1 Vector vs . Raster - based Algorithms for Cross Country Movement Planning

The problem of cross country movement planning is to find the least cost path between a source and a destination given a polygonal partitioning of the plane. This paper presents the comparison between a vector-based algo­ rithm and several raster-based algorithms for solving the cross country move­ ment planning problem. Besides three known raster methods (standard, more­ connected, and quadtree), a new method, extended raster approach, has been designed and implemented . The latter finds better solutions because of the higher degree of freedom when moving through a rasterized terrain, that is, more directions can be followed. The vector method of Mitchell and Papadim­ itriou has also been implemented for comparison . Assuming a reasonable sized terrain with a reasonable accuracy all methods have performance problems . Therefore, a hierarchical approach is presented which can be applied in both the vector and raster domain . This approach will find the optimal path in contrast to other hierarchical approaches, which do not guarantee to find the optimal path, but often return a good path . The performance improvement should make the hierarchical approach suitable for interactive movement plan­ ning tasks. Introduction The cross country movement (CCM) problem is also known as the Weighted Region (Least Cost Path) Problem [15, 22] . The unit cost of traversing a given region (poly­ gon) is uniform within the region, but varies between regions and is based on soil, vegetation, and so on . Finding an optimal path, that is, locating a corridor from a given source location to a given destination location [3, 6, 10] is not only used for travelling . It can also be applied in other planning situations, such as building high­ ways, railways, pipelines and other transport systems. The cost function is based on optimization criteria such as time, safety, fuel usage, impact, length, etc . Note that the CCM-problem is very different from the more common linear route planning in a road network, because the cost of using an element (polygon) is not fixed . Section 2 contains the description of four different raster-based algorithms for the CCM planning problem. The vector-based approach of Mitchell and Papadimitriou