The Fusion as a Novel Binary Operation on Medial Axes

This paper presents a novel type of binary operation on medial axes: fusion of medial axes. A method for fusing medial axes of two-dimensional objects is described. The method is applicable to a pair of the medial axes of adjacent multiply-connected polygonal domains in the plane. The algorithm computes the medial axis from a structure called Delaunay graph which embodies information about adjacency in the Voronoi diagram of the edges and vertices. It is shown how Delaunay graphs can be merged and hence how the fused medial axis can be computed from individual Delaunay graphs. The main singularity of the fusing operation is that to construct the medial axis for a union of two adjacent figures in is not necessary to explicitly union the figures. This makes sense in those cases when two figures sharing finite number of polygonal chains overlap in the plane and cannot be united. Such problem of overlapped polygons occurs frequently in handling geospatial map objects in GIS (for example, bridge and road different level parts within an interchange). The complexity of the proposed method is O(n log n) where n is a number of vertices both in two polygonal figures.