Smooth Surface Reconstruction using Doo-Sabin Subdivision Surfaces

A new technique for the reconstruction of a smooth surface from a set of 3D data points is presented. The reconstructed surface is represented by an everywhere Ccontinuous subdivision surface which interpolates all the given data points. The new technique consists of two major steps. First, an ef£cient surface reconstruction method is applied to produce a polyhedral approximation to the given data set M . A Doo-Sabin subdivision surface that smoothly passes through all the points in the given data set M is then constructed. The Doo-Sabin subdivision surface is constructed by iteratively modifying the vertices of the polyhedral approximation until a new control mesh M̄ , whose Doo-Sabin subdivision surface interpolates M , is reached. This iterative process converges for meshes of any size and any topology. Therefore the surface reconstruction process is well-de£ned. The new technique has the advantages of both a local method and a global method, and the surface reconstruction process can reproduce special features such as edges and corners faithfully.