Visualization of 4D Vector Field Topology. (10th July 2018)

• Record Type: Journal Article
• Authors: Hofmann, Lutz; Rieck, Bastian; Sadlo, Filip
• Is Part Of: Computer graphics forum. Volume 37:Number 3(2018)
• Page Start: 301
• Page End: 313
• Publication Date: 2018-07-10
• Subjects: CCS Concepts -- Human‐centered computing → Visualization techniques -- Applied computing → Mathematics and statistics; Computer graphics -- Periodicals; 006.605
• DOI: 10.1111/cgf.13421
• Languages: English
• ISSNs: 0167-7055

Abstract

Abstract: 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.