In 3D computer graphics, a DooâÂÂSabin subdivision surface is a type of subdivision surface based on a generalization of bi-quadratic uniform B-splines, whereas Catmull-Clark was based on generalized bi-cubic uniform B-splines. The subdivision refinement algorithm was developed in 1978 by Daniel Doo and Malcolm Sabin.
The Doo-Sabin process generates one new face at each original vertex, new faces along each original edge, and new faces at each original face. A primary characteristic of the DooâÂÂSabin subdivision method is the creation of four faces and four edges (valence 4) around every new vertex in the refined mesh. A drawback is that the faces created at the original vertices may be triangles or n-gons that are not necessarily coplanar.
DooâÂÂSabin surfaces are defined recursively. Like all subdivision procedures, each refinement iteration, following the procedure given, replaces the current mesh with a "smoother", more refined mesh. After many iterations, the surface will gradually converge onto a smooth limit surface.
Just as for CatmullâÂÂClark surfaces, DooâÂÂSabin limit surfaces can also be evaluated directly without any recursive refinement, by means of the technique of Jos Stam. The solution is, however, not as computationally efficient as for CatmullâÂÂClark surfaces because the DooâÂÂSabin subdivision matrices are not (in general) diagonalizable.