Aproximation of Curves

B. Zatko (Ústav teorie riadenia a robotiky SAV, Bratislava)

Abstract:

A topological approach to approximation of planar curves is described. The approximation is built on the basic notions of intrinsic geometry of metric spaces: on the notion of a shortest path in a polygonally bounded compact set and on the notion of a geodesic diameter of a polygon. Geometric properties of the shortest path in a polgonally bounded compact set are summarized and the most effective algorithm for the shortest path problem solution in a polygonally bounded compact set is described. The approximation of planar Jordan curves and arcs has found applications in computer aided geometric design, computer graphics and line drawing image processing. Examples of approximation of planar Jordan curves and arcs in implicit forms are presented.