Presentation on theme: "Planar Convex Hull 2013 / 5 / 9 Group 4 Sungheon Park Jeongho Son CS504 Presentation [CS504 Presentation]"— Presentation transcript:
Planar Convex Hull 2013 / 5 / 9 Group 4 Sungheon Park Jeongho Son CS504 Presentation [CS504 Presentation]
Contents CS504 Presentation Definition of convex hull Bruteforce algorithm Graham’s scan Divide and conquer Quickhull Jarvis’ method
What is convex hull? CS504 Presentation Let S be a set of points in the plane. Intuition: Imagine the points of S as being pegs; the convex hull of S is the shape of a rubber-band stretched around the pegs.
Chan’s Algorithm CS504 Presentation Stage 2 (After Stage 1) m = 8 r = 4
Chan’s Algorithm CS504 Presentation Stage 2 Using Graham’s Scan
Chan’s Algorithm CS504 Presentation Stage3 : Jarvis’s March How to merge these r hulls into a single hull? IDEA : treat each hull as a “fat point” and run Jarvis’s March! # of iteration is at most m –to guarantee the time complexity O(nlogh)
Summary CS504 Presentation Finding the convex hull of a set of points is an important problem that is often part of a larger problem Many different algorithms –Graham’s Scan –Quickhull –Divide-and-Conquer –Jarvis’s March –Chan’s algorithm