Shortest paths in simple polygons with polygon-meet constraints
نویسندگان
چکیده
We study a constrained version of the shortest path problem in simple polygons, in which the path must visit a given target polygon. We provide a worst-case optimal algorithm for this problem and also present a method to construct a subdivision of the simple polygon to efficiently answer queries to retrieve the shortest polygon-meeting paths from a single-source to the query point. The algorithms are linear, both in time and space, in terms of the complexity of the two polygons. 2004 Published by Elsevier B.V.
منابع مشابه
Single-Point Visibility Constraint Minimum Link Paths in Simple Polygons
We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path. The method is based on partitioning a portion of $P$ into a number of faces of equal link distance from a source point. This partitioning is essentially a shor...
متن کاملShortest Paths in Polygonal Domains with Polygon-Meet Constraints
In this paper, we study the problem of finding the shortest path in a polygonal domain in which the path should meet (touch or cross) a simple polygon in the domain. Our method uses the continuous Dijkstra paradigm and the idea of wavelet reflection and solves the problem in worst-case optimal time O(n log n).
متن کاملComputing the Fréchet distance between simple polygons
We present the first polynomial-time algorithm for computing the Fréchet distance for a non-trivial class of surfaces: simple polygons. For this, we show that it suffices to consider homeomorphisms that map an arbitrary triangulation of one polygon to the other polygon such that diagonals of the triangulation are mapped to shortest paths in the other polygon.
متن کاملOptimal Mesh Algorithms for Proximity and Visibility Problems in Simple Polygons*
We present optimal parallel algorithms that run in O p n time on a p n pn mesh connected computer for a number of fundamental problems concerning proximity and vis ibility in a simple polygon These include computing shortest paths shortest path trees shortest path partitions all farthest neighbors the visibility polygon of a point the weak visibility polygon of an edge and the ray shooting problem
متن کاملOptimal Mesh Computer Algorithms for Simple Polygons
We present optimal parallel algorithms that run in O(p n) time on a p n p n mesh-connected computer for a number of fundamental problems concerning visibility and distance properties inside a simple polygon. These include computing shortest paths, shortest path trees, shortest path partitions, all-farthest neighbors (both internal and external), the visibility polygon of a point, the weak visib...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Inf. Process. Lett.
دوره 91 شماره
صفحات -
تاریخ انتشار 2004