In computer graphics, Doo–Sabin subdivision surface is a type of subdivision surface based on a generalization of biquadratic uniform Bsplines. It was developed in 1978 by Daniel Doo and Malcolm Sabin ^{[1]} ^{[2]}.
This process generates one new face at each original vertex, n new faces along each original edge, and n x n new faces at each original face. A primary characteristic of the Doo–Sabin subdivision method is the creation of four faces around every vertex. A drawback is that the faces created at the vertices are not necessarily coplanar.
Doo–Sabin surfaces are defined recursively. Each refinement iteration replaces the current mesh with a smoother, more refined mesh, following the procedure described in ^{[2]}. After many iteration, the surface will gradually converge onto a smooth limit surface. The figure below show the effect of two refinement iterations on a Tshaped quadrilateral mesh.
Just as for Catmull–Clark surfaces, Doo–Sabin limit surfaces can also be evaluated directly without any recursive refinement, by means of the technique of Jos Stam ^{[3]}. The solution is, however, not as computationally efficient as for CatmullClark surfaces because the Doo–Sabin subdivision matrices are not in general diagonalizable.
