On Efficient Shortest Path Computation on Terrain Surface: A Direction-Oriented Approach

With the advance of the geo-positioning technology, the terrain surface data has become increasingly popular and has drawn much research attention from both academia and industry. Answering a shortest-path query for a given source and a given destination on a terrain surface is a fundamental problem and has many applications including Geographical Information System and 3D virtual games. We observe that all existing exact algorithms are only aware of the position of the source point and is unaware of the information of the destination point. Motivated by this, in this paper, we propose an efficient algorithm, namely direction-oriented algorithm (DIO Algorithm), for answering shortest-path queries on a terrain surface. The algorithm properly guides the search along a direction towards the destination instead of blindly searching all possible directions from the source point. To this end, we convert the geodesic shortest path problem to a shortest obstacle-free Euclidean path problem in the 2D planar unfolding of the terrain surface. Based on this conversion, we derive for each part of the terrain surface a lower bound on the length of the shortest path from the source to the destination passing through the part with a novel method. The lower bounds provide useful information that can be used to decide the visiting order of the parts on the terrain surface and guides the search of finding the destination quickly. Our experiments verified that our algorithm runs faster than the state-of-the-art by more than one order of magnitude.