Reduced Connectivity for Local Bilinear Jacobi Sets

• Published in: 2022 IEEE WORKSHOP ON TOPOLOGICAL DATA ANALYSIS AND VISUALIZATION (TOPOINVIS 2022) pp. 39 - 48
• Main Authors: Klotzl, Daniel, Krake, Tim, Zhou, Youjia, Stober, Jonathan, Schulte, Kathrin, Hotz, Ingrid, Wang, Bei, Weiskopf, Daniel
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.10.2022
• Subjects: Clutter; Data analysis; Data visualization; Discrete mathematics; Human computer interaction; Human-centered computing; Jacobian matrices; Mathematics; Mathematics of computing; Visualization; Visualization techniques; Visualization techniques; Human-centered computing; Discrete mathematics; Visualization; Mathematics of computing
• ISBN: 9781665493543; 1665493550; 9781665493550; 1665493542
• DOI: 10.1109/TopoInVis57755.2022.00011

We present a new topological connection method for the local bilinear computation of Jacobi sets that improves the visual representation while preserving the topological structure and geometric configuration. To this end, the topological structure of the local bilinear method is utilized, which is given by the nerve complex of the traditional piecewise linear method. Since the nerve complex consists of higher-dimensional simplices, the local bilinear method (visually represented by the 1-skeleton of the nerve complex) leads to clutter via crossings of line segments. Therefore, we propose a homotopy-equivalent representation that uses different collapses and edge contractions to remove such artifacts. Our new connectivity method is easy to implement, comes with only little overhead, and results in a less cluttered representation.