Polygonal covering on the hexagonal grid: two parallel algorithms

Two parallel algorithms for polygonal covering of patterns digitized on the hexagonal grid are presented. Both algorithms require operations having a local support of a 6-pixel neighborhood. The first algorithm provides a polygon with at most six sides, oriented along the six principal directions in the hexagon tessellated plane. The second algorithm provides a nearly convex polygon, with more than six sides, which fits the pattern more closely. The latter algorithm is less sensitive to pattern rotation and is more suited to practical applications. The concavity tree can also be built by considering the concavity regions, obtained by computing the difference between the covering polygon and the pattern, and by iteratively applying the same polygonal covering algorithm. The nodes of the concavity tree can be labeled with parameters related to geometrical features of the corresponding concavity regions