We propose a method to approximate a polygonal object by a deformable smooth surface, namely the t-skin defined by Edelsbrunner [5] for all 0 < t < 1. We guarantee that they are homeomorphic and their Hausdorff distance is at most > 0. This construction make it possible for fully automatic, smooth and robust deformation between two polygonal objects with different topologies. En route to our re...

In this paper we introduce a discontinuous Galerkin method on polygonal meshes. This method arises from the Discontinuous Galerkin Composite Finite Element Method (DGFEM) for source problems on domains with micro-structures. In the context of the present paper, the flexibility of DGFEM is applied to handle polygonal meshes. We prove the a priori convergence of the method for both eigenvalues an...

In 2007, Arkin et al. [3] initiated a systematic study of the complexity of the Hamiltonian cycle problem on square, triangular, or hexagonal grid graphs, restricted to polygonal, thin, superthin, degree-bounded, or solid grid graphs. They solved many combinations of these problems, proving them either polynomially solvable or NP-complete, but left three combinations open. In this paper, we pro...

Polygon approximation plays a vital role in abquitious applications like multimedia, geographic and object recognition. An extensive number of polygonal approximation techniques for digital planar curves have been proposed over the last decade, but there are no survey papers on recently proposed techniques. Polygon is a collection of edges and vertices. Objects are represented using edges and v...

Strange attractors are stable sets of vector field flows that have a fractal geometric structure in one dimension, and smooth surface behaviour in the other two. Previous visualization methods show the flow dynamics well, but not the fractal structure. Here we approximate the attractor by polygonal surfaces, which reveal the fractal geometry. We start with a polygonal approximation which neglec...

A common task in automated manufacturing processes is that of orienting (or feeding) parts prior to assembly. In this paper, we propose a new type of feeder. We consider sensorless orientation of polygonal parts with elevated edges by pull actions with an overhead finger. We show that any asymmetric convex polygonal part can be oriented by a sequence of pull operations. We give an O(n) algorith...

Several fundamental problems in Computational Geometry come from the eld of Facility Location. In this paper we consider some problems that belong to the interplay between these two areas. Given a set S of points in the plane: (1) nd a polygonal chain with one corner belonging to S such that minimizes the maximum distance, (2) nd a polygonal chain with k corners belonging to S such that minimiz...

Mode characteristics for two-dimensional equilateral-polygonal microresonators are investigated based on symmetry analysis and finite-difference time-domain numerical simulation. The symmetries of the resonators can be described by the point group CNv, accordingly, the confined modes in these resonators can be classified into irreducible representations of the point group CNv. Compared with cir...

We present a finite volume scheme for anisotropic diffusion on evolving hypersurfaces. The underlying motion is assumed to be described by a fixed, not necessarily normal, velocity field. The ingredients of the numerical method are an approximation of the family of surfaces by a family of interpolating polygonal meshes, where grid vertices move on motion trajectories, a consistent finite volume...

The regularity and singularity of variational solutions of problems u = f in ; @u @ T @ 2 u @ 2 = g on 1; u = 0 on 2; @u @ = 0 on 3 with suitable compatibility conditions at vertices of 1 for bounded polygonal domains R are studied by combining Grisvard's (cf. Grisvard[4]) results with perturbation theory and the method of continuity. The variational solutions are proved to be in H( ) H( 1) for...