Total Curvature and Spiralling Shortest Paths
نویسندگان
چکیده
منابع مشابه
Total Curvature and Spiralling Shortest Paths
This paper gives a partial confirmation of a conjecture of Agarwal, Har-Peled, Sharir, and Varadarajan that the total curvature of a shortest path on the boundary of a convex polyhedron in R3 cannot be arbitrarily large. It is shown here that the conjecture holds for a class of polytopes for which the ratio of the radii of the circumscribed and inscribed ball is bounded. On the other hand, an e...
متن کاملShortest paths between shortest paths
We study the following problem on recon guring shortest paths in graphs: Given two shortest st paths, what is the minimum number of steps required to transform one into the other, where each intermediate path must also be a shortest s-t path and must di er from the previous one by only one vertex. We prove that the shortest recon guration sequence can be exponential in the size of the graph and...
متن کاملBounded-Curvature Shortest Paths through a Sequence of Points
We consider the problem of computing shortest paths, whose curvature is constrained to beat most one almost everywhere, and that visit a sequence of n points in the plane in a givenorder. This problem arises naturally in path planning for point car-like robots in the presenceof polygonal obstacles, and is also a sub-problem of the Dubins Traveling Salesman Problem.We show that, ...
متن کاملShortest Paths of Bounded Curvature for the Dubins Interval Problem
The Dubins interval problem aims to find the shortest path of bounded curvature between two targets such that the departure angle from the first target and the arrival angle at the second target are constrained to two respective intervals. We propose a new and a simple algorithm to this problem based on the minimum principle of Pontryagin.
متن کاملCurvature-Constrained Shortest Paths in a Convex Polygon
Let B be a point robot moving in the plane, whose path is constrained to have curvature at most 1, and let P be a convex polygon with n vertices. We study the collision-free, optimal path-planning problem forB moving between two configurations insideP (a configuration specifies both a location and a direction of travel). We present an O(n2 log n) time algorithm for determining whether a collisi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Computational Geometry
سال: 2003
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-003-0001-z