Shape Delaunay tessellations are a generalization of the classical Delaunay triangulation of a finite set of points in the plane, where the empty circle condition is replaced by emptiness of an arbitrary convex compact shape. We present some new and basic properties of shape Delaunay tessellations, concerning flipping, subgraph structures, and recognition.

The Delaunay project is concerned with creating a customizable layout-driven approach to querying multimedia digital libraries. Delaunay layouts can be fully specified from scratch by a layout designer to accommodate different classes of users and tasks. In this paper, we overview the main aspects of the Delaunay project and present our approach to the layout specification and enhancement of vi...

The temperature fields inside a collapsing bubble near a plane rigid wall are investigated. We develop a numerical method based on the boundary element method combined with the finite volume method. In this method, the adaptive unstructured grids which are generated by Delaunay triangulation are used inside the largely deformable bubble to consider the heat transfer of the internal gas. We comp...

The Delaunay terminal edge algorithm for triangulation improvement proceeds by iterative Lepp selection of a point M which is midpoint of a Delaunay terminal edge in the mesh. The longest edge bisection of the associated terminal triangles (sharing the terminal edge) can be seen as a first step in the Delaunay insertion of M . The method was introduced as a generalization of non-Delaunay longes...

This work investigates the Delaunay refinement for curved complexes. A manifold complex is defined as an unambiguous representation for the geometric objects required by a partial differential equation solver. The Chew’s and Ruppert’s Delaunay refinement algorithms, including an extension for curved complexes, are described under a new and arbitrary dimensional perspective. A theorem for strong...

We prove that there are superexponentially many combinatorially distinct d-dimensional neighborly Delaunay triangulations on n points. These are the first examples of neighborly Delaunay triangulations that cannot be obtained via a stereographic projection of an inscribed cyclic polytope, and provide the current best lower bound for the number of combinatorial types of Delaunay triangulations. ...

Isotropic tetrahedron meshes generated by Delaunay refinement algorithms are known to contain a majority of well-shaped tetrahedra, as well as spurious sliver tetrahedra. As the slivers hamper stability of numerical simulations we aim at removing them while keeping the triangulation Delaunay for simplicity. The solution which explicitly perturbs the slivers through random vertex relocation and ...

Updating a Delaunay triangulation when data points are slightly moved is the bottleneck of computation time in variational methods for mesh generation and remeshing. Utilizing the connectivity coherence between two consecutive Delaunay triangulations for computation speedup is the key to solving this problem. Our contribution is an effective filtering technique that confirms most bi-cells whose...

Anisotropic meshes are triangulations of a given domain in the plane or in higher dimensions, with elements elongated along prescribed directions. Anisotropic triangulations are known to be well suited for interpolation of functions or solving PDEs. Assuming that the anisotropic shape requirements for mesh elements are given through a metric field varying over the domain, we propose a new appro...

In this paper, we are concerned with Delaunay triangulations of the vertex set of a piecewise flat (pwf) surface. We first propose the notion of well-formed Voronoi diagrams and establish a precise dual relationship between them and proper Delaunay triangulations on pwf surfaces. Then we provide an algorithm which, given any input manifold triangle mesh, constructs aDelaunay mesh: a manifold tr...