Approximating Polygonal Curves in Two and Three Dimensions

Abstract We discuss the weighted minimum number polygonal approximation problem. Eu and Toussaint ( 1994, CVGIP: Graphical Models Image Process. 56 , 231–246) considered this problem subject to the parallel-strip error criterion in R 2 with L q distance metrics, and they concluded that it can be solved in O ( n 2 ) time by using the Cone intersection method. In this note, we clarify part of their discussion and show that solving their problem correctly requires O ( n 2 log n ) time. Also, we discuss the weighted minimum number problem subject to the line segment error criterion. When input curves are strictly monotone in R 3 , we demonstrate that if the L 1 or L ∞ metric is used, this problem also can be solved in O ( n 2 ) time.