An Art Gallery Approach to Submap Meshing

Abstract

The Art Gallery Theorem and its lemmas have been used since the 1990s in the area of computer graphics to decompose orthogonal polygons into convex sub-regions. This paper extends and improvises Art Gallery concepts to non-orthogonal, generic polygons to perform a multiblock decomposition of faces into a set of maximal, single-loop, convex sub-faces. Concepts such as staircase, dent and notch are used to categorize face concavities and virtual vertices are inserted on smoother concave boundary bends. Multiblocking is performed without the need for Delaunay triangulation with the aid of a notch diagram. A light-weight, mesher-native topology builder that uses virtual topological elements is proposed to construct a virtual topology network from a notch diagram. Subsequently, virtual faces are processed for transfinite meshing . Results indicate the advantage of the proposed technique over existing procedures in terms of orthogonality and anisotropy.

Using virtual topology operations to generate analysis topology

“…Virtual volume partitioning could be used, for example, to allow an analyst to virtually decompose a domain for Hex meshing. Splitting operations do exist to partition edges and faces and have been utilized to decompose domains and generate a virtual topology network of multi-block faces for quad meshing [11]. Sheffer [12] described the generation of Hex meshes using a medial axis approach to virtually decompose an initial volume into sub-volumes mesh-able by means of basic meshing methods.…”

Enhanced medial-axis-based block-structured meshing in 2-D

“…[33]) and 1-and 2-sided templates are proposed simple candidates. Submappable regions can be meshed by a number of 0-sided 1-sided 2-sided 3-sided 5-sided 6-sided methods [13,34,35]. Two examples of submapped meshes are shown in Fig.…”

Application of FEM Mesh Generation Algorithm for Digital Processing of Handmade Sketches

“…In the context of recent scientific studies on non-conventional methods the Art Gallery Approach to submap meshing introduced by Mukharjee [11] is interesting. One of the main tasks is to walk along the face of boundary to identify its curvatures and put them into specified categories.…”