Computing a rectilinear shortest path amid splinegons in plane
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We reduce the problem of computing a rectilinear shortest path between two given points s and t in the splinegonal domain to the problem of computing a rectilinear shortest path between two points in the polygonal domain. As part of this, we define a polygonal domain from and transform a rectilinear shortest path computed in to a path between s and t amid splinegon obstacles in . When comprises of h pairwise disjoint splinegons with a total of n vertices, excluding the time to compute a rectilinear shortest path amid polygons in , our reduction algorithm takes O(n + h n) time. For the special case of comprising of concave-in splinegons, we have devised another algorithm in which the reduction procedure does not rely on the structures used in the algorithm to compute a rectilinear shortest path in polygonal domain. As part of these, we have characterized few of the properties of rectilinear shortest paths amid splinegons which could be of independent interest.
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