Doo–Sabin subdivision surface

In 3D computer graphics, a Doo–Sabin 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.

A primary characteristic of the Doo–Sabin 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.

[3] The solution is, however, not as computationally efficient as for Catmull–Clark surfaces because the Doo–Sabin subdivision matrices are not (in general) diagonalizable.

A Doo-Sabin mesh after 2 levels of refinement. The new faces come from vertices, edges and faces of the original mesh (colored dark, white, and midtone respectively).
Two Doo–Sabin refinement iterations on a ⊥-shaped quadrilateral mesh