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

41 Citations (Scopus)

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
LanguageEnglish
Title of host publicationProceedings of IEEE Visualization 2001
EditorsT. Ertl, K. Joy, A. Varshney
Place of PublicationNew York
PublisherIEEE
Pages341-347
Number of pages7
Volume571
ISBN (Print)078037200X
Publication statusPublished - 2001

Publication series

NameIEEE conference on visualisation
PublisherIEEE
ISSN (Print)1070-2385

Fingerprint

Splines
Least squares approximations
Triangulation
Linear systems
Polynomials

Keywords

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

Cite this

Haber, J., Zeilfelder, F., Davydov, O., & Seidel, H-P. (2001). Smooth approximation and rendering of large scattered data sets. In T. Ertl, K. Joy, & A. Varshney (Eds.), Proceedings of IEEE Visualization 2001 (Vol. 571, pp. 341-347). (IEEE conference on visualisation ). New York: IEEE.
Haber, Jorg ; Zeilfelder, Frank ; Davydov, Oleg ; Seidel, Hans-Peter. / Smooth approximation and rendering of large scattered data sets. Proceedings of IEEE Visualization 2001. editor / T. Ertl ; K. Joy ; A. Varshney. Vol. 571 New York : IEEE, 2001. pp. 341-347 (IEEE conference on visualisation ).
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Haber, J, Zeilfelder, F, Davydov, O & Seidel, H-P 2001, Smooth approximation and rendering of large scattered data sets. in T Ertl, K Joy & A Varshney (eds), Proceedings of IEEE Visualization 2001. vol. 571, IEEE conference on visualisation , IEEE, New York, pp. 341-347.

Smooth approximation and rendering of large scattered data sets. / Haber, Jorg; Zeilfelder, Frank; Davydov, Oleg; Seidel, Hans-Peter.

Proceedings of IEEE Visualization 2001. ed. / T. Ertl; K. Joy; A. Varshney. Vol. 571 New York : IEEE, 2001. p. 341-347 (IEEE conference on visualisation ).

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

TY - GEN

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N2 - 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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Haber J, Zeilfelder F, Davydov O, Seidel H-P. Smooth approximation and rendering of large scattered data sets. In Ertl T, Joy K, Varshney A, editors, Proceedings of IEEE Visualization 2001. Vol. 571. New York: IEEE. 2001. p. 341-347. (IEEE conference on visualisation ).