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 Constr. Time

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 ε-error. However, these methods are computationally inefficient and thus not wellsuited for real-time applications.