A contouring program based on dual kriging interpolation

Abstract

For contouring very large data sets, such as those arising from 3-D finite element computations, for instance, or in numerical cartography, a computer program based on dual kriging interpolation was developed at École Polytechnique for the Castor project (a multidisciplinary research and development work in computational software for hydroelectric projects). The dual kriging technique presented here simplifies considerably the handling of interpolated data and is especially useful for 3-D applications. It also containsspline interpolation as a particular case and theleast squares method as a limit case. In order to minimize the computational effort, several original features have been incorporated in this program: (1) the concept ofdistance of influence was introduced to allow the algorithm, when evaluating the interpolation value at a given location, to discard data points that are situated too far apart; (2)arbitrary geometric domains are decomposed into simpler regions, inside which the requested contours are drawn directly by scanning vertical slices from left to right, instead of building each contour line sequentially as in direct contouring; (3) contour lines may also be stored in arandom access database (this last feature was added to enable the automatic assembly of isovalue surfaces in 3-D applications such as stress analysis); and (4) contours can be smoothed by interpolating separately the sequences ofX andY coordinates for each contour line. This process, calledparametric kriging, permits the efficient compression of the number of data points necessary to record contours.