Reduced Connectivity for Local Bilinear Jacobi Sets
arXiv:2208.07148 · doi:10.1109/TopoInVis57755.2022.00011
Abstract
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.
IEEE Workshop on Topological Data Analysis and Visualization in conjunction with IEEE VIS 2022. ACM 2012 CCS - Human-centered computing, Visualization, Visualization techniques; Mathematics of computing, Discrete mathematics