Time: 14h15, Thursday, March 31, 2016
Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract:

The talk includes the following parts:
Part 1: Introduction
1.1 Computing geometric shortest paths and related problems
1.2 An exact method for computational geometry: the method of orienting curves (MOC)
1.3 An approximate method for computational geometry: the method
of multiple shooting (MMS)

Part 2: Overview: Convexity and Geometric Shortest Path Problem
2.1 Convex sets
2.2 Relations between convexity and geometric shortest path problem

Part 3: Geodesic Convex Sets in Simple Polygons in 2D
3.1 Geodesic convex sets and geodesic convex hulls
3.2 Some computational aspects of geodesic convex sets and convex hulls
3.3 Blaschke-type theorem for geodesic convex sets

Part 4: Convex Hull of a Finite Set of Points
4.1 MOC for computing the convex hull of a finite planar point set
4.2 Restricted area technique for 3D convex hulls
4.3 Restricted area technique for Delaunay triangulation

Part 5: Exact Solution for Minimizing a Sum of Euclidean Norms

Part 6:  Exact Shortest Paths along a Sequence of Triangles in 3D

Part 7: Approximate Shortest Paths in Some Closed Regions
7.1 Approximate shortest paths in simple polygons
7.2 Approximate shortest paths on convex polytopes
7.3 Approximate shortest descending paths on convex terrains