AUTOMATIC CONTOURING USING BICUBIC FUNCTIONS

A method is described for using a digital computer to construct contour maps automatically. Contour lines produced by this method have correct relations to given discrete data points regardless of the spatial distribution of these points. The computer-generated maps are comparable to those drawn manually. The region to be contoured is divided into quadrilaterals whose vertices include the data points. After supplying values at each of the remaining vertices by using a surface-fitting technique, bicubic functions are constructed on each quadrilateral to form a smooth surface through the data points. Points on a contour line are obtained from these surfaces by solving the resulting cubic equations. The bicubic functions may be used for other calculations consistent with the contour maps, such as interpolation of equally spaced values, calculation of cross-sections, and volume calculations. © 1972 Society of Exploration Geophysicists.