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We introduce a surface approximation technique to address the problem of fitting a surface to a given set of curves. The originality of the method lies in its ability to take into account the continuous aspect of the data, and also in the possibility to arbitrarily select the regularity (C0, C1, or higher) of the approximant obtained. We demonstrate the efficiency of the approach by constructing a bathymetry map of the Marianas trench based upon a set of SONAR (SOnic Navigation And Ranging) bathymetry ship track data.