Finding shortest isothetic path inside a 3D digital object

Abstract

The problem of finding shortest isothetic path between two points is well studied in the context of two dimensional objects. But it is relatively less explored in higher dimensions. An algorithm to find a shortest isothetic path between two points of a 3D object is presented in this paper. The object intersects with some axis parallel equi-distant slicing planes giving one or more isothetic polygons. We call these polygons as slices. The slice containing the source and destination points are called source and destination slice respectively. A graph is constructed by checking the overlap among the slices on consecutive planes. We call it slice overlap graph. Our algorithm first finds the source and destination slice. Thereafter, it finds the minimum set of slices Πst from the slice overlap graph, that need to be traversed to find SIP. Finally BFS is applied to find a SIP through these set of slices. The advantage of this procedure is that it does not search the whole object to find a SIP, rather only a part of the object is considered, therefore making the search faster.