Despite intensive research, 3D representation is still an open research issue in computer graphics. In this paper, we propose a novel B-Spline surface modelling technique. Unlike previous work, our approach deals with unstructured point cloud data. By representing objects in a common parameter space, one of the most challenging problems, i.e. automatic dense correspondence between objects, is solved with little effort. Supporting level of detail (LOD) control, our approach is particularly efficient for 3D object rendering. Furthermore, the representation is compact - over 90% compression rate is achieved. It also allows efficient 3D objects comparison and metamorphosis.