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Estimation of a surface with known discontinuities for automatic contouring purposes

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Abstract

As an aid to automatic contouring, a method has been designed to estimate a surface with known discontinuities. Through a primary estimation process the surface is assumed to be known at the nodes of a regular grid. These known values are termed data points. A distance rEI is defined between a known data point I, and any given point E to be estimated. This distance is increased, as explained, by a “penalty” if one discontinuity (or more) is found in between these points. At each data point I the tangential quadric to the surface is computed, using the data points K in a neighborhood of I, which will be defined. The value at E is then a linear combination of these tangential quadrics in the neighborhood of E. For this combination, a weighting pEI is used, related as a decreasing function of rEI. The underlying assumptions of the method are given, together with the way to compute quadrics and the properties of the weights pEI. An application package has been written in FORTRAN and two examples are given in this paper.

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Pouzet, J. Estimation of a surface with known discontinuities for automatic contouring purposes. Mathematical Geology 12, 559–575 (1980). https://doi.org/10.1007/BF01034744

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  • DOI: https://doi.org/10.1007/BF01034744

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