Comparison of four approximating subdivision surface schemes

Abstract

The idea of subdivision surfaces was first introduced in 1978, and there are many- methods proposed till now. A subdivision surface is defined as the limit of repeated recursive refinements. In this thesis, we studied the properties of approximating sub division surface schemes. We started by modeling a complex surface with splines that typically requires a number of spline patches, which must be smoothly joined, making splines burdensome to use. Unlike traditional spline surfaces, subdivision surfaces are defined algorithmically. Subdivision schemes generalize splines to domains of arbitrary topology.. Thus, subdivision functions can be used to model complex surfaces without the need to deal with patches. We studied four well-known schemes Catmull-Clark, Doo-Sabin, Loop and the y/%- subdivision. The first two of these schemes are quadrilateral and the other two are triangular surface subdivision schemes. Modeling sharp features, such as creases, cor ners or darts, using subdivision schemes requires some modifications in subdivision procedures and sometimes special tagging in the mesh. We developed the rules of \/3- subdivision to model such features and compared the results with the extended Loop scheme. We have implemented exact normals of Loop and \/3-8ubdivision since using interpolated normals causes creases and other sharp features to appear smooth. Keywords: computational geometry and object modeling, subdivision surfaces, Loop, Catmull-Clark, Doo-Sabin, -\/3-subdivision, modeling sharp features.