Abstract
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 ) and geometric continuity 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.
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