Path-Planning by Tessellation of Obstacles

We describe two algorithms for static path-planning, with the aim of deriving the trajectory that always maximises the distance of the path from the nearest obstacle. The bubble algorithm allocates individual pixels to generating points, growing the area owned by each point at a globally constant rate to ensure that boundaries are equidistant between neighbouring points. The geometric algorithm derives the same "perfect path", but without examining pixels individually, and thus with good performance. It compares geometric elements pairwise to generate segments of the boundaries, then intersects these segments to derive the perfect path. The geometric algorithm is the lowest-complexity algorithm yet described that derives this perfect path.