### Abstract

Language | English |
---|---|

Title of host publication | Proceedings of IEEE Visualization 2001 |

Editors | T. Ertl, K. Joy, A. Varshney |

Place of Publication | New York |

Publisher | IEEE |

Pages | 341-347 |

Number of pages | 7 |

Volume | 571 |

ISBN (Print) | 078037200X |

Publication status | Published - 2001 |

### Publication series

Name | IEEE conference on visualisation |
---|---|

Publisher | IEEE |

ISSN (Print) | 1070-2385 |

### Fingerprint

### Keywords

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

### Cite this

*Proceedings of IEEE Visualization 2001*(Vol. 571, pp. 341-347). (IEEE conference on visualisation ). New York: IEEE.

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - Smooth approximation and rendering of large scattered data sets

AU - Haber, Jorg

AU - Zeilfelder, Frank

AU - Davydov, Oleg

AU - Seidel, Hans-Peter

PY - 2001

Y1 - 2001

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

AB - 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

KW - scattered data approximation

KW - least squares approximation

KW - terrain visualization

KW - data compression

M3 - Conference contribution book

SN - 078037200X

VL - 571

T3 - IEEE conference on visualisation

SP - 341

EP - 347

BT - Proceedings of IEEE Visualization 2001

A2 - Ertl, T.

A2 - Joy, K.

A2 - Varshney, A.

PB - IEEE

CY - New York

ER -