ACM Transactions on Graphics vol:25 issue:2 pages:340-355
In this article, we propose a new subdivision scheme based on uniform Powell-Sabin spline subdivision. It belongs to the class of vector subdivision schemes; for each vertex, we have three control points that form a control triangle tangent to the surface instead of one control point. The main advantage of this scheme is that we can choose the values of the normals in the initial vertices which results in more design possibilities. At first sight, it is an approximating scheme because the control points change each iteration. However, the point where the control triangle is tangent to the surface remains the same. Therefore, it is an interpolating scheme. In the regular regions, we use the uniform Powell-Sabin rules, and we develop additional subdivision rules for the new vertices in the neighborhood of extraordinary vertices. The scheme yields C-1 continuous surfaces. We also do the convergence analysis based on the eigenproperties of the subdivision matrix and the properties of the characteristic map.