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Quantifying the effect of a control point on the sign of curvature

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Abstract

We present a method for computing the domain, where a control point is free to move so that the corresponding planar curve is regular and of constant sign of curvature along a subinterval of its parametric domain of definition. The approach encompasses all curve representations that adopt the control-point paradigm and is illustrated for a quintic Bézier curve and a B-spline curve of degree 10.

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References

  • J. W. Bruce P. J. Giblin (1988) Curves and singularities Cambridge University Press Cambridge Occurrence Handle0664.58001

    MATH  Google Scholar 

  • A. R. Forrest (1980) ArticleTitleThe twisted cubic curve: a computer-aided geometric design approach CAD 12 IssueID4 165–172

    Google Scholar 

  • I. Juhász (2006) ArticleTitleOn the singularity of a class of parametric curves CAGD 23 146–156 Occurrence Handle1083.65012

    MATH  Google Scholar 

  • Y.-M. Li R. J. Cripps (1997) ArticleTitleIdentification of inflection points and cusps on rational curves CAGD 14 491–497 Occurrence Handle0896.65014 Occurrence Handle1456016

    MATH  MathSciNet  Google Scholar 

  • D. Manocha J. F. Canny (1992) ArticleTitleDetecting cusps and inflection points in curves CAGD 9 1–24 Occurrence Handle0757.65012 Occurrence Handle1166698

    MATH  MathSciNet  Google Scholar 

  • J. Monterde (2001) ArticleTitleSingularities of rational Bézier curves CAGD 18 805–816 Occurrence Handle0983.68223 Occurrence Handle1857999

    MATH  MathSciNet  Google Scholar 

  • A. Pogorelov (1987) Geometry MIR Publishers Moscow

    Google Scholar 

  • Pottmann, H., DeRose, T. D.: Classicication using normal curves. In: SPIE: Curves and Surfaces in Computer Vision and Graphics, vol. II, 1610, 217–227 (1991).

  • M. Sakai (1999) ArticleTitleInflection points and singularities on planar rational cubic curve segments CAGD 16 149–156 Occurrence Handle0914.68195

    MATH  Google Scholar 

  • M. C. Stone T. D. DeRose (1989) ArticleTitleA geometric characterization of cubic curves ACM Trans. Graph. 8 IssueID3 143–163 Occurrence Handle10.1145/77055.77056

    Article  Google Scholar 

  • Q. Yang G. Wang (2004) ArticleTitleInflection points and singularities on C-curves CAGD 21 207–213 Occurrence Handle1069.65539

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Naval Architecture and Marine Engineering, National Technical University of Athens, Zografou Campus, Iroon Polyterneiou 9, 15780, Zografou, Greece

    E. I. Karousos, A. I. Ginnis & P. D. Kaklis

Authors
  1. E. I. Karousos
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  2. A. I. Ginnis
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  3. P. D. Kaklis
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Correspondence to P. D. Kaklis.

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Karousos, E.I., Ginnis, A.I. & Kaklis, P.D. Quantifying the effect of a control point on the sign of curvature. Computing 79, 249–259 (2007). https://doi.org/10.1007/s00607-006-0202-2

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  • DOI: https://doi.org/10.1007/s00607-006-0202-2

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