Construction of near-boundary Voronoi mesh layers for planar domains

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.