38-Issue 3

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The Dependent Vectors Operator
(The Eurographics Association and John Wiley & Sons Ltd., 2019) Hofmann, Lutz; Sadlo, Filip; Gleicher, Michael and Viola, Ivan and Leitte, Heike
In this paper, we generalize the parallel vectors operator due to Peikert and Roth to arbitrary dimension, i.e., to four-dimensional fields and beyond. Whereas the original operator tested for parallelism of two (derived) 2D or 3D vector fields, we reformulate the concept in terms of linear dependency of sets of vector fields, and propose a generic technique to extract and filter the solution manifolds.We exemplify our approach for vortex cores, bifurcations, and ridges as well as valleys in higher dimensions.
Visualization of Equivalence in 2D Bivariate Fields
(The Eurographics Association and John Wiley & Sons Ltd., 2019) Zheng, Boyan; Rieck, Bastian; Leitte, Heike; Sadlo, Filip; Gleicher, Michael and Viola, Ivan and Leitte, Heike
In this paper, we show how the equivalence property leads to the novel concept of equivalent regions in mappings from Rn to Rn. We present a technique for obtaining these regions both in the domain and the codomain of such a mapping, and determine their correspondence. This enables effective investigation of variation equivalence within mappings, and between mappings in terms of comparative visualization. We implement our approach for n = 2, and demonstrate its utility using different examples.