A direction dependent least-cost-path algorithm for roads and canals

In planning routes for roads and canals, topography is often a significant constraint. Among the infinite number of possible trajectories between two points, the selected path should be a good approximation to the one with the least cost, and should avoid extremes of slopes. In the case of a canal, the number of uphill reaches of the trajectory should be minimised. This paper presents a least-cost-path algorithm developed to find the best path given the topography, the start and end-points of the linear feature (canal or road) and a function relating slope, distance and cost. The algorithm is based on dynamic programming techniques adapted to solve problems on the grid, or raster structure usually used in Geographical Information Systems. The algorithm was programmed and used to solve hypothetical problems. Although real cost functions were not used, the results were coherent and showed the algorithm's capabilities.