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.[1][2]

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).

The Doo-Sabin process generates one new face at each original vertex, n new faces along each original edge, and n2 new faces at each original face. 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.

Evaluation

Doo–Sabin 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.[2] After many iterations, the surface will gradually converge onto a smooth limit surface.

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 Catmull–Clark surfaces because the Doo–Sabin subdivision matrices are not (in general) diagonalizable.

Two Doo–Sabin refinement iterations on a ⊥-shaped quadrilateral mesh

See also
  1. D. Doo: A subdivision algorithm for smoothing down irregularly shaped polyhedrons, Proceedings on Interactive Techniques in Computer Aided Design, pp. 157 - 165, 1978 (pdf)
  2. D.Doo, M.Sabin: Behaviour of recursive division surfaces near extraordinary points, Computer Aided Design, pp. 356-360, 1978 ()
  3. Jos Stam, Exact Evaluation of Catmull–Clark Subdivision Surfaces at Arbitrary Parameter Values, Proceedings of SIGGRAPH'98. In Computer Graphics Proceedings, ACM SIGGRAPH, 1998, 395–404 (pdf Archived 2018-05-09 at the Wayback Machine, downloadable eigenstructures)


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