E Cohen, T Lyche, and R F Riesenfeld. Discrete B-splines And Subdivision Techniques In Computer Aided Design And Computer Graphics. Computer Graphics and Image Processing, 14:87-111, 1980.

Google Scholar

[7]

C de Boor. Cutting Corners Always Works. Computer Aided Geometric Design, 4:125-131, 1987.

Digital Library

Google Scholar

[8]

D Doo and M Sabin. Behaviour Of Recursive Division Surfaces Near Extraordinary Points. Computer-Aided Design, 10:356-360, 1978.

Crossref

Google Scholar

[9]

N Dyn, D Levin, and J A Gregory. A 4-point Interpolatory Subdivision Scheme For Curve Design. Computer Aided Geometric Design, 4:257-268, 1987.

Digital Library

Google Scholar

[10]

G Farin. Designing C1 Surfaces Consisting Of Triangular Cubic Patches. Computer-Aided Design, 14:253- 256, 1982.

Crossref

Google Scholar

[11]

A R Forrest. Notes On Chaikin's Algorithm. Technical Report Memo CGP74/1, University of East Anglia, Norwich, UK, 1974.

Google Scholar

[12]

M Halstead, M Kass, and T DeRose. Efficient, Fair Interpolation Using Catmull-Clark Surfaces. Computer Graphics (SIGGRAPH 93 Conference Proceedings), 27:35-44, 1993.

Digital Library

Google Scholar

[13]

H Hoppe, T DeRose, T Duchamp, M Halstead, H Jin, J McDonald, J Schweitzer, and W Stuetzle. Piecewise Smooth Surface Reconstruction. Computer Graphics (SIGGRAPH 94 Conference Proceedings), 28:295- 302, 1994.

Digital Library

Google Scholar

[14]

L Kobbelt. Interpolatory Subdivision On Open Quadrilateral Nets With Arbitrary Topology. Computer Graphics Forum (Eurographics 96), 1996.

Google Scholar

[15]

C Loop. Smooth Subdivision Surfaces Based On Triangles. Master's thesis, University of Utah, Dept. of Mathematics, 1987.

Google Scholar

[16]

C Loop. Smooth Spline Surfaces Over Irregular Meshes. Computer Graphics (SIGGRAPH 94 Conference Proceedings), 28:303-310, 1994.

Digital Library

Google Scholar

[17]

A Nasri. Polyhedral Subdivision Methods For Freeform Surfaces. PhD thesis, University of East Anglia, 1984.

Google Scholar

[18]

A Nasri. Polyhedral Subdivision Methods For Freeform Surfaces. ACM ToG, 6:29-73, 1987.

Digital Library

Google Scholar

[19]

A Nasri. Surface Interpolation On Irregular Network With Normal Conditions. Computer Aided Geometric Design, 8:89-96, 1991.

Digital Library

Google Scholar

[20]

A Nasri. Curve Interpolation In Recursively Generated B-spline Surfaces Over Arbitrary Topology. Computer Aided Geometric Design, 14:13-30, 1997.

Digital Library

Google Scholar

[21]

J Peters. Joining Smooth Patches Around A Vertex To Form A Ck Surface. Computer Aided Geometric Design, 9:387-411, 1992.

Digital Library

Google Scholar

[22]

J Peters. Smooth Free-form Surfaces Over Irregular Meshes Generalizing Quadratic Splines. Computer Aided Geometric Design, 10:347-361, 1993.

Digital Library

Google Scholar

[23]

J Peters. C1 Surface Splines. SlAM J Num Anal, 32:645-666, 1995.

Digital Library

Google Scholar

[24]

H Prautzsch. Freeform Splines. Computer Aided Geometric Design, 14:201-206, 1997.

Digital Library

Google Scholar

[25]

U. Reif. A Unified Approach To Subdivision Algorithms Near Extraordinary Vertices. Computer Aided Geometric Design, 12:153-174, 1995.

Digital Library

Google Scholar

[26]

R F Riesenfeld. On Chaikin's Algorithm. Computer Graphics and Image Processing, 4:304-310, 1975.

Crossref

Google Scholar

[27]

M A Sabin. Recursive Division. In J Gregory, editor, The Mathematics of Surfaces, pages 269-282. Clarendon Press, Oxford, 1986. ISBN 0 19 853609 7.

Google Scholar

[28]

M A Sabin. Cubic Recursive Division With Bounded Curvature. In P J Laurent, Ale Mehaute, and L L Schumaker, editors, Curves and Surfaces, pages 411-414. Academic Press, 1991. ISBN 0 12 438660 1.

Digital Library

Google Scholar

[29]

D J T Storry and A A Ball. Design Of An N-sided Surface Patch From Hermite Boundary Data. Computer Aided Geometric Design, 6:111-120, 1989.

