and Visualization (IDAV), Department of Computer Science, University of California, Davis, CA 95616, USA; {ihotz,zfeng,bhamann,kijoy}@ucdavis.edu Summary. 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 “tex- ture” for a two-dimensional surfaces. The texture parameters as the fabric density reflect the physical properties of the tensor field. This method is especially appro- priate 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 al- low 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 genera- tion 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 eigenval- ues 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. 1 Introduction Tensor data play an important role in several mathematical, physical, and technical disciplines. Mathematically, a tensor is a linear function that relates different vectorial quantities. Its high dimensionality makes it very complex and difficult to understand. Since the physical interpretation and significance of its mathematical features is highly application-specific, we focus on sym- metric tensor fields of second order that are similar to stress, strain tensor fields. Such fields appear, for example, in geomechanics and solid state physics, which are our major application areas. Here tensors are used, for example, to express the response of a material to applied forces. In contrast to other types