This paper describes the design and evaluation of a new type of tensor glyph, the Tender glyph, which visualizes the difference between two tensors. Following symmetry, continuity, and disambiguity principles used twice previously for tensor glyphs (VisSym-2004 and VIS-2010), the authors approach exemplifies algebraic design principles.
The authors decompose tensor difference into shape and orientation differences. The angular extent of a view-aligned arc or sector shows the amount of orientation difference (the amount of tensor difference that can be attributed to a change in orientation). The orientation difference metric is designed to smoothly to go zero as one tensor becomes isotropic. This ensures continuity, which is a specialized form of the visual-data correspondence algebraic vis principle.
The shape difference is shown via a composite superquadric checkboard glyph, inspired by checkerboard interleaved displays of two co-registered images. Greater differences in tensor shape, lead to more visually striking discontinuities in the checkerboard glyph shape, which nicely implements visual-data correspondence. The identity of the two tensors is shown via roughly opponent colors, so swapping the two tensors will result in a visually similar glyph, which avoids a hallucinator. Increasing tensor magnitude is shown with increasing color saturation (visual-data correspondence again).