Blending two parametric curves

Segments of two given curves can be blended to produce a segment of a new curve. Blending can provide a smooth transition from one curve to another and can give various degrees of smoothness at the endpoints of the blend, where the smoothness is measured analogously to parametric continuity C(n)C(n) and geometric continuity G(n)G(n). Blending can provide an approximation to a given curve segment. The accuracy of the approximation to short segments obtained by different blending formulas is compared via asymptotic analysis. Finally, it is shown how to find a blend that is a parametric polynomial whose parameter is approximately an arc length parameter.