Smallest paths in simple rectilinear polygons
Webb28 mars 2024 · A minimum link path is a polygonal path between two points s and t inside a simple polygon P with n vertices that has the minimum number of links. Minimum link paths are fundamentally different from traditional Euclidean shortest path, which has the shortest length among all the polygonal paths without crossing edges of P . WebbIt is shown that shortest-path queries can be performed optimally in time O(logh + logn) (plus O(k) time for reporting the k edges of the path) using a data structure with O(n) space and preprocessing time, and that minimum-link- path queries can also be performed in optimal time. Expand 12 PDF Save Alert
Smallest paths in simple rectilinear polygons
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WebbSuch paths have already been studied, e.g. in [4, 9, 14, 15], where shortest rectilinear paths in the LI-metric are sought. Instead, we are interested in shortest rectilinear paths in the link distance metric. We will restrict ourselves in this paper ... Definition 1 Let P be a simple rectilinear polygon. A (rectilinear) path 7r (in P) Webb1 apr. 2024 · We compute shortest paths connecting two axis-aligned rectilinear simple polygons in the domain consisting of axis-aligned rectilinear obstacles in the plane. The …
WebbA rectilinear path is a path composed only of horizontal and vertical line segments. Such paths may be constrained by requiring that they lie only within certain areas. One way of … WebbA classical problem of geometry is the following: given a convex polygon in the plane, find an inscribed polygon of shortest circumference. In this paper we generalize this problem …
WebbGraph algorithms and computational geometry form separate communities with separate conferences such as the International Workshop on Graph-Theoretic Concepts in Computer Science and the ACM Symposium on Computational Geometry, respectively, but they also meet in broader algorithms conferences, and there has been much interplay between the … WebbThe number of rectilinear blocks n is 7, and that of shapes t is 6. The task is to pack these seven items into the rectangular container so as to minimize the height of the container. Figure 1: An instance of the rectilinear block packing problem and a solution We de ne the bounding box of item Ri as the smallest rectangle that encloses Ri, and
Webb1 mars 1999 · In this paper we present optimal sequential and parallel algorithms to compute a minimum rectilinear link path in a trapezoided region R. Our parallel algorithm requires O (log n) time using a...
Webb17 mars 2024 · The geodesic edge center of a polygon is a point c inside the polygon that minimizes the maximum geodesic distance from c to any edge of the polygon, where geodesic distance is the shortest path distance inside the polygon. We give a linear-time algorithm to find a geodesic edge center of a simple polygon. This improves on the … hightower deli hughes landingWebbUnlike in the case of simple polygon, the rectilinear link center may be disconnected. Lemma 2.1 also holds in the rectilinear setting. The main steps in their algorithm are the same as in those of Djidjev et al. [25]. We omit the details and summarize the result in the following: Theorem 2.15 (Nilsson and Schuierer [69]) The rectilinear link ... small silver bugs in bathroomWebb1 jan. 2005 · K. M. McDonald and J. G. Peters, “Smallest paths in simple rectilinear polygons,” IEEE Trans. CAD, 11,7 July 1992, 864–875. Google Scholar K. Mikami and K. Tabuchi, “A computer program for optimal routing of printed circuit connectors,” IFIPS Proc., Vol. H47, 1968, 1475–1478. Google Scholar hightower deli 2 riverwayWebb27 apr. 2012 · This Demonstration illustrates an algorithm for finding the shortest path that stays inside a polygon and connects two given interior points. Aside from the start and … hightower creek vineyards hiawassee gaWebb32find min-linkrectilinearpaths in rectilinear polygonal domains. 33Previous Work. Linear-time algorithms have been given for finding min-link 34paths in simple polygons [9,10,21–23]. The link distance map can also be built 35in linear time [21–23] for simple polygons, with the standard query performance. hightower deli allen parkwayWebbWe present a data structure that allows to preprocess a rectilinear polygon with n vertices such that, for any two query points, the shortest path in the rectilinear link or L 1-metric … hightower deli 77042Webb7 nov. 1994 · There exists a shortest path from S to T which is not x-, y-, or xy-monotone. However, C S is the rectilinear polygon without holes, so we can use the algorithm of … small silver bugs in house