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Smooth Approximation and Rendering of Large Scattered Data Sets

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From Nano to Space

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Abstract

We present an efficient method to automatically compute a smooth approximation of large functional scattered data sets given over arbitrarily shaped planar domains. Our approach is based on the construction of a C 1-continuous bivariate cubic spline and our method offers optimal approximation order. Both local variation and non-uniform distribution of the data are taken into account by using local polynomial least squares approximations of varying degree. Since we only need to solve small linear systems and no triangulation of the scattered data points is required, the overall complexity of the algorithm is linear in the total number of points. Numerical examples dealing with several real world scattered data sets with up to millions of points demonstrate the efficiency of our method. The resulting spline surface is of high visual quality and can be efficiently evaluated for rendering and modeling. In our implementation we achieve real-time frame rates for typical fly-through sequences and interactive frame rates for recomputing and rendering a locally modified spline surface.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Jörg Haber, Frank Zeilfelder & Hans-Peter Seidel

  2. Justus-Liebig-Universität Giessen, Germany

    Oleg Davydov

Authors
  1. Jörg Haber
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  2. Frank Zeilfelder
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  3. Oleg Davydov
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  4. Hans-Peter Seidel
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Editor information

Editors and Affiliations

  1. Institut für Wirtschaftsinformatik, Leibniz Universität Hannover, Königsworther Platz 1, 30167, Hannover, Germany

    Michael H. Breitner

  2. Products, Qimonda AG, 81726, München, Germany

    Georg Denk

  3. M2 — Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Peter Rentrop

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Haber, J., Zeilfelder, F., Davydov, O., Seidel, HP. (2008). Smooth Approximation and Rendering of Large Scattered Data Sets. In: Breitner, M.H., Denk, G., Rentrop, P. (eds) From Nano to Space. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74238-8_11

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