Efficient Approximation of Convex Polygons

We present algorithms for the approximation of a convex n-gon by a convex k-gon (k<n) which inscribes or circumscribes the original polygon. Our algorithms run in O(n+(n-k) log n) time and are easy to implement. Their accuracy, in the sense of area-difference, is analyzed and shown to be of the best order possible for a general algorithm. In particular, this analysis settles a question raised by O'Rourke on the performance of the approximation algorithm of Dori and Ben-Bassat.