Determination of Gradient and Curvature Constrained Optimal Paths

This article provides an analysis of gradient and curvature constraints on path form and length, with particular reference to road, rail and pipeline route selection. Initially we examine the case of a single (global) gradient constraint and a planar surface, with or without boundaries and obstacles. This leads on to a consideration of surface representation using rectangular lattices and procedures for determining shortest gradient-constrained paths across such surfaces. Gradient-Constrained Distance Transforms (GCDTs) are introduced as a new procedure to enable such optimal paths to be computed, and examples are provided for a range of landform profiles and gradients. Horizontal and vertical curvature constraints are then analysed and incorporated into final solution paths as subsequent stages of the optimisation process. Such paths may then be used as pre-analysed input to detailed cost and engineering models in order to speed up, and where possible improve, the quality and cost-effectiveness of route selection.