We present a novel approach to surface reconstruction based on the Delaunay complex. First we give a simple and fast algorithm that picks locally a surface at each vertex. For that, we introduce the concept of /spl lambda/-intervals. It turns out that for smooth regions of the surface this method works very well and at difficult parts of the surface yields an output well-suited for postprocessing. As a postprocessing step we propose a topological clean up and a new technique based on linear programming in order to establish a topologically correct surface. These techniques should be useful also for many other reconstruction schemes.