Given a triangulation T of n points in the plane, we are interested in the minimal set of edges in T such that T can be reconstructed from this set (and the vertices of T ) using constrained Delaunay triangulation. We show that this minimal set consists of the non locally Delaunay edges of T , and that its cardinality is less than or equal to n+ i=2 (if i is the number of interior points in T )...

In this paper we discuss a new algorithm that for any input quality constrained Delaunay triangulation with minimum interior angle greater than or equal to 30 , produces a quality nonobtuse boundary and/or interface Delaunay triangulation by the Delaunay insertion of a nite number of boundary and/or interface points. A boundary (interface) obtuse triangle is a triangle that has an obtuse angle ...

This paper describes the software DEpthLAUNAY. The main goal of the application is to compute Delaunay depth layers and levels of a planar point set [ACH]. Some other geometric structures can be computed as well (convex hull, convex layers and levels, Voronoi diagram and Voronoi levels, Delaunay triangulation, Delaunay empty circles, etc.) The application has been developed using CGAL [CGAL].

Computing the Delaunay triangulation of n points requires usually a minimum of (n log n) operations, but in some special cases where some additional knowledge is provided, faster algorithms can be designed. Given two sets of points, we prove that, if the Delaunay triangulation of all the points is known, the Delaunay triangulation of each set can be computed in randomized expected linear time.

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...