THE BISECTOR OF A POINT AND A PLANE PARAMETRIC CURVE

The bisector of a fixed point p and a smooth plane curve C-i.e., the l ocus traced by a point that remains equidistant with respect to p and C-is investigated in the case that C admits a regular polynomial or ra tional parameterization. It is shown that the bisector may be regarded as (a subset of) a ''variable-distance'' offset curve to C which has the attractive property, unlike fixed-distance offsets, of being gener ically a rational curve. This ''untrimmed bisector'' usually exhibits irregular points and self-intersections similar in nature to those see n on fixed-distance offsets. A trimming procedure, which identifies th e parametric subsegments of this curve that constitute the true bisect or, is described in detail. The bisector of the point p and any finite segment of the curve C is also discussed.