Jacobi Set Driven Search for Flexible Fiber Surface Extraction

TL;DR

This paper introduces an output-sensitive method for extracting fiber surfaces in bivariate scalar fields using Jacobi sets, significantly reducing computational effort compared to traditional traversal methods.

Contribution

It presents a novel approach leveraging Jacobi sets to efficiently identify and compute relevant fiber surface components in bivariate fields.

Findings

Reduces search space for fiber surface extraction

Supports analysis of relevant fiber surfaces near Jacobi edges

Improves efficiency over existing traversal methods

Abstract

Isosurfaces are an important tool for analysis and visualization of univariate scalar fields. Earlier works have demonstrated the presence of interesting isosurfaces at isovalues close to critical values. This motivated the development of efficient methods for computing individual components of isosurfaces restricted to a region of interest. Generalization of isosurfaces to fiber surfaces and critical points to Jacobi sets has resulted in new approaches for analyzing bivariate scalar fields. Unlike isosurfaces, there exists no output sensitive method for computing fiber surfaces. Existing methods traverse through all the tetrahedra in the domain. In this paper, we propose the use of the Jacobi set to identify fiber surface components of interest and present an output sensitive approach for its computation. The Jacobi edges are used to initiate the search towards seed tetrahedra that contain the fiber surface, thereby reducing the search space. This approach also leads to effective analysis of the bivariate field by supporting the identification of relevant fiber surfaces near Jacobi edges.