Cartographic line simplification and polygon CSG formulæ in O(nlog * n) time

The cartographers' favorite line simplification algorithm recursively selects from a list of data points those to be used to represent a linear feature, such as a coastline, on a map. A constructive solid geometry (CSG) conversion for a polygon takes a list of vertices and produces a formula representing the polygon as an intersection and union of primitive halfspaces. By using a data structure that supports splitting convex hulls and finding extreme points, both were known to have O(n log n) time solutions in the worst-case. This paper shows that both are easier than sorting by presenting an O(n log*n) algorithm for maintaining convex hulls under splitting at extreme points. It opens the question of whether there is a practical, linear-time solution.