Tensor fields are at the heart of many science and engineering disciplines. Many tensor visualization methods separate the tensor into component eigenvectors and visualize those instead. Eigenvectors are normally ordered according to their eigenvalues: the eigenvectors corresponding to the smallest, median, or largest eigenvalues are in their corresponding groups. We show that this ordering strategy is undesirable for liquid crystal systems and propose a new approach, where the vectors are grouped to minimize some local energy. The grouping process is reminiscent of the epitaxial expansion in the anchoring of liquid crystals on a surface. The new algorithm is successfully applied to a liquid crystal system to study the biaxiality structure near a defect.