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Drawing Curves

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Mathematical Progress in Expressive Image Synthesis III

Part of the book series: Mathematics for Industry ((MFI,volume 24))

Abstract

We propose a method to determine piecewise cubic Bézier curves passing through given points. Our main purpose is to draw accurate graphs of mathematical functions with smaller data. A program drawing such graphs using our method is realized in a computer algebra and outputs the graphs in a source file of TeX and then transforms it into a PDF file. Our method is also useful for numerical calculation of a given area enclosed by a curve and for numerical integration of functions.

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Notes

  1. 1.

    Moreover if the curve is defined outside [a, b], we use the points \(P_{-1}\) and \(P_{N+1}\) to define Bézier curves).

References

  1. T. Oshima, \({\sf os}\)_\(\sf {muldif.rr}\), a library for a computeralgebra Risa/Asir, 2008–2015, ftp://akagi.ms.u-tokyo.ac.jp/pub/math/muldif/

  2. \(\sf Risa/Asir\), an open source general computer algebrasystem, http://www.math.kobe-u.ac.jp/Asir/asir.html

  3. T. Oshima, Fractional calculus of Weyl algebra and Fuchsiandifferential equations, MSJ Memoirs. 28, (Mathematical Society of Japan, 2012), http://projecteuclid.org/euclid.msjm/1413220558

  4. E. Catmull, R. Rom, in A class of local interpolating splines, eds. by R.E. Barnhill, R.F. Reisenfeld, Computer Aided Geometric Design, (Academic Press, New York, 1974), pp. 317–326

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  6. C. Yuksel, S. Schaefer, J. Keyser, Parameterization and applications of Catmull-Rom curves. Comput.-Aided Des. 43, 747–755 (2011)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Josai University, 2-3-20 Hirakawacho, Chiyodaku, Tokyo, 102-0093, Japan

    Toshio Oshima

Authors
  1. Toshio Oshima
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Corresponding author

Correspondence to Toshio Oshima .

Editor information

Editors and Affiliations

  1. Grad. School of Info. Sci. and Tech, Hokkaido University, Sapporo, Hokkaido, Japan

    Yoshinori Dobashi

  2. Kyushu University, Fukuoka, Japan

    Hiroyuki Ochiai

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© 2016 Springer Science+Business Media Singapore

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Oshima, T. (2016). Drawing Curves. In: Dobashi, Y., Ochiai, H. (eds) Mathematical Progress in Expressive Image Synthesis III. Mathematics for Industry, vol 24. Springer, Singapore. https://doi.org/10.1007/978-981-10-1076-7_11

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  • DOI: https://doi.org/10.1007/978-981-10-1076-7_11

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-1075-0

  • Online ISBN: 978-981-10-1076-7

  • eBook Packages: EngineeringEngineering (R0)

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