Convex Hull of the Union of Convex Objects in the Plane: an Adaptive Analysis

We prove a tight asymptotic bound of ( log(n/)) on the worst case computational complexity of the convex hull of the union of two convex objects of sizes summing to n requiring orientation tests to certify the answer. Our algorithm is deterministic, it uses portions of the convex hull of input objects to describe the final convex hull, and it takes advantage of easy instances, such as those where large parts of two objects are horizontally or vertically separated.

• Type: Conference
• Year: 2008
• Where: CCCG
• Authors: Jérémy Barbay, Eric Y. Chen
• Keywords: CCCG 2008, Computational Geometry, Convex Hull, Convex Objects, Final Convex Hull