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Polygonizing Implicit Surfaces in a Purely Functional Way

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Implementation of Functional Languages (IFL 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2011))

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Abstract

Implicit surfaces are defined by a real valued function. They can easily be defined and manipulated and have therefore gained great popularity in computer graphics. This paper presents a purely functional implementation of a well known algorithm to polygonize implicit surfaces, based on spatial partitioning by means of octrees. While conventional implementations are laden with practical issues, our implementation in Clean is straightforward, implements the algorithm very concisely and makes essential use of lazy evaluation.

Further we present two enhancements to this basic algorithm: Introducing a memo function greatly improves time efficiency. The appearance of a visualized implicit surface can be greatly enhanced by providing normal vector information. For calculating normal vectors we adopt a lazy implementation of automatic differentiation.

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Author information

Authors and Affiliations

  1. Computing Science Institute, University of Nijmegen, The Netherlands

    Thorsten H.-G. Zörner, Pieter Koopman, Marko van Eekelen & Rinus Plasmeijer

Authors
  1. Thorsten H.-G. Zörner
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  2. Pieter Koopman
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  3. Marko van Eekelen
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  4. Rinus Plasmeijer
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Informatik II, RWTH Aachen, Ahornstr. 55, 52056, Aachen, Germany

    Markus Mohnen

  2. KUN Nijmegen, Toernooiveld 1, 6525, ED Nijmegen, The Netherlands

    Pieter Koopman

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© 2001 Springer-Verlag Berlin Heidelberg

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Zörner, T.HG., Koopman, P., van Eekelen, M., Plasmeijer, R. (2001). Polygonizing Implicit Surfaces in a Purely Functional Way. In: Mohnen, M., Koopman, P. (eds) Implementation of Functional Languages. IFL 2000. Lecture Notes in Computer Science, vol 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45361-X_10

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  • DOI: https://doi.org/10.1007/3-540-45361-X_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41919-8

  • Online ISBN: 978-3-540-45361-1

  • eBook Packages: Springer Book Archive

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