Construction of near-boundary Voronoi mesh layers for planar domains

TL;DR

This paper presents a novel Voronoi meshing method that constructs high-quality, boundary-adjacent mesh layers with a hybrid structure, accurately approximating planar domains with smooth and sharp boundary features.

Contribution

It introduces a self-organizing algorithm for creating near-boundary Voronoi meshes with a hybrid structure, combining convex polygons and layered orthogonal structures.

Findings

Produces meshes with boundary edges closely approximating domain boundaries.

Creates a hybrid mesh structure with convex polygons in the interior.

Ensures layered orthogonal structure near sharp boundary corners.

Abstract

We consider problem of constructing purely Voronoi mesh where the union of uncut Voronoi cells approximates the planar computational domain with piecewise-smooth boundary. Smooth boundary fragments are approximated by the Voronoi edges and Voronoi vertices are placed near summits of sharp boundary corners. We suggest self-organization meshing algorithm which covers the boundary of domain by a almost-structured band of non-simplicial Delaunay cells. This band consists of quadrangles on the smooth boundary segment and convex polygons around sharp corners. Dual Voronoi mesh is double layered orthogonal structure where central line of the layer approximates the boundary. Overall Voronoi mesh has a hybrid structure and consists of high quality convex polygons in the core of the domain and orthogonal layered structure near boundaries.