Path-cost Analysis and Real-Time Path Computation in Weighted Regions

The Weighted Region Problem is defined as the problem of finding a cost-optimal path in a weighted planar polygonal subdivision. Searching for paths on a grid representation of the scene is fast and easy to implement. However, grid representations do not capture the exact geometry of the scene. Hence, grid paths can be inaccurate or might not even exist at all. Methods that work on an exact representation of the scene can approximate an optimal path up to an arbitrarily small -error. However, these methods are computationally inefficient and thus not well-suited for real-time applications. In this paper, we analyze the quality of optimal paths on a 8-neighbor-grid. We prove that the costs of such a path in a scene with weighted regions can be arbitrarily high in the general case. If all regions are aligned with the grid, we prove that the costs are at