Parallel Vectors Extraction using Bézier Clipping
Computer Graphics Forum (Eurographics Conference on Visualization), 2026
Abstract
In this paper, we propose a novel local feature extraction algorithm for the parallel vectors (PV) operator. Our method is based on Bézier clipping, which is a bracketing-based root finding method that is commonly-used in computer-aided geometric design. Compared to Bézier bisection, our clipping method exhibits significantly faster convergence and reduces duplicate solutions. Compared to the general Newton-Raphson algorithm, the success of our approach does not depend on the quality of an initial guess. The Bézier-based formulation readily generalizes to polynomial higher-order interpolants, such as for tricubic interpolation. With this, we derive the acceleration in the Sujudi-Haimes vortex coreline criterion directly from the vector field interpolant. In addition, we describe the cross product of two polynomial vector fields in arbitrary polynomial degree, which can be used to approximate non-polynomial interpolants. Further, we examine the effect of Newton refinement on the proposed Bézier clipping method. We evaluate our Bézier clipping method thoroughly on a range of different data sets.Download
preprintBibTeX
@article{Dassler26EuroVis,
author = {Da{\ss}ler, Nico and G{\"u}nther, Tobias},
title = {Parallel Vectors Extraction using B{\'e}zier Clipping},
journal = {Computer Graphics Forum (Eurographics Conference on Visualization)},
volume = {45},
number = {3},
year = {2026},
publisher = {Eurographics},
address = {Nottingham, United Kingdom},
}