EAR-Oracle: On Efficient Indexing for Distance Queries between Arbitrary Points on Terrain Surface

Due to the advancement of geo-positioning technology, the terrain data has become increasingly popular and has drawn a lot of research effort from both academia and industry. The distance computation on the terrain surface is a fundamental and important problem that is widely applied in geographical information systems and 3D modeling. As could be observed from the existing studies, online computation of the distance on the terrain surface is very expensive. All existing index-based methods are only efficient under the case where the distance query must be performed among a small set of predefined points-of-interest known apriori. But, in general cases, they could not scale up to sizable datasets due to their intolerable oracle building time and space consumption. In this paper, we studied the arbitrary point-to-arbitrary point distance query on the terrain surface in which no assumption is imposed on the query points, and the distance query could be performed between any two arbitrary points. We propose an indexing structure, namely Efficient Arbitrary Point-to-Arbitrary Point Distance Oracle (EAR-Oracle), with theoretical guarantee on the accuracy, oracle building time, oracle size and query time. Our experiments demonstrate that our oracle enjoys excellent scalability and it scales up to enormous terrain surfaces but none of the existing index-based methods could be able to. Besides, it significantly outperforms all existing online computation methods by orders of magnitude in terms of the query time.