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Title POLYLLA: Polygonal Meshing Algorithm based on Terminal-Edge Regions
Authors sergio salinas, Nancy Hitschfeld, Alejandro Ortiz-Bernardin, hang si
Publication date March 2022
Abstract This paper presents an algorithm to generate a new kind of
polygonal mesh obtained from triangulations. Each polygon is
built from a terminal-edge region surrounded by edges that are not the
longest-edge of any of the two triangles that share
them. The algorithm is termed Polylla and is divided into three phases. The
first phase consists of labeling each edge of
the input triangulation according to its size; the second phase builds
polygons (simple or not) from terminal-edges regions
using the label system; and the third phase transforms each non simple
polygon into simple ones. The final mesh contains
polygons with convex and non convex shape. Since Voronoi-based meshes are
currently the most used polygonal meshes,
we compare some geometric properties of our meshes against constrained
Voronoi meshes. Several experiments were run to
compare the shape and size of polygons, the number of final mesh points and
polygons. For the same input, Polylla meshes
contain less polygons than Voronoi meshes and the algorithm is simpler and
faster than the algorithm to generate constrained
Voronoi meshes. Finally, we have validated Polylla meshes by solving the
Laplace equation on an L-shaped domain using
the virtual element method (VEM). We show that the numerical performance of
the VEM using Polylla meshes and Voronoi
meshes is similar
Journal name Engineering with Computers
Publisher Springer-Verlag (Berlin/Heidelberg, Germany)
Reference URL View reference page