Smooth approximation and rendering of large scattered data sets

Jorg Haber, Frank Zeilfelder, Oleg Davydov, Hans-Peter Seidel

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

43 Citations (Scopus)


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
Original languageEnglish
Title of host publicationProceedings of IEEE Visualization 2001
EditorsT. Ertl, K. Joy, A. Varshney
Place of PublicationNew York
Number of pages7
ISBN (Print)078037200X
Publication statusPublished - 2001

Publication series

NameIEEE conference on visualisation
ISSN (Print)1070-2385


  • scattered data approximation
  • least squares approximation
  • terrain visualization
  • data compression

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