Glyph-Based Multi-field Visualization - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 125

13.2.3 Spatial Dimensionality: 3D

Geometric shapes are often used to represent multiple data values. Superquadrics
and Angle-Preserving Transformations by Barr [ 1 ] introduces such an approach for
creating and simulating three-dimensional scenes. The author defines a mathematical
framework used to explicitly define a family of geometric primitives (superquadrics)
from which their position, size, and surface curvature can be altered by modifying
a set of different parameters. Example glyphs include a torus, star-shape, ellipsoid,
hyperboloid or toroid. In addition, the paper describes a group of invertible transforms
developed to bend and twist mathematical objects in three dimensions into a new
form where shape properties such as volume, surface area and arc length is conserved.
De Leeuw and van Wijk [ 13 ] present an interactive probe-glyph for visualizing
multiple flow characteristics in a small region. In particular, the authors focus on
visualizing six components: velocity, curvature, shear, acceleration, torsion and con-
vergence. The construction of the glyph is given by, (1) a curved vector arrow where
the length and direction represents the velocity, and the arc shape is mapped to the
curvature, (2) a membrane perpendicular to the flow where its displacement to the
center is mapped to acceleration, (3) candy stripes on the surface of the velocity
arrow illustrates the amount of torsion, (4) a ring describes the plane perpendicular
to the flow over time (shear-plane), and finally (5) the convergence and divergence
of the flow is mapped to a “lens” or osculating paraboloid. Placement of such probes
are interactively placed by users along a streamline to show local features in more
detail.
Data Visualization Using Automatic, Perceptually-Motivated Shapes by Shaw
et al. [ 21 ] describes an interactive glyph-based framework for visualizing multi-
dimensional data through the use of superquadrics. The author uses the set of
superquadrics defined by Barr [ 1 ] and describes a method for mapping data attributes
appropriately to shape properties such that visual cues effectively convey data dimen-
sionality without depreciating the cognition of global data patterns. They map in
decreasing order of data importance, values to location, size, color and shape (of
which two dimensions are encoded by shape). Using superellipsoids as an example,
the authors applied their framework on two different data sets.
Superquadric Tensor Glyphs by Kindlmann [ 9 ] introduces a novel approach of
visualizing tensor fields using superquadric glyphs. Superquadric tensor glyphs
address the problems of asymmetry and ambiguity prone in previous techniques
(e.g. cuboids and ellipsoids). The author provides an explicit and implicit parameter-
ization of the primitives defined by Barr [ 1 ] that uses geometric anisotropy metrics
c l , c s to quantify the certainty of a tensor based on shape, and a user-controlled

edge sharpness parameter

c p ,

. The parametrization forms a barycentric triangular
domain of tensor glyphs that change in shape, flatness and orientation under dif-
ferent tensor eigen vectors. A subset of the family of superquadrics is chosen and
applied towards visualizing a DT-MRI tensor field which is then compared against
an equivalent ellipsoid visualization.

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