Fast Fiber Line Extraction for 2D Bivariate Scalar Fields

TL;DR

This paper addresses the problem of fast, exact fiber-line extraction for 2D bivariate scalar fields, where fibers are the preimages $f^{-1}(P)$ of a control polygon $P$ under a map $f: D \rightarrow \mathbb{R}^2$. The authors propose a novel approach that combines Klacansky’s exact per-edge preimage technique with a dual bounding volume hierarchy (BVH) traversal to prune search space, alongside an accelerated extraction algorithm that maps FSCP edges back to the domain via marching triangles. They demonstrate substantial performance gains across four datasets and FSCPs of up to 2997 edges, showing speedups of several orders of magnitude over naive methods and favorable comparison with existing fast methods, especially for large FSCPs. The work enables interactive, large-scale multivariate visualization tasks such as field equivalence analyses and sets the stage for extending the framework to 3D domains and further false-positive reductions, with potential integration into related multivariate visualization pipelines.

Abstract

Extracting level sets from scalar data is a fundamental operation in visualization with many applications. Recently, the concept of level set extraction has been extended to bivariate scalar fields. Prior work on vector field equivalence, wherein an analyst marks a region in the domain and is shown other regions in the domain with similar vector values, pointed out the need to make this extraction operation fast, so that analysts can work interactively. To date, the fast extraction of level sets from bivariate scalar fields has not been researched as extensively as for the univariate case. In this paper, we present a novel algorithm that extracts fiber lines, i.e., the preimages of so called control polygons (FSCP), for bivariate 2D data by joint traversal of bounding volume hierarchies for both grid and FSCP elements. We performed an extensive evaluation, comparing our method to a two-dimensional adaptation of the method proposed by Klacansky et al., as well as to the naive approach for fiber line extraction. The evaluation incorporates a vast array of configurations in several datasets. We found that our method provides a speedup of several orders of magnitudes compared to the naive algorithm and requires two thirds of the computation time compared to Klacansky et al. adapted for 2D.

Figures (3)

• Figure 1: Continuous scatterplot for each dataset's range.
• Figure 2: Visualization of the 9 control polygons in the codomian. Number of edges: (a)=3, (b)=4, (c)=8, (d)=16, (e)=38, (f)=60, (g)=126, (h)=232, and (i)=2997.
• Figure 3: Plot the dataset Red Sea in the case (II).