Minimum Link Path Finding Methods in 2D Polygons

The author surveys methods for finding a path between two arbitrary points within a 2D polygon under the link-distance metric. Early algorithms limited to simple polygons are explored first, and categorized into two different approaches. These methods are then evaluated for expansion into non-simple polygons (i.e. spaces with “Obstacles” within the polygon boundary). Then, the problem of finding a minimum link path with obstacles is examined. Visibility based approaches are discussed, and similarities and optimizations made to algorithms for simple polygons are discussed. A critique of these methods based on bit-precision is noted, as well as related problems such as rectilinear variants, combined metrics (link and Euclidean distance), and pre-processing algorithms which charge a large amount of work to building an initial data structure, which then can perform arbitrary link distance queries quickly.