2010
DOI: 10.1007/978-3-642-11620-9_20
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## Abstract:This paper gives an overview of two recent techniques for high-quality surface constructions: polar layout and the guided approach. We demonstrate the challenge of high-quality surface construction by examples since the notion of surface quality lacks an overarching theory. A key ingredient of high-quality constructions is a good layout of the surface pieces. Polar layout simplifies design and is natural where a high number of pieces meet. A second ingredient is separation of shape design from surface represen… Show more

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##### Cited by 7 publications
(3 citation statements)
##### References 52 publications
(28 reference statements)
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“…Some typical polar meshes are shown in Figure 4.10 (A) and (B). Polar constructions work well where a high number of surface pieces join; in fact their shape improves with valence whereas that of star-shaped constructions deteriorates with higher valence [83]. Notably, Catmull-Clark subdivision surfaces visibly oscillate for a cylinder mesh whose top cycle is collapsed to a high-valent pole.…”
Section: Polar Constructionsmentioning
confidence: 99%
See 1 more Smart Citation
“…Some typical polar meshes are shown in Figure 4.10 (A) and (B). Polar constructions work well where a high number of surface pieces join; in fact their shape improves with valence whereas that of star-shaped constructions deteriorates with higher valence [83]. Notably, Catmull-Clark subdivision surfaces visibly oscillate for a cylinder mesh whose top cycle is collapsed to a high-valent pole.…”
Section: Polar Constructionsmentioning
confidence: 99%
“…By contrast, polar subdivision [71] achieves not only good shape at the pole, but yields a C 2 subdivision such that the rings are all degree bi-3. C 2 subdivision with pieces all of degree bi-3 is noteworthy since in the star-shape setting, obtaining a C 2 subdivision with rings of degree bi-3 is a long-unsolved problem (see [83,Sect 5] for an unorthodox earlier solution).…”
Section: Polar Constructionsmentioning
confidence: 99%
“…Their scheme is non‐uniform, allows only a single extraordinary vertex in the mesh, and uses special subdivision rules along every chain of edges emanating from an extraordinary vertex. Peters and Karčiauskas [PK10] also discuss low‐degree 2‐flexible subdivision schemes by breaking the assumption on stationarity instead. They gain more flexibility by using an accelerated refinement, where a greater number of spline patches are introduced at every subdivision step.…”
Section: Analysis Of Subdivision Surfacesmentioning
confidence: 99%