1997
DOI: 10.1145/263834.263851
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The simplest subdivision scheme for smoothing polyhedra

Abstract: Given a polyhedron, construct a new polyhedron by connecting every edge-midpoint to its four neighboring edge-midpoints. This refinement rule yields a C 1 surface and the surface has a piecewise quadratic parametrization except at a finite number of isolated points. We analyze and improve the construction.

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Cited by 156 publications
(80 citation statements)
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“…Default parameters are additionally used to close holes that are in the original surface mesh and are created by removing defective faces. In cases where closing holes keep re-introducing problems with the surface, the surface mesh is refined successively, smoothened, and coarsened, where "Midpoint subdivision" [38], "Laplacian smooth" [39] and "Quadratic edge collapse decimation" [40] are employed for these procedures, respectively. The surface mesh is processed again using basic filters to remove defective faces that may be re-introduced during the mesh coarsening.…”
Section: Molecular Surface Computation and Discretizationmentioning
confidence: 99%
“…Default parameters are additionally used to close holes that are in the original surface mesh and are created by removing defective faces. In cases where closing holes keep re-introducing problems with the surface, the surface mesh is refined successively, smoothened, and coarsened, where "Midpoint subdivision" [38], "Laplacian smooth" [39] and "Quadratic edge collapse decimation" [40] are employed for these procedures, respectively. The surface mesh is processed again using basic filters to remove defective faces that may be re-introduced during the mesh coarsening.…”
Section: Molecular Surface Computation and Discretizationmentioning
confidence: 99%
“…The quincunx split of the quad by the c-patch reminds of the Zwart-Powell element [23,18], simplest subdivision [17] and 4-8 subdivision [21] due to the underlying box-spline directions.…”
Section: Some Alternative Mesh Smoothing Techniques On the Gpumentioning
confidence: 99%
“…Among the many attempts to the study of the order of smoothness, Doo and Sabin [9] considered necessary conditions on the subdivision matrices, Ball and Storry [1] studied the continuity of moving tangent planes, and Reif [35] introduced the notion of "characteristic maps", formulating a C 1 continuity condition in terms of the regularity and injectivity of the characteristic maps and eigenvalues of the subdivision matrices. The C 1 -continuity result was applied to analyze several interesting schemes in [37,29,30,11,42,39]. Moreover, in the papers of Prautzsch [31] and of Zorin [43], the result of Reif [35] was extended to orders of smoothness higher than 1.…”
Section: Figure 2: Subdivision Templates Of the Catmull-clark Scheme mentioning
confidence: 99%