A solution to the Path Planning problem using angle preprocessing

The Path Planning problem is a common topic for Robotics and Computational Geometry. Many important results have been found to this classic problem, some of them based on plane or space tessellation. The new approach we propose in this paper computes a partition of the plane called the Polar Diagram, using angle properties as criterion of construction. Compared to some other plane partitions as Voronoi Diagrams, this tessellation can be computed much more efficiently for different geometric objects.The polar diagram used as preprocessing can be applied to many geometric problems where the solution can be given by angle processing, such as Visibility or Path Planning problems.