Convergence and Normal Continuity Analysis of Nonstationary Subdivision Schemes Near Extraordinary Vertices and Faces

被引：8

作者：

Conti, Costanza ^{[1
]}

Donatelli, Marco ^{[2
]}

Romani, Lucia ^{[3
]}

Novara, Paola ^{[2
]}

机构：

[1] Univ Firenze, Dipartimento Ingn Ind, Viale Morgagni 40-44, I-50134 Florence, Italy

[2] Univ Insubria, Dipartimento Sci & Alta Tecnol, Via Valleggio 11, I-22100 Como, Italy

[3] Alma Mater Studiorum Univ Bologna, Dipartimento Matemat, Piazza Porta San Donato, I-40126 Bologna, Italy

来源：

CONSTRUCTIVE APPROXIMATION | 2019年 / 50卷 / 03期

关键词：

Nonstationary subdivision; Extraordinary vertex; face; Convergence; Normal continuity; B-SPLINE SURFACES; EXPONENTIAL POLYNOMIALS; APPROXIMATION; CONSTRUCTION; REPRODUCTION; ORDER;

D O I：

10.1007/s00365-019-09477-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Convergence and normal continuity analysis of a bivariate nonstationary (level-dependent) subdivision scheme for 2-manifold meshes with arbitrary topology is still an open issue. Exploiting ideas from the theory of asymptotically equivalent subdivision schemes, in this paper we derive new sufficient conditions for establishing convergence and normal continuity of any rotationally symmetric, nonstationary subdivision scheme near an extraordinary vertex/face.

引用

页码：457 / 496

页数：40

共 18 条

[1] Convergence and Normal Continuity Analysis of Nonstationary Subdivision Schemes Near Extraordinary Vertices and Faces
Costanza Conti
Marco Donatelli
Lucia Romani
Paola Novara
Constructive Approximation, 2019, 50 : 457 - 496
[2] Subdivision schemes with optimal bounded curvature near extraordinary vertices
Ma, Yue
Ma, Weiyin
COMPUTER GRAPHICS FORUM, 2018, 37 (07) : 455 - 467
[3] A UNIFIED APPROACH TO SUBDIVISION ALGORITHMS NEAR EXTRAORDINARY VERTICES
REIF, U
COMPUTER AIDED GEOMETRIC DESIGN, 1995, 12 (02) : 153 - 174
[4] Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices
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Jiang, Qingtang
COMPUTER AIDED GEOMETRIC DESIGN, 2006, 23 (05) : 419 - 438
[5] Nonstationary Subdivision Schemes and Multiresolution Analysis
SIAM News, 6 (1745):
[6] Nonstationary subdivision schemes and multiresolution analysis
Cohen, A
Dyn, N
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1996, 27 (06) : 1745 - 1769
[7] Tuning subdivision by minimising Gaussian curvature variation near extraordinary vertices
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COMPUTER GRAPHICS FORUM, 2006, 25 (03) : 263 - 272
[8] Analysis and Convergence of Hermite Subdivision Schemes
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FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2023, 23 (01) : 165 - 218
[9] Analysis and Convergence of Hermite Subdivision Schemes
Bin Han
Foundations of Computational Mathematics, 2023, 23 : 165 - 218
[10] Convergence analysis of Hermite subdivision schemes of any arity
Zhang, Zeze
Zheng, Hongchan
Zhou, Jie
APPLIED NUMERICAL MATHEMATICS, 2023, 183 : 279 - 300

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