Shortest Paths in Euclidean spaces
Sanjiv Kapoor (IIT Delhi)
The Shortest Path problem in Euclidean domains is an important
problem for terrain navigation and path planning which arise
in Motion Planning. Both 2-dimensional and 3-dimensional Path Planning
problems have been well studied.
This talk will first describe solutions to the shortest path problem in
2-dimensional Euclidean space, populated with polygonal obstacles.
The technique of wavefront propogation will be discussed.
and we will describe solutions to the
geodesic path problem on the surface of a 3-dimensional polyhedron.
The problem, of obvious interest in terrain navigation, had
previously been shown to have complexity O(n2). We
will outline a solution of complexity O(nlog2n).
Extensions of the methodology to the Weighted regions shortest path problem
will also be discussed.