Region extraction in mesh intersection

TL;DR

This paper introduces a novel region extraction algorithm for mesh intersections bounded by curved segments, enabling precise numerical integration in Isogeometric Analysis applications.

Contribution

The work generalizes existing algorithms to handle regions bounded by arbitrary curved segments, expanding their applicability in advanced computational methods.

Findings

Algorithm allows accurate numerical integration in spline spaces.

Applicable to contact problems, mortar methods, and quasi-interpolation.

Enhances mesh intersection analysis for curved geometries.

Abstract

Region extraction is a very common task in both Computer Science and Engineering with several applications in object recognition and motion analysis, among others. Most of the literature focuses on regions delimited by straight lines, often in the special case of intersection detection among two unstructured meshes. While classical region extraction algorithms for line drawings and mesh intersection algorithms have proved to be able to deal with many applications, the advances in Isogeometric Analysis require a generalization of such problem to the case in which the regions to be extracted are bounded by an arbitrary number of curved segments. In this work we present a novel region extraction algorithm that allows a precise numerical integration of functions defined in different spline spaces. The presented algorithm has several interesting applications in contact problems, mortar methods, and quasi-interpolation problems.