A triangulation of a surface is called q-equivelar if each of its vertices is incident with exactly q triangles. In 1972 Altshuler had shown that an equivelar triangulation of torus has a Hamiltonian Circuit. Here we present a necessary and sufficient condition for existence of a contractible Hamiltonian Cycle in equivelar triangulation of a surface. AMS classification : 57Q15, 57M20, 57N05.

In this paper, we propose a method for solving the problem triangulation of a domain between convex polyhedrons in ddimensional space using Delaunay triangulation in O(N) time. Novelty of our work is in using a modified Delaunay triangulation algorithm with constraints.

Machine vision systems based on 3D triangulation are employed in a range of industries from automotive and electronics manufacturing to lumber mills. While the basic concept of measurement using triangulation is simple, there are a number of important details that must be addressed when implementing such systems. These include how laser-based 3D triangulation systems are configured and how lase...

A wireless sensor network can be represented by a graph. While the network graph is extremely useful, it often exhibits undesired irregularity. Therefore, special treatment of the graph is required by a variety of network algorithms and protocols. In particular, many geometry-oriented algorithms depend on a type of subgraph called Delaunay triangulation. However, when location information is un...

Introduction: Requirements Engineering process is a crucial phase in software development. In order to achieve a successful design of health information systems (HISs), applying the best methodologies is essential. Therefore, the aim of the present study was to design pediatrics Epilepsy Information System (EPIS) as well as the use of triangulation approach in elicitation and validation of epil...

As a global optimization problem, planar minimum weight triangulation problem has attracted extensive research attention. In this paper, a new asymmetric graph called one-sided β-skeleton is introduced. We show that the one-sided circle-disconnected ( √ 2β)skeleton is a subgraph of a minimum weight triangulation. An algorithm for identifying subgraph of minimum weight triangulation using the on...

This paper presents a brief survey of some problems and solutions related to the triangula-tion of surfaces. A surface (a two dimensional manifold, in the context of this paper) can be represented as a three dimensional function on a planar disk. In that sense, the triangulation of the disk induces a triangulation of the surface. Hence the emphasis of this paper is on triangula-tion on a plane....

I Given a finite point set X ⊂ Rd . Then there exists simplicial a complex called Delaunay triangulation of this point set such that I X is the set of vertices of the triangulation I The union of all its simplices is the convex hull of X . I (Delaunay property): For any given d-simplex Σ ⊂ Ω belonging to the triangulation, the interior of its circumsphere does not contain any vertex xk ∈ X . I ...

We consider a robot swarm in an unknown polygon. All robots have only a limited communication range. We then look for a triangulation of the polygon using the robots as vertices such that the number of robots used for the triangulation is minimized. All edges in the triangulation have a length smaller than the communication range. For this Online Minimum Relay Triangulation Problem, we present ...