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Quartic Spline Approximation of a Circle by Piecewise Bézier Curves with High Smoothness and Accuracy

Published: 22 October 2018 Publication History

Abstract

In this paper1, by piecewise Bézier curves we construct G4 quartic spline approximations of a circle which converge with order eight.

References

[1]
T. Dokken, M. Dæhlen, T. Lyche, and K. Mørken. 1990. Good approximation of circles by curvature-continuous Bézier curves. Computer Aided Geometric Design, 7 (1990), 33--41.
[2]
C. Apprich, A. Dieterich, K. Höllig, and E. Nava-Yazdani. 2017. Cubic spline approximation of a circle with maximal smoothness and accuracy. Computer Aided Geometric Design, 56 (2017), 1--3.
[3]
M. Goldapp. 1991. Approximation of circular arcs by cubic polynomials. Computer Aided Geometric Design, 8, 3 (1991), 227--238.
[4]
Seok Hur, and Tae-wan Kim. 2011. The best G1 cubic and G2 quartic Bézier approximations of circular arcs. Journal of Computational and Applied Mathematics, 236, (2011), 1183--1192.
[5]
Kovač, Boštjan, and Žagar, Emil. 2016. Curvature approximation of circular arcs by low-degree parametric polynomials. Journal of Numerical Mathematic, 24, 2 (2016), 95--104.
[6]
S.H. Kim, and Y.J. Ahn. 2007. An approximation of circular arcs by quartic Bézier curves. Computer- Aided Design, 39, 6(2007), 490--493.
[7]
F. Ghomanjani, and M. H. Farahi, M. 2014. Gachpazan, Optimal control of time-varying linear delay systems based on the Bezier curves. Comp. Appl. Math, 33, 3(2014), 687--715.

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  1. Quartic Spline Approximation of a Circle by Piecewise Bézier Curves with High Smoothness and Accuracy

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      cover image ACM Other conferences
      CSAE '18: Proceedings of the 2nd International Conference on Computer Science and Application Engineering
      October 2018
      1083 pages
      ISBN:9781450365123
      DOI:10.1145/3207677
      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      Published: 22 October 2018

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      Author Tags

      1. Bezier curve
      2. approximation order
      3. geometric smoothness
      4. quartic spline

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      • Research-article
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      • Refereed limited

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      CSAE '18

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      CSAE '18 Paper Acceptance Rate 189 of 383 submissions, 49%;
      Overall Acceptance Rate 368 of 770 submissions, 48%

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