PROJECT PRESENTATION CONVEX HULL PROBLEM Radhika Bibikar CSE

PROJECT PRESENTATION CONVEX HULL PROBLEM Radhika Bibikar CSE 5311 Dr. Gautam Das

INTRODUCTION Convex Hull Smallest enveloping polygon of N different points Algorithms: Graham Scan Jarvis March Divide and Conquer 2

ALGORITHMS Graham’s Scan Complexity – O(n logn) Phases: Select anchor point p 0 Sort by polar angle with respect to p 0 Scan counter clockwise maintaining the stack 3

ALGORITHMS Jarvis March Complexity – O(n logn) Phases: Select lowest and highest points Form right chain with respect to polar angle Form left chain with respect to polar angle to negative x - axis 4

ALGORITHMS Divide and Conquer Complexity – O(n logn) Phases : Sort points with respect to x Divide points in equal subsets and recursively find convex hulls Merge hulls using upper and lower tangents 5

CONVEX HULL APPLICATIONS Applications Computer visualization Visual pattern matching Geographical Information Systems (GIS) Path finding 6

ONION CONVEX HULL A sequence on nested convex hull are called the onionpeeling Applications: Study of Earth atmosphere Network protocols (CDMA) Image Processing Secure Fingerprinting 7

ONION TRIANGULATION Rotating Calipers – linear time algorithm Applications: Fingerprint Identification Motion Planning 8

DEMO 9