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Glyphs for Asymmetric Second‐Order 2D Tensors
Author(s) -
Seltzer Nicholas,
Kindlmann Gordon
Publication year - 2016
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12890
Subject(s) - glyph (data visualization) , tensor (intrinsic definition) , computer science , isotropy , rotation (mathematics) , curse of dimensionality , visualization , geometry , mathematics , artificial intelligence , physics , quantum mechanics
Tensors model a wide range of physical phenomena. While symmetric tensors are sufficient for some applications (such as diffusion), asymmetric tensors are required, for example, to describe differential properties of fluid flow. Glyphs permit inspecting individual tensor values, but existing tensor glyphs are fully defined only for symmetric tensors. We propose a glyph to visualize asymmetric second‐order two‐dimensional tensors. The glyph includes visual encoding for physically significant attributes of the tensor, including rotation, anisotropic stretching, and isotropic dilation. Our glyph design conserves the symmetry and continuity properties of the underlying tensor, in that transformations of a tensor (such as rotation or negation) correspond to analogous transformations of the glyph. We show results with synthetic data from computational fluid dynamics.