Bisector curves of planar rational curves

This paper presents a simple and robust method for computing the bisector o f two planar rational curves. We represent the correspondence between the f oot points on two planar rational curves C-1(t) and C-2(r) as an implicit c urve F(t,r) = 0, when F(t,r) is a bivariate polynomial B-spline function. G iven two rational curves of degree m in the xy-plane, the curve F(t,r) = 0 has degree 4m - 2, which is considerably lower than that of the correspondi ng bisector curve in the xy-plane. (C) 1999 Elsevier Science Ltd. All right s reserved.