Algorithms for triangulation of a discrete frame of points based on cluster analysis

This article discusses the issues of restoring a surface from its discrete values in a certain area. Way in TS (topographic surface) modeling is the way of function restoration according to its discrete values in some field, more exactly, according to values obtained straightly as a result of geodesic measurement. Traditional approach is to seek a suitable surface, that may be stretched over the stated frame-work of points with the next definition of its peculiarities and structural lines. Moreover, regularization stage of chaotic set of initial data (ID) often precedes the stage of function restoration, although the task of regularization itself is complicated enough. Nowadays, two basic approaches exist to decide the task of function. Restoration on the stated chaotic set of its initial data (ID): 1) spline function construction, that will allow with the help of single equation to describe the surface, plane and differentiated enough; 2) surface construction, that represents the whole complex of joined final elements (FE). The article proposes a new approach to the restoration of the topographic surface, in which the most characteristic lines are first determined (watershed, thalweg, ravine, etc.).

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