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Visualization of 4D Vector Field Topology
Author(s) -
Hofmann Lutz,
Rieck Bastian,
Sadlo Filip
Publication year - 2018
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13421
Subject(s) - visualization , computer science , clipping (morphology) , topology (electrical circuits) , projection (relational algebra) , vector field , representation (politics) , invariant (physics) , intersection (aeronautics) , field (mathematics) , artificial intelligence , algorithm , mathematics , geometry , pure mathematics , philosophy , linguistics , engineering , combinatorics , politics , political science , law , mathematical physics , aerospace engineering
In this paper, we present an approach to the topological analysis of four‐dimensional vector fields. In analogy to traditional 2D and 3D vector field topology, we provide a classification and visual representation of critical points, together with a technique for extracting their invariant manifolds. For effective exploration of the resulting four‐dimensional structures, we present a 4D camera that provides concise representation by exploiting projection degeneracies, and a 4D clipping approach that avoids self‐intersection in the 3D projection. We exemplify the properties and the utility of our approach using specific synthetic cases.