On Rectilinear Link Distance
نویسنده
چکیده
Given a simple polygon P without holes all of whose edges are axis-parallel, a rectilinear path in P is a path that consists of axis-parallel segments only and does not cross any edge of P. The length of such a path is defined as the number of segments it consists of and the rectilinear link distance between two points in P is defined as the length of the shortest path connecting the two points. We devise a data structure usiag O(nlogn) storage such that given any two query points 8 and t in P, we can efficiently compute a shortest path from 8 to t. For the case where both query points are vertices of P the query time is 0(1 + I), where 1 is the length of a shortest path. If the query points are arbitrary points inside P then the query time becomes o (log n + I). The path that is found is not only optimal in the rectilinear link metric, it is shown to be optimal in the LI-metric as well. As a second problem we compute the diameter of a rectilinear polygon P. The diameter of P is the maximum distance between any two points in P. It is shown that the exact diameter can be computed in time O( n log n) and an approximation with an error of at most three in O( n) time.
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ورودعنوان ژورنال:
- Comput. Geom.
دوره 1 شماره
صفحات -
تاریخ انتشار 1991