Curve Interpolation with Arbitrary End Derivatives

Abstract.

An algorithm for interpolating data points with end derivative constraints is presented. The interpolating curve passes through the given points and at the same time assumes the derivatives specified. For degree p interpolation, up to p−1 derivatives may be specified, resulting in C ^p−1 continuous curve interpolants. The method is useful to piece individual curve segments together or to create closed curves with various degrees of smoothness.