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In computer graphics, Doo–Sabin subdivision surface is a type of subdivision surface based on a generalization of bi-quadratic uniform B-splines. It was developed in 1978 by Daniel Doo and Malcolm Sabin.〔D. Doo: ''A subdivision algorithm for smoothing down irregularly shaped polyhedrons'', Proceedings on Interactive Techniques in Computer Aided Design, pp. 157 - 165, 1978 ((pdf ))〕〔D. Doo and M. Sabin: ''Behavior of recursive division surfaces near extraordinary points'', Computer-Aided Design, 10 (6) 356–360 (1978), ((doi ), (pdf ))〕 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. == Evaluation == Doo–Sabin surfaces are defined recursively. Each refinement iteration replaces the current mesh with a smoother, more refined mesh, following the procedure described in.〔 After many iterations, the surface will gradually converge onto a smooth limit surface. The figure below show the effect of two refinement iterations on a T-shaped 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.〔 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 ), (downloadable eigenstructures ))〕 The solution is, however, not as computationally efficient as for Catmull-Clark surfaces because the Doo–Sabin subdivision matrices are not in general diagonalizable. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Doo–Sabin subdivision surface」の詳細全文を読む スポンサード リンク
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