The following paper discusses the application of two subdivision algorithms for the purpose of finding an optimal way of rendering smooth spherical surfaces. Subdivision algorithms are used on three dimensional models. These algorithms typically manipulate the original object to produce one that is more visually pleasing and more realistic to the object we are attempting to recreate. We applied two popular subdivision algorithms to some simple meshes to compare their outcomes. In this project we implemented some of these algorithms in order to gain some insight into how these algorithms differ in the way that they are transforming the input mesh. Our desired goal was to see if there is any basis for which we can say that one algorithm outperforms the other. Our comparison runs through several iterations of subdivision and compares their theses meshes visually. In comparing these meshes our desired visual outcome is a mesh that is more smooth or more spherical. Another metric we looked at was the number of faces being produced for each mesh. In addition, we compared the algorithms in terms of the time they took to perform subdivision. These metrics form the basis for our comparison of performance and we discuss the details of these further in this paper.In our results we found that the two algorithms we are comparing perform quite similarly on certain meshes with respect to the visual output and the time they take to perform subdivision. On meshes of different types however the algorithms might output visually distinguishable meshes upon repeated subdivisions. Finding what factors influence whether the algorithms perform similarly provides an avenue for future work.

This thesis presents a new technique for the reconstruction of a smooth surface from a set of 3D data points. The reconstructed surface is represented by an everywhere -continuous subdivision surface which interpolates all the given data points. And the topological structure of the reconstructed surface is exactly the same as that of the data points. The new technique consists of two major steps. First, use an efficient surface reconstruction method to produce a polyhedral approximation to the given data points. Second, construct a Doo-Sabin subdivision surface that smoothly passes through all the data points in the given data set. A new technique is presented for the second step in this thesis. The new technique iteratively modifies the vertices of the polyhedral approximation 1CM until a new control meshM, whose Doo-Sabin subdivision surface interpolatesM, is reached. It is proved that, for any mesh M with any size and any topology, the iterative process is always convergent with Doo-Sabin subdivision scheme. 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.