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√3-subdivision

Author:

Leif KobbeltAuthors Info & Claims

SIGGRAPH '00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques

Pages 103 - 112

https://doi.org/10.1145/344779.344835

Published: 01 July 2000 Publication History

Abstract

A new stationary subdivision scheme is presented which performs slower topological refinement than the usual dyadic split operation. The number of triangles increases in every step by a factor of 3 instead of 4. Applying the subdivision operator twice causes a uniform refinement with tri-section of every original edge (hence the name √3-subdivision) while two dyadic splits would quad-sect every original edge. Besides the finer gradation of the hierarchy levels, the new scheme has several important properties: The stencils for the subdivision rules have minimum size and maximum symmetry. The smoothness of the limit surface is C² everywhere except for the extraordinary points where it is C¹. The convergence analysis of the scheme is presented based on a new general technique which also applies to the analysis of other subdivision schemes. The new splitting operation enables locally adaptive refinement under built-in preservation of the mesh consistency without temporary crack-fixing between neighboring faces from different refinement levels. The size of the surrounding mesh area which is affected by selective refinement is smaller than for the dyadic split operation. We further present a simple extension of the new subdivision scheme which makes it applicable to meshes with boundary and allows us to generate sharp feature lines.

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√3-subdivision

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Published In

cover image ACM Conferences

SIGGRAPH '00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques

July 2000

547 pages

ISBN:1581132085

Chairmen:
Judith R. Brown
Coralville, IA
,
Kurt Akeley

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SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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ACM Press/Addison-Wesley Publishing Co.

United States

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Published: 01 July 2000

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SIGGRAPH '00 Paper Acceptance Rate 59 of 304 submissions, 19%;

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

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https://doi.org/10.3390/math11020486
Ma WWang XMa Y(2023)An Unified λ-subdivision Scheme for Quadrilateral Meshes with Optimal Curvature Performance in Extraordinary RegionsACM Transactions on Graphics10.1145/361840042:6(1-15)Online publication date: 5-Dec-2023
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Christiansen TBærentzen JPaulsen RHannemose M(2023)Neural Representation of Open SurfacesComputer Graphics Forum10.1111/cgf.1491642:5Online publication date: 10-Aug-2023
https://doi.org/10.1111/cgf.14916
Jena HJena M(2023)An introduction to a hybrid trigonometric box spline surface producing subdivision schemeNumerical Algorithms10.1007/s11075-023-01565-295:1(73-116)Online publication date: 9-Jul-2023
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Zhang JTian YLi X(2022)Improved non-uniform subdivision scheme with modified Eigen-polyhedronVisual Computing for Industry, Biomedicine, and Art10.1186/s42492-022-00115-25:1Online publication date: 11-Jul-2022
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