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A SMALL SAMPLE of CONTOUR SMOOTHING

The pair of images on the left are intended to show how our smoothing (bottom) disguises the sharp breaks in the contours (top), thus preventing the recognition of the underlying TIN structure. As a great mathematician once observed, after a structure is completed, one should no longer be able to see the scaffolding (Carl Friederich Gauss: Titan of Science, by G. W. Dunnington, Exposition Press, N. York, 1985) An unsmooth set of contours would have a very unappealing appearance and thus be only marginally interpretable (from Creation of Smooth Contours over Irregularly Distributed Data Using Local Surface Parches, by M. J. McCullagh, Geographic Analysis, 1981)
Broadly, there are three approaches to contour smoothing. The most popular and least reliable is the contour-by-contour interpolation of smooth curves. It may lead to curves crossing each other as well as curves crossing TIN edges on the wrong side. If the interpolation is more complex, under tight conditions the interpolated curves could develop wavelike patterns. The second method consists of the application of three-dimensional patches to the TIN with complex conditions along the TIN edges. The third method, which we call Eclectic Procedure, takes a little from those two approaches. Its effectiveness depends of the size of the TIN elements: the bigger they are, the smoother the results. The bottom figure on the left is a small sample of our work. You can see more on contour crossings, smoothing, and wavelike patterns in the NEXT pages.

A small TIN with smoothed contours