We modify the incremental algorithm for computing Voronoi diagrams in the Euclidean metric proposed by Ohya, Iri and Murota 6] in order to obtain an algorithm for computing Voronoi diagrams (resp. Delaunay triangulations) in Man-hattan and Maximum metric, that is rather simply to implement. We generalize the notions of \Voronoi diagram" and \Delaunay triangulation" in such a way that these stru...

Yuanxin Liu: Computations of Delaunay and higher order triangulations, with applications to splines. (Under the direction of Jack Snoeyink.) Digital data that consist of discrete points are frequently captured and processed by scientific and engineering applications. Due to the rapid advance of new data gathering technologies, data set sizes are increasing, and the data distributions are becomi...

being one of the major research fields in the robotics discipline, the robot motion planning problem deals with finding an obstacle-free start-to-goal path for a robot navigating among workspace obstacles. such a problem is also encountered in path planning of intelligent vehicles and automatic guided vehicles (agvs). traditional (exact) algorithms have failed to solve the problem effectively s...

In this article, recent works on 2D Constrained Delaunay triangulation(CDT) algorithms have been reported. Since the review of CDT algorithms presented by de Floriani(Issues on Machine Vision, Springer Vienna, pg. 95–104, 1989), different algorithms for construction and applications of CDT have appeared in literature each concerned with different aspects of computation and different suitabiliti...

This work presents two generalizations of the algorithm for obtaining a constrained Delaunay triangulation of a general planar graph presented in Vig97] and Vig95]. While the rst generalization works with elliptical distances, the second one can deal with a set of deforming ellipses associated to each point of the plane. The pseudo-code of the procedures involved in the algorithms is included, ...

This paper presents the requirements for a surface mesh to be valid. Aside from validity, it also discusses conditions for geometric similarity, which quantitatively describes how the surface mesh “matches” the model geometry. The surface mesh generation method presented here uses the parameter space of a model face to generate a coarse triangulation. In order to avoid the mapping problem, the ...

We describe an algorithm which generates tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular facets. The principal idea is to modify the constraints in such a way as to make them appear in an unconstrained triangulation of the vertex set a priori. The vertex set positions are randomized to guarantee existence of a unique triangulation which sa...