DEpthLAUNAY is a C++ software developed with CGAL allowing the user to compute the following structures related to a given set of points in the plane:

• Convex hull
• Convex layers
• Convex levels
• Delaunay triangulation
• Delaunay layers
• Delaunay levels
• Voronoi diagram

Deeper description:

The aim of this application is to compute the Delaunay depth of a point with respect to a set of points, and some structures derived from Delaunay Depth as Delaunay Layers and Levels. Other well-known geometrical structures, like the Delaunay Triangulation, Voronoi Diagram, Convex Hull and Convex Hull Layers and levels can be computed also.

The program has been developed using CGAL (Computational Geometry Algorithms Library) \cite{CGAL}. In particular it uses its functions and objects to construct the Delaunay Triangulation of a point set in the plane. From the point of view of the programmer, the program has three layers of code:

• The inner is CGAL, a robust library that triangulates the points.
• The intermediate layer is an object named CNube, whose aim is to create a set of functions such that a programmer could use CGAL without knowing that library, using only CNube. As CGAL, CNube is independent of the operating system.
• The external layer is the part that shows the information in the screen. This layer depends on the operating system. At the moment it uses Microsoft Windows.

The program has been developed in C++ with OOP, using Microsoft Visual Studio .NET and Microsoft Windows XP as platforms.

From the user's point of view, the program can be divided in three parts: The input of data (points) in the program, the visualization and the output of the computed structures. Possibly the most interesting part is the visualization, because the computation and rendering of triangulation, Voronoi diagram, etc. are done in real time.