DEGENERATE POINT CURVE AND CURVE/CURVE BISECTORS ARISING IN MEDIAL AXIS COMPUTATIONS FOR PLANAR DOMAINS WITH CURVED BOUNDARIES/

The medial axis of a planar domain is the locus of points having at le ast two distinct closest points on the domain boundary. Segments of th e medial axes of domains with curved boundaries fall into the two broa d categories of point/curve bisectors and curve/curve bisectors. Certa in ''degenerate'' forms of these bisectors, of a different intrinsic n ature than the general instances and requiring appropriate algorithm m odifications, arise generically in medial-axes computations. These inc lude (i) point/curve bisectors where the point lies on the curve; (ii) curve/curve bisectors where the two curves are identical, i.e., the s elf-bisector of a curve; and (iii) curve/curve bisectors for distinct curves that share (with various orders of continuity) a common endpoin t. We elucidate the geometrical nature of these special bisector forms , and develop algorithms (or algorithm modifications) for computing th em. Together with existing algorithms for generic bisectors, they comp rise a full complement of basic tools required in medial-axis computat ions. (C) 1998 Elsevier Science B.V.