# Glyph-based Comparative Visualization for Diffusion Tensor Fields

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).