Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition—the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners into useful geometric models is referred to as surface reconstruction. In this paper, we present a procedure for reconstructing a tensor product B-spline surface from a set of scanned 3D points. Unlike previous work which considers primarily the problem of fitting a single B-spline patch, our goal is to directly reconstruct a surface of arbitrary topological type. We must therefore define the surface as a network of B-spline patches. A key ingredient in our solution is a scheme for automatically constructing both a network of patches and a parametrization of the data points over these patches. In addition, we define the B-spline surface using a surface spline construction, and demonstrate that such an approach leads to an efficient procedure for fitting the surface while maintaining tangent plane continuity. We explore adaptive refinement of the patch network in order to satisfy user-specified error tolerances, and demonstrate our method on both synthetic and real data.

In computer graphics and geometric modeling, shapes are often represented by triangular meshes.With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace.Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit.Multiresolution analysis offers a simple, unified, and theoretically sound approach to dealing with these problems.Lounsbery et al. have recently developed a technique for creating multiresolution representations for a restricted class of meshes with subdivision connectivity.Unfortunately, meshes encountered in practice typically do not meet this requirement.In this paper we present a method for overcoming the subdivision connectivity restriction, meaning that completely arbitrary meshes can now be converted to multiresolution form.The method is based on the approximation of an arbitrary initial mesh M by a mesh M J that has subdivision connectivity and is guaranteed to be within a specified tolerance.The key ingredient of our algorithm is the construction of a parametrization of M over a simple domain.We expect this parametrization to be of use in other contexts, such as texture mapping or the approximation of complex meshes by NURBS patches.