A New Class of Trigonometric B-Spline Curves

被引：2

作者：

Albrecht, Gudrun ^{[1
]}

Mainar, Esmeralda ^{[2
]}

Pena, Juan Manuel ^{[2
]}

Rubio, Beatriz ^{[2
]}

机构：

[1] Univ Nacl Colombia, Sch Math, Medellin Campus, Medellin 4309511, Colombia

[2] Univ Zaragoza, Dept Appl Math, Univ Res Inst Math & Its Applicat IUMA, Zaragoza 50009, Spain

来源：

SYMMETRY-BASEL | 2023年 / 15卷 / 08期

关键词：

trigonometric curves; B-splines; B-basis; total positivity;

D O I：

10.3390/sym15081551

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We construct one-frequency trigonometric spline curves with a de Boor-like algorithm for evaluation and analyze their shape-preserving properties. The convergence to quadratic B-spline curves is also analyzed. A fundamental tool is the concept of the normalized B-basis, which has optimal shape-preserving properties and good symmetric properties.

引用

页数：22

共 38 条

[1] Spatial Pythagorean-Hodograph B-Spline curves and 3D point data interpolation [J].

Albrecht, Gudrun ;

Beccari, Carolina Vittoria ;

Romani, Lucia .

COMPUTER AIDED GEOMETRIC DESIGN, 2020, 80

[2] Planar Pythagorean-Hodograph B-Spline curves [J].

Albrecht, Gudrun ;

Vittoria Beccari, Carolina ;

Canonne, Jean-Charles ;

Romani, Lucia .

COMPUTER AIDED GEOMETRIC DESIGN, 2017, 57 :57-77

[3]

Alfeld P, 1995, MATHEMATICAL METHODS FOR CURVES AND SURFACES, P11

[4]

[Anonymous], 1993, Fundamentals of Computer Aided Geometric Design

[5] A Novel Approach of Hybrid Trigonometric Bezier Curve to the Modeling of Symmetric Revolutionary Curves and Symmetric Rotation Surfaces [J].

Bibi, Samia ;

Abbas, Muhammad ;

Misro, Md Yushalify ;

Hu, Gang .

IEEE ACCESS, 2019, 7 :165779-165792

[6] TOTALLY POSITIVE BASES FOR SHAPE-PRESERVING CURVE DESIGN AND OPTIMALITY OF B-SPLINES [J].

CARNICER, JM ;

PENA, JM .

COMPUTER AIDED GEOMETRIC DESIGN, 1994, 11 (06) :633-654

[7]

Farin G., 1997, CURVES SURFACES COMP

[8] Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form [J].

Farouki, Rida T. ;

Giannelli, Carlotta ;

Sestini, Alessandra .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2016, 42 (01) :199-225

[9] Identification and "reverse engineering" of Pythagorean-hodograph curves [J].

Farouki, Rida T. ;

Giannelli, Carlotta ;

Sestini, Alessandra .

COMPUTER AIDED GEOMETRIC DESIGN, 2015, 34 :21-36

[10] THE CONFORMAL-MAP Z-]Z2 OF THE HODOGRAPH PLANE [J].

FAROUKI, RT .

COMPUTER AIDED GEOMETRIC DESIGN, 1994, 11 (04) :363-390

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