Chapter 5: 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 C¹-continuous subdivision surface which interpolates all the given data points. The new technique consists of two major steps. First, an efficient 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 Mmacr, 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 processes well-defined. 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.