In this paper, we consider the problem of determining in polynomial time whether a given planar point set P of n points admits 4-connected triangulation. We propose a necessary and sufficient condition for recognizing P , and present an O(n) algorithm of constructing a 4-connected triangulation of P . Thus, our algorithm solves a longstanding open problem in computational geometry and geometric...

triangulation of points on a plane, called Genetic Minimum Weight Triangulation (GMWT for short), is presented based on the rationale of genetic algorithms. Polygon crossover and its algorithm for triangulations are proposed. New adaptive genetic operators, or adaptive crossover and mutation operators, are introduced. It is shown that the new method for the minimum weight triangulation can obta...

We show that every triangulation on a closed surface, except the sphere, with minimum degree at least 4 can be obtained from an irreducible triangulation by two kinds of local deformations, called 4-splitting and addition of an octahedron and that every triangulation on the sphere can be obtained from the octahedron by them. c © 2002 Elsevier Science B.V. All rights reserved.

A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. We prove that every irreducible triangulation of a surface with Euler genus g ≥ 1 has at most 13g − 4 vertices. The best previous bound was 171g − 72.

In this paper, we introduce a new approach to mesh an animated implicit surface for rendering purposes. This approach is based on a double triangulation of the surface. In the first triangulation, the vertices are the nodes of a finite element model. The aim of this model is to uniformly and dynamically sample the surface. It is robust, efficient and prevents the inversion of triangles. The sec...

considered the case in which the images are in the same imaging plane and the optical axes of the two images are parallel. The triangulation error is inversely proportional to the product of baseline x focal length. At a given focal length, a wider baseline reduces triangulation error but increases both geometric and photometric distortions in images which in turn makes matching of these images...

BACKGROUND Prolongation of action potential duration (APD) is considered a major antiarrhythmic mechanism (class 2I), but paradoxically, it frequently is also proarrhythmic (torsade de pointes). METHODS AND RESULTS The cardiac electrophysiological effects of 702 chemicals (class 2I or HERG channel block) were studied in 1071 rabbit Langendorff-perfused hearts. Temporal instability of APD, tri...

One of most famous theorems in computational geometry is the duality between Voronoi diagram and Delaunay triangulation in Euclidean space. This paper proposes an extension of that theorem to the Voronoi diagram and Delaunay-type triangulation in dually at space. In that space, the Voronoi diagram and the triangulation can be computed e ciently by using potential functions. We also propose high...

A triangulation of points in , or a tetrahedronization of points in , is used in many applications. It is not necessary to fulfill the Delaunay criteria in all cases. For large data (more then points), parallel methods are used for the purpose of decreasing time complexity. A new approach for fast and effective parallel CPU and GPU triangulation, or tetrahedronization, of large data sets in or ...

We propose a new data structure to compute the Delaunay triangulation of a set of points in the plane. It combines good worst case complexity, fast behavior on real data, small memory occupation and the possibility of fully dynamic insertions and deletions. The location structure is organized into several levels. The lowest level just consists of the triangulation, then each level contains the ...