Dpt de Math. Rech.

Surface Approximation

from Partial Data

D. Apprato (Pau), C. Gout (INSA Rouen), A. Guessab (Pau), D. Komatitsc (Harvard), P. Sénéchal (UMR 5831, Pau)

Works presented at two International Conference:

  • Journées Pau-Saragosse 1995 (Theory)
  • Seminar UC Berkeley, USA, 1996 (Th. Aspect)
  • Luminy, 1996, Colloque Modélisation
  • Albuquerque, USA 1999, Talk - SIAM Conf. (Num. Ex.-Geometric Design)
  • IEEE IGARSS Hawaii, USA 2000 (Volume processing )

Publications:

  • (data: surface patches) Presentation of the method : CRAS Paris (D.A., C. G.), pp. 445-448, 1997.
  • (data: surface patches) Convergence of the method, error & implementation : Comp. & Math. with Appl. submitted 2000.
  • Algorithm & application to real datasets : Math. Geology 32 (8), pp. 969-983, 2000. (D.A, C.G.,P.S.)
  • (data: bathymetry) Submitted (D.A., C.G.,D.K.) (Ship track data--> application to the bathymetry of the Marianas trench)
  • (data : partial data) Quadrature formulas, work in progress (A. Guessab; A. Draux).

 

Geophysical Data

Postcript files 3D blocks from Vallée d'Ossau, Pyrénées, France.

FIGURE 6 : Mathematical Geology 32 (8), pp. 969-983, 2000.
Initial raw data file without deleted patch (top) and approximant (bottom)
In this example, from the initial data file, a big patch has been deleted, and one can see that the obtained approximant is excellent.
Postcript files : 2D view of raw data and 2D view of raw data with deleted patch

 

FIGURE 8 : Mathematical Geology 32 (8), pp. 969-983, 2000.
Raw data file (top) and reconstructed surface.
Postcript file of 2D data view

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