An increasing need for automated 3D city reconstruction models is being driven by a variety of applications, from tourism to disaster management. The arrival of LIDAR (Light Detection and Ranging) - airborne laser altimetry - now provides rapid elevation models of terrain and buildings. LIDAR data contains X, Y and Z coordinates only, it does not provide any building information. The challenge is to convert the data into CAD-type models containing walls, roof planes and terrain which can be rapidly displayed from any 3D viewpoint. This paper shows an alternative method to locate building blocks and identify the roof structures with the use of the Delaunay Triangulation and its dual Voronoi diagram.