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An Introduction to Guided and Polar Surfacing

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

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

Abstract

This paper gives an overview of two recent techniques for high-quality surface constructions: polar layout and the guided approach. We demonstrate the challenge of high-quality surface construction by examples since the notion of surface quality lacks an overarching theory. A key ingredient of high-quality constructions is a good layout of the surface pieces. Polar layout simplifies design and is natural where a high number of pieces meet. A second ingredient is separation of shape design from surface representation by creating an initial guide shape and leveraging classical approximation-theoretic tools to construct a final surface compatible with industry standards, either as a finite number of polynomial patches or as a subdivision process. An example construction generating guided C 2 surfaces from patches of degree bi-3 highlights the power of the approach.

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Author information

Authors and Affiliations

  1. Department of Computer and Information Science and Engineering, University of Florida, USA

    Jörg Peters

  2. Faculty of Mathematics and Informatics, Vilnius University, Lithuania

    Kȩstutis Karčiauskas

Authors
  1. Jörg Peters
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  2. Kȩstutis Karčiauskas
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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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Peters, J., Karčiauskas, K. (2010). An Introduction to Guided and Polar Surfacing. 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_20

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  • DOI: https://doi.org/10.1007/978-3-642-11620-9_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11619-3

  • Online ISBN: 978-3-642-11620-9

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