Finding shortest path on land surface

Finding shortest paths is a fundamental operator in spatial databases. Recently, terrain datasets have attracted a lot of attention from both industry and academia. There are some interesting issues to be studied in terrain datasets which cannot be found in a traditional two-dimensional space. In this paper, we study one of the issues called a slope constraint which exists in terrain datasets. In this paper, we propose a problem of finding shortest paths with the slope constraint. Then, we show that this new problem is more general than the traditional problem of finding shortest paths without considering the slope constraint. Since finding shortest paths with the slope constraint is costly, we propose a new framework called surface simplification so that we can compute shortest paths with the slope constraint efficiently. Under this framework, the surface is "simplified" such that the complexity of finding shortest paths on this simplified surface is lower. We conducted experiments to show that the surface simplification is very efficient and effective not only for the new problem with the slope constraint but also the traditional problem without the slope constraint.

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