A point-based 3D surface modelling technique combined with a new point rendering technique is presented. Surfaces are modelled by specifying a set of unorganized points on the surface. An implicit representation of the surface through these points minimizing the bending energy is then calculated using radial basis functions while guaranteeing a specifiable continuity. The surface is directly rendered view-dependently in an output-sensitive multiresolution manner without the creation of a polygonal mesh representation. This is done by the local generation of 3D surface points for the rendering adapted to the output device. A new texturing technique using the material properties of the points is presented.