Reduced Connectivity for Local Bilinear Jacobi Sets

TL;DR

This paper introduces a new topological connection method for local bilinear Jacobi sets that reduces visual clutter while maintaining topological and geometric accuracy, enhancing interpretability.

Contribution

It proposes a homotopy-equivalent representation using collapses and edge contractions to improve visual clarity of Jacobi sets.

Findings

Reduces visual clutter in Jacobi set representations

Preserves topological and geometric structures

Easy to implement with minimal overhead

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.