Degenerate point/curve and curve/curve bisectors arising in medial axis computations for planar domains with curved boundaries

Abstract The medial axis of a planar domain is the locus of points having at least two distinct closest points on the domain boundary. Segments of the medial axes of domains with curved boundaries fall into the two broad categories of point/curve bisectors and curve/curve bisectors. Certain “degenerate” forms of these bisectors, of a different intrinsic nature than the general instances and requiring appropriate algorithm modifications, arise generically in medial-axes computations. These include (i) point/curve bisectors where the point lies on the curve; (ii) curve/curve bisectors where the two curves are identical, i.e., the self-bisector of a curve; and (iii) curve/curve bisectors for distinct curves that share (with various orders of continuity) a common endpoint . We elucidate the geometrical nature of these special bisector forms, and develop algorithms (or algorithm modifications) for computing them. Together with existing algorithms for generic bisectors, they comprise a full complement of basic tools required in medial-axis computations.

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