New lower and upper bounds for shortest distance queries on terrains

Abstract

The increasing availability of massive and accurate laser data enables the processing of spatial queries on terrains. As shortest-path computation, an integral element of query processing, is inherently expensive on terrains, a key approach to enabling efficient query processing is to reduce the need for exact shortest-path computation in query processing. We develop new lower and upper bounds on terrain shortest distances that are provably tighter than any existing bounds. Unlike existing bounds, the new bounds do not rely on the quality of the triangulation. We show how use of the new bounds speeds up query processing by reducing the need for exact distance computations. Speedups of of nearly an order of magnitude are demonstrated empirically for well-known spatial queries.

Distance Oracle on Terrain Surface

“…Our natural goal of answering each P2P distance query is to return the corresponding distance in a short time. However, none of the existing studies [26,6,34,24,20,19,2,3,12] could achieve this goal satisfactorily.…”

“…Due to a variety of applications in different domains as described in Section 1.1, computing geodesic distances [26,6,34,24,20,19,2,3,12] is very important and is very fundamental to other proximity queries such as nearest neighbor queries [9,10,29,35,20,19], range queries [20,19] and reverse nearest neighbor queries [36,20].…”

“…The time complexities of the algorithms for computing exact geodesic distances proposed by [26,6,34], are O(N 2 log N ), O(N 2 ), O(N log 2 N ) and O(N 2 log N ), respectively, which is still very large when N is large. In the literature [29,35,20,19], the algorithm proposed in [6] is recognized as a stateof-the-art fastest algorithm. Many existing papers [29,35,20,19] adopt this for finding the geodesic distance.…”

“…In the literature [29,35,20,19], the algorithm proposed in [6] is recognized as a stateof-the-art fastest algorithm. Many existing papers [29,35,20,19] adopt this for finding the geodesic distance. According to [19], the algorithm proposed in [6] took more than 300 seconds on a terrain with 200K vertices, which is very slow.…”

“…With the advance of geo-spatial positioning and computer graphics technology, digital terrain data has become increasingly popular nowadays, and it has been used in many applications such as Microsoft's Bing Maps and Google Earth in the industry community. The terrain data has also attracted considerable attention from the academic community [8,10,29,35,24,36,20,19].…”