Interpolating a Topographical Map of the Ocean Floor
Given the depth of 14 arbitrary points in a rectangular region of the ocean. our team created detailed three-dimensional and two-dimensional grid and contour maps that clearly highlighted dangerous shallows. Because the ocean floor was assumed to be smooth and without cliffs, the team chose to use a smooth surface fitting bicubic spline method to interpolate the given data. However, the team needed to first create an irregularly spaced 14 × 14 grid in the x−y plane with one grid line passing through each of the data points. The unknown points on the grid were approximated using an inverse-distance-squared scheme with factors that accounted not only for the depths of given data points, but also for trends in the change of depths between any two original data points. Once all the irregular grid points were known, either by approximation or from the original data, the team ran an IMSL bicubic spline subroutine to generate a regularly spaced, fine mesh grid of interpolated depths, which were then plotted with the aid of a Mathlib graphics program.
© 1986 Published by Elsevier B.V.
David Ho, Kurt Overley, Lee Short, H.A. Krieger, Interpolating a topographical map of the ocean floor, Mathematical Modelling, Volume 7, Issue 4, 1986, Pages 561-576, ISSN 0270-0255, http://dx.doi.org/10.1016/0270-0255(86)90034-5. (http://www.sciencedirect.com/science/article/pii/0270025586900345)