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Logarithmic Curvature and Torsion Graphs

  • Conference paper
Mathematical Methods for Curves and Surfaces (MMCS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5862))

Abstract

This paper introduces logarithmic curvature and torsion graphs for analyzing planar and space curves. We present a method for drawing these graphs from any differentiable parametric curves and clarify the characteristics of these graphs. We show several examples of theses graphs drawn from planar and 3D Bézier curves. From the graphs, we can see some interesting properties of curves that cannot be derived from the curvature or torsion plots.

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References

  1. Farin, G.: Curves and Surfaces for CAGD, 5th edn. Morgan Kaufmann Publishers, San Francisco (2002)

    Google Scholar 

  2. Farin, G.: Class A Bézier curves. Computer Aided Geometric Design 23(7), 573–581 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Farouki, R.T., Moon, H.P., Ravani, B.: Algorithms for Mikowski products and implicitly-defined complex sets. Advances in Computational Mathematics 13(3), 199–229 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fukuda, R., Yoshida, N., Saito, T.: Interactive Control of 3D Class-A Bezier Curves, SIGGRAPH ASIA, Sketches (2008)

    Google Scholar 

  5. Gray, A., Abbena, E., Salamon, S.: Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd edn. Chapman & Hall, Boca Raton (2006)

    MATH  Google Scholar 

  6. Harada, T.: Study of Quantitative Analysis of the Characteristics of a Curve. FORMA 12(1), 55–63 (1997)

    Google Scholar 

  7. Harada, T., Yoshimoto, F., Moriyama, M.: An aesthetic curve in the field of industrial Design. In: Proceedings of IEEE Symposium on Visual Languages, pp. 38–47 (1999)

    Google Scholar 

  8. Klass, R.: Correction of local surface irregularities using reflection lines. Computer Aided Design 12(2), 73–77 (1980)

    Article  Google Scholar 

  9. Miura, K.T.: A general equation of aesthetic curves and its self-affinity. Computer-Aided Design and Applications 3(1-4), 457–464 (2006)

    Article  Google Scholar 

  10. Poeschl, T.: Detecting surface irregularities using isophotes. Computer Aided Geometric Design 1(2), 163–168 (1984)

    Article  MATH  Google Scholar 

  11. Yoshida, N., Saito, T.: Interactive Aesthetic Curve Segments: The Visual Computer (Proc. of Pacific Graphics) 22(9-11), 896–905 (2006)

    Google Scholar 

  12. Yoshida, N., Saito, T.: Quasi-Aesthetic Curves in Rational Cubic Bézier Forms. Computer-Aided Design and Applications 4(1-4), 477–486 (2007)

    Article  Google Scholar 

  13. Yoshida, N., Hiraiwa, T., Saito, T.: Interactive Control of Planar Class A Bézier Curves using Logarithmic Curvature Graphs. Computer-Aided Design and Applications 5(1-4), 121–130 (2008)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Nihon University, Chiba, 275-8575, Japan

    Norimasa Yoshida & Ryo Fukuda

  2. Tokyo University of Agriculture and Technology, Tokyo, 185-8588, Japan

    Takafumi Saito

Authors
  1. Norimasa Yoshida
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  2. Ryo Fukuda
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  3. Takafumi Saito
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Oslo, Norway

    Morten Dæhlen  & Tom Lyche  & 

  2. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Norway

    Michael Floater

  3. INSA de Rennes, Rennes, France

    Jean-Louis Merrien

  4. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Oslo, Norway

    Knut Mørken

  5. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA

    Larry L. Schumaker

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© 2010 Springer-Verlag Berlin Heidelberg

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Yoshida, N., Fukuda, R., Saito, T. (2010). Logarithmic Curvature and Torsion Graphs. In: Dæhlen, M., Floater, M., Lyche, T., Merrien, JL., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2008. Lecture Notes in Computer Science, vol 5862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11620-9_28

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  • DOI: https://doi.org/10.1007/978-3-642-11620-9_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11619-3

  • Online ISBN: 978-3-642-11620-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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