Towards Glyphs for Uncertain Symmetric Second‐Order Tensors

Abstract

AbstractMeasured data often incorporates some amount of uncertainty, which is generally modeled as a distribution of possible samples. In this paper, we consider second‐order symmetric tensors with uncertainty. In the 3D case, this means the tensor data consists of 6 coefficients – uncertainty, however, is encoded by 21 coefficients assuming a multivariate Gaussian distribution as model. The high dimension makes the direct visualization of tensor data with uncertainty a difficult problem, which was until now unsolved. The contribution of this paper consists in the design of glyphs for uncertain second‐order symmetric tensors in 2D and 3D. The construction consists of a standard glyph for the mean tensor that is augmented by a scalar field that represents uncertainty. We show that this scalar field and therefore the displayed glyph encode the uncertainty comprehensively, i.e., there exists a bijective map between the glyph and the parameters of the distribution. Our approach can extend several classes of existing glyphs for symmetric tensors to additionally encode uncertainty and therefore provides a possible foundation for further uncertain tensor glyph design. For demonstration, we choose the well‐known superquadric glyphs, and we show that the uncertainty visualization satisfies all their design constraints.