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

We describe and analyze the complexity of a procedure for computing and updating a Delaunay triangulation of a set of points in the plane subject to incremental insertions and deletions. Our method is based on a recent algo rithm of Guibas, Knuth, and Sharir for constructing Delaunay triangulations by incremental point insertion only. Our implementation features several meth ods that are not us...

We show that any planar PSLG with n vertices has a conforming triangulation by O(n) nonobtuse triangles, answering the question of whether a polynomial bound exists. The triangles may be chosen to be all acute or all right. A nonobtuse triangulation is Delaunay, so this result improves a previous O(n) bound of Eldesbrunner and Tan for conforming Delaunay triangulations. In the special case that...

The Delaunay triangulation is one of the most popular and most often used methods in problems related to the generation of meshes. A lot of the optimal properties of Delaunay triangulation are known in 2D, where it has been intensively studied during the last twenty years, although the fundamentals were formulated early in the twentieth century (Voronoi, 1908 and Delaunay, 1934). This thesis pr...

In this paper, we investigate the tight bound of the stretch factor of the Delaunay triangulation by studying the stretch factor of the chain (Xia 2011). We define a sequence Γ = (Γ1,Γ2,Γ3, . . .) where Γi is the maximum stretch factor of a chain of i circles, and show that Γ is strictly increasing. We then present an improved lower bound of 1.5932 for the stretch factors of the Delaunay triang...

This chapter discusses geometric models of biomolecules and geometric constructs, including the union of ball model, the weigthed Voronoi diagram, the weighted Delaunay triangulation, and the alpha shapes. These geometric constructs enable fast and analytical computaton of shapes of biomoleculres (including features such as voids and pockets) and metric properties (such as area and volume). The...

In this paper we present our experience with the solution how to make the implementation of 3D Delaunay triangulation more stable. A brief overview of possible methods is given. The proper solution is found in geometric predicates. Tests of two different implementations of them are provided and results of incorporating one of them into our implementation of 3D Delaunay triangulator are presente...

We study the expected time behaviour of the Jumpand-walk paradigm when the set of sites is controlled by a binary search tree or a well-balanced 2-d tree. Throughout the paper, we shall assume that we are given a Delaunay triangulation on N sites uniformly distributed in the unit 2-dimensional square, [0; 1]. We are requested to locate a query point q, which will be assumed to be bounded away f...

ÐAn adaptive image segmentation scheme is proposed employing the Delaunay triangulation for image splitting. The tessellation grid of the Delaunay triangulation is adapted to the semantics of the image data by combining region and edge information. To achieve robustness against imaging conditions (e.g., shading, shadows, illumination, and highlights), photometric invariant similarity measures, ...