## Abstract

We consider the problem of approximating a smooth surface f(x,y), based on n scattered samples {(x_{i}, y_{i}, z_{i})_{i}^{n} = 1} where the sample values {z_{i}} are contaminated with noise: z_{i} = f(x_{i}, y_{i}) + ε_{i}. We present an algorithm that generates a PLS (Piecewise Linear Surface) f′, defined on a triangulation of the sample locations V = {(x_{i}, y_{i})_{i}^{n}=1}, approximating f well. Constructing the PLS involves specifying both the triangulation of V and the values of f′ at the points of V. We demonstrate that even when the sampling process is not noisy, a better approximation for f is obtained using our algorithm, compared to existing methods. This algorithm is useful for DTM (Digital Terrain Map) manipulation by polygon-based graphics engines for visualization applications.

Original language | English (US) |
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Pages (from-to) | 61-68 |

Number of pages | 8 |

Journal | Proceedings Visualization |

State | Published - 1994 |

Externally published | Yes |

Event | Proceedings of the 1994 IEEE Visualization Conference - Washington, DC, USA Duration: Oct 17 1994 → Oct 21 1994 |

## All Science Journal Classification (ASJC) codes

- Engineering(all)