The idea of subdivision surfaces was first introduced in 1978, and there are many methods proposed till now. The subdivision surface itself is defined as the limit of repeated recursive refinements. In this thesis, we studied the properties of approximating subdivision surface schemes. We started by modeling a complex surface with splines which 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 three well-known schemes Catmull-Clark, Doo-Sabin and Loop with the newly proposed Square Root 3-subdivision. The first two of them quadrilateral and the other two triangular surface subdivision schemes, respectively. Modeling sharp features, such as creases, corners or darts, using subdivision schemes requires some modifications in subdivision procedures and sometimes special tagging in the mesh. We developed the rules of Square Root 3-subdivision to model such features and compared the results with the extended Loop scheme. We have implemented exact normals of Loop and Square Root 3-subdivision since using interpolated normals causes creases and other sharp features to appear smooth.