Adaptive Subdivision Schemes for Triangular Meshes

Of late we have seen an increase in the use of subdivision techniques for both modeling and animation. They have given rise to a new surface called the subdivision surface which has many advantages over traditional Non Uniform Rational B-spline (NURB) surfaces. Subdivision surfaces easily address the issues related to multiresolution, refinement, scalability and representation of meshes. Many schemes have been introduced that take a coarse mesh and refine it using subdivision. They can be mainly classified as Approximating — in which the original coarse mesh is not preserved, or Interpolating — wherein the subdivision forces the refined mesh to pass through the original points of the coarse mesh. The schemes used for triangular meshes are chiefly the Loop scheme, which is approximating in nature and the Modified Butterfly scheme which is interpolating. Subdivision schemes are cost intensive at higher levels of subdivision. In this paper we introduce two methods of adaptive subdivision for triangular meshes that make use of the Loop scheme or the Modified Butterfly scheme to get approximating or interpolating results respectively. The results are obtained at a lower cost when compared with those obtained by regular subdivision schemes. The first method uses the angles between the normal of a face and the normals of its adjacent faces to develop an adaptive method of subdivision. The other method relies on user input, i.e. the user specifies which parts of the mesh should be subdivided. This process can be automated by segmentation techniques, e.g. watershed segmentation, to get the areas in the mesh that need to be subdivided. We compare our methods for various triangular meshes and present our results