Digital Library

Google Scholar

[30]

J Zheng, T Sederberg, and M A Sabin. Eigenanalysis Of Non-Uniform Doo-Sabin Surfaces. Technical report, Brigham Young University, Department of Computer Science (appears as an appendix in the electronic version of this paper), November 1997.

Google Scholar

[31]

D Zorin, P Schr6der, and W Sweldens. Interpolating Subdivision For Meshes With Arbitrary Topology. Computer Graphics (SIGGRAPH 96 Conference Proceedings), 30:189-192, 1996.

Digital Library

Google Scholar

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Feng YShen LLi XYuan CJiang X(2024)Patching Non-Uniform Extraordinary PointsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.327166930:8(4683-4693)Online publication date: Aug-2024
https://doi.org/10.1109/TVCG.2023.3271669
Wang XMa W(2024)Rational reparameterization of unstructured quadrilateral meshes for isogeometric analysis with optimal convergenceComputers & Mathematics with Applications10.1016/j.camwa.2023.09.050151:C(304-325)Online publication date: 1-Feb-2024
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Uwitije RWang XDeng J(2024)Nonlinear Weighted Subdivision SchemesCommunications in Mathematics and Statistics10.1007/s40304-023-00383-1Online publication date: 25-May-2024
https://doi.org/10.1007/s40304-023-00383-1
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Index Terms

Non-uniform recursive subdivision surfaces
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Numerical differentiation
    2. Quadrature

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Published In

SIGGRAPH '98: Proceedings of the 25th annual conference on Computer graphics and interactive techniques

July 1998

472 pages

ISBN:0897919998

DOI:10.1145/280814

Chairmen:
Steve Cunningham
California State Univ. Stanislaus, Trulock, CA
,
Walt Bransford
Thrillistic
,
Michael F. Cohen,
General Chairs:
Srinivas Aluru
Georgia Institute of Technology
,
May Dongmei Wang
Georgia Institute of Technology and Emory University
,
Program Chairs:
Christopher C. Yang
Drexel University
,
T. M Murali
Virginia Tech

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Published: 24 July 1998

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Cited By

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Feng YShen LLi XYuan CJiang X(2024)Patching Non-Uniform Extraordinary PointsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.327166930:8(4683-4693)Online publication date: Aug-2024
https://doi.org/10.1109/TVCG.2023.3271669
Wang XMa W(2024)Rational reparameterization of unstructured quadrilateral meshes for isogeometric analysis with optimal convergenceComputers & Mathematics with Applications10.1016/j.camwa.2023.09.050151:C(304-325)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1016/j.camwa.2023.09.050
Uwitije RWang XDeng J(2024)Nonlinear Weighted Subdivision SchemesCommunications in Mathematics and Statistics10.1007/s40304-023-00383-1Online publication date: 25-May-2024
https://doi.org/10.1007/s40304-023-00383-1
Marsala MMantzaflaris AMourrain BWhyman SGammon M(2024)From CAD to representations suitable for isogeometric analysis: a complete pipelineEngineering with Computers10.1007/s00366-024-02065-040:6(3429-3447)Online publication date: 23-Sep-2024
https://doi.org/10.1007/s00366-024-02065-0
Peng KTan JZhang L(2023)Polynomial-Based Non-Uniform Ternary Interpolation Surface Subdivision on Quadrilateral MeshMathematics10.3390/math1102048611:2(486)Online publication date: 16-Jan-2023
https://doi.org/10.3390/math11020486
Yang X(2023)Point-normal subdivision curves and surfacesComputer Aided Geometric Design10.1016/j.cagd.2023.102207104(102207)Online publication date: Jul-2023
https://doi.org/10.1016/j.cagd.2023.102207
Gérot CIvrissimtzis I(2023)Bivariate non-uniform subdivision schemes based on L-systemsApplied Mathematics and Computation10.1016/j.amc.2023.128156457:COnline publication date: 15-Nov-2023
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Wood MRendall TAllen CKedward LTaylor NFincham JLeppard N(2022)Subdivision Multi-Resolution Systems for Three-dimensional Aerodynamic OptimisationAIAA SCITECH 2022 Forum10.2514/6.2022-1864Online publication date: 29-Dec-2022
https://doi.org/10.2514/6.2022-1864
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
https://doi.org/10.1186/s42492-022-00115-2
Wei XLi XQian KHughes TZhang YCasquero H(2022)Analysis-suitable unstructured T-splines: Multiple extraordinary points per faceComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2021.114494391(114494)Online publication date: Mar-2022
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Extended subdivision surfaces: Building a bridge between NURBS and Catmull-Clark surfaces

Non-uniform recursive Doo-Sabin surfaces

Eigenanalysis and Continuity of Non-Uniform Doo-Sabin Surfaces