Superquadric Tensor Glyphs

Abstract

Tensor field visualization is a challenging task due in part to the multi-variate nature of individual tensor samples. Glyphs convey tensor variables by mapping the tensor eigenvectors and eigenvalues to the orientation and shape of a geometric primitive, such as a cuboid or ellipsoid. Though widespread, cuboids and ellipsoids have problems of asymmetry and visual ambiguity. Cuboids can display misleading orientation for tensors with underlying rotational symmetry. Ellipsoids differing in shape can be confused, from certain viewpoints, because of similarities in profile and shading. This paper addresses the problems of asymmetry and ambiguity with a new tunable continuum of glyphs based on superquadric surfaces. Superquadric tensor glyphs enjoy the necessary symmetry properties of ellipsoids, while also imitating cuboids and cylinders to better convey shape and orientation, where appropriate. The new glyphs are demonstrated on fields of diffusion tensors from the human brain.