Doo–Sabin subdivision surface
Type of polygon mesh in computer graphics
From Wikipedia, the free encyclopedia
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]
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 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. Later work has noted that classical Doo-Sabin subdivision can exhibit shape defects near extraordinary points; for convex input meshes these include flatness at the extraordinary point and nearby oscillation.[3]
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.[4] The solution is, however, not as computationally efficient as for Catmull–Clark surfaces because the Doo–Sabin subdivision matrices are not (in general) diagonalizable.
See also
- Expansion (equivalent geometric operation) - facets are moved apart after being separated, and new facets are formed
- Conway polyhedron notation - a set of related topological polyhedron and polygonal mesh operators
- Catmull-Clark subdivision surface
- Loop subdivision surface
