Visualization of Equivalence in 2D Bivariate Fields

Abstract

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.