Approximating Complex Surfaces by Triangulation of Contour Lines

Abstract

An algorithm is described for obtaining an optimal approximation, using triangulation, of a three-dimensional surface defined by randomly distributed points along contour lines. The combinatorial problem of finding the best arrangement of triangles is treated by assuming an adequate objective function. The optimal triangulation is found using classical methods of graph theory. An illustrative example gives the procedure for triangulation of contour lines of a human head for use in radiation therapy planning.