The Computational Geometry (GC) is a quite recent field that dates back to twenty-odd years ago. CG is a branch of computer science that tries to solve geometric computing problems by building analytical and computational tools. Opposite to classical geometry, CG deals with finite or countable sets of geometric objects (i.e. points, lines, planes, or general figures) and its approach is oriented to real problem solving and computer based. Computer graphics, manufacturing, scientific visualization, computer vision, astrophysics, molecular biology, material science and fluid mechanics are just few fields where CG is used.

In spite of such wide spread diffusion in the other areas of computer science, the impact of CG into statistics, in my opinion, is underestimated, as well as the impact of statistics into CG.

In this talk, the basic CG concepts, tasks and tools will be presented and the connection with the statistical theory will be shown. Particular attention will be paid to:

1. Convex hulls and alpha-hulls
2. Voronoi Tessellation and Delaunay Triangulation.
3. Minimum spanning tree.

A brief review of the algorithms to solve the previous geometrical problems will be provided. The statistical interpretation, their applications in data analysis and statistical contributions to CG will be pointed out.

More deeply, two procedures to detect outliers in the framework of the multivariate data analysis and of the time series analysis, based on the convex hull, will be presented. These procedures are non-parametric and handle the masking and swamping effects in the case of multiple outliers.

A non-parametric discriminant rule, based on the Voronoi diagram, will be presented. Such discriminant function is useful for non-linear and non-convex data structures.

Furthermore, future developments and applications will be discussed.