# Computing a rectilinear shortest path amid splinegons in plane

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.

READ FULL TEXT