Visibility Graphs and Motion Planning Kittiphan Techakittiroj for

Visibility Graphs and Motion Planning Kittiphan Techakittiroj for the Degree of Master of Science Department of Computer Science, Ball State University, IN, USA Committee: Prof. Jay S. Bagga Prof. Clinton P. Fuelling Prof. J. Michael Mc. Grew Contributions: Theory and Implementation Presentation Outline: • Graph Theory • Visibility Graph • Motion Planning & Application

Graph Theory • Graph: vertices + edges • Path • Tree

Creation & Search Creation: • Complete Graph • Convex Hull • Simple Polygon from Points Search: • Breadth First Search • Depth First Search

Minimum Distance • Minimum Distance Spanning Tree • Single Source Shortest Path • Eccentricity of a Graph • Radius and Diameter of a Graph

Geometry • Polygon • Obstacle • Path

Visibility Graph • Visibility Edge • Visibility Graph • Segment Endpoint Visibility Graph • Polygon Visibility Graph

Advance Visibility Graph • • • Condensed Graph Contracted Graph Invisibility Edge Invisibility Graph Degree of Invisibility (Edge) • Degree of Invisibility (Vertex)

Motion Planning is to find the best path for moving a point among a set of obstacle. Process of Planning • Finding visibility graphs as a set of paths. • Applying geometric or graph algorithms.

Applications Computer networks: A good place (by distance) for a server Weakest points in the network Shortest path of connecting two machines Spanning length of a network Consultant: Cost estimation of wiring system Building design: One factor of a good place to put a light One factor of a weak place to get in Medical treatment: Amplitude of X-ray Mobile robot: Shortest path for movement Traveling: Shortest path for traveling