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 S 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 P from S and transform a rectilinear shortest path computed in P to a path between s and t amid splinegon obstacles in S. When S comprises of h pairwise disjoint splinegons with a total of n vertices, excluding the time to compute a rectilinear shortest path amid polygons in P, our reduction algorithm takes O(n + h lgn) time. For the special case of S 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.