arXiv subjects

Andreas Bærentzen

Publications and source records attributed to Andreas Bærentzen.

2 recordsLinked to original sources

arXiv2026

On The Topology of Polygonal Meshes

This paper is an introductory and informal exposition on the topology of polygonal meshes. We begin with a broad overview of topological notions and discuss how homeomorphisms, homotopy, and homology can be used to characterise topology. We move on to define polygonal meshes and make a distinction between intrinsic topology and extrinsic topology which depends on the space in which the mesh is immersed. A distinction is also made between quantitative topological properties and qualitative properties. Next, we outline proofs of the Euler and the Euler-Poincaré formulas. The Betti numbers are then defined in terms of the Euler-Poincaré formula and other mesh statistics rather than as cardinalities of the homology groups which allows us to avoid abstract algebra. Finally, we discuss how it is possible to cut a polygonal mesh such that it becomes a topological disc.

math.HO↗

arXiv2020

Skeletonization via Local Separators

We propose a new algorithm for curve skeleton computation which differs from previous algorithms by being based on the notion of local separators. The main benefits of this approach are that it is able to capture relatively fine details and that it works robustly on a range of shape representations. Specifically, our method works on shape representations that can be construed as a spatially embedded graphs. Such representations include meshes, volumetric shapes, and graphs computed from point clouds. We describe a simple pipeline where geometric data is initially converted to a graph, optionally simplified, local separators are computed and selected, and finally a skeleton is constructed. We test our pipeline on polygonal meshes, volumetric shapes, and point clouds. Finally, we compare our results to other methods for skeletonization according to performance and quality.

cs.CG↗