Specified-precision computation of curve/curve bisectors

The bisector of two plane curve segments (other than lines and circles) has, in general, no simple - i.e., rational - parameterization, and must therefore be approximated by the interpolation of discrete data. A procedure for computing ordered sequences of point/tangent/curvature data along the bisectors of polynomial or rational plane curves is described, with special emphasis on (i) the identification of singularities (tangent-discontinuities) of the bisector; (ii) capturing the exact rational form of those portions of the bisector with a terminal footpoint on one curve; and (iii) geometrical criteria that characterize extrema of the distance error for interpolants to the discretely-sampled data. G(1) piecewise-parabolic and G(2) piecewise-cubic approximations (with O(h(4)) and O(h(6)) convergence) are described which, used in adaptive schemes governed by the exact error measure, can be made to satisfy any prescribed geometrical tolerance.