3D computer graphics 3D computer graphics, or “3D graphics,” sometimes called CGI, 3D-CGI or three-dimensional computer graphics are graphics that use a three-dimensional representation of geometric data (often Cartesian) that is stored in the computer for th ...

, a Doo–Sabin subdivision surface is a type of

subdivision surface In the field of 3D computer graphics, a subdivision surface (commonly shortened to SubD surface) is a curved surface represented by the specification of a coarser polygon mesh and produced by a recursive algorithmic method. The curved surface, t ...

based on a generalization of '' bi-quadratic'' uniform

B-spline In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Any spline function of given degree can be expresse ...

s, whereas Catmull-Clark was based on generalized ''

bi-cubic In mathematics, bicubic interpolation is an extension of cubic interpolation (not to be confused with cubic spline interpolation, a method of applying cubic interpolation to a data set) for interpolating data points on a two-dimensional regular g ...

'' uniform B-splines. The subdivision refinement algorithm 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
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D.Doo, M.Sabin: ''Behaviour of recursive division surfaces near extraordinary points'', Computer Aided Design, pp. 356-360, 1978

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 ('' Degree (graph theory), 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 In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two toge ...

that are not necessarily

coplanar In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. Howe ...

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. 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 Jos Stam (born 28 December 1965 in The Hague, Netherlands) is a researcher in the field of computer graphics, focusing on the simulation of natural physical phenomena for 3D- computer animation. He achieved technical breakthroughs with the simulat ...

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

diagonalizable In linear algebra, a square matrix A is called diagonalizable or non-defective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P and a diagonal matrix D such that or equivalently (Such D are not unique.) F ...

External links

Doo–Sabin surfaces
3D computer graphics Multivariate interpolation {{Comp-sci-stub

Evaluation

See also

External links