Abstract: A common way of blending between two planar curves is to linearly interpolate their signed curvature functions and to reconstruct the intermediate curve from the interpolated curvature values. But if both input curves are closed, this strategy can lead to open intermediate curves. We present a new algorithm for solving this problem, which finds the closed curve whose curvature is closest to the interpolated values. Our method relies on the definition of a suitable metric for measuring the distance between two planar curves and an appropriate discretization of the signed curvature functions.

M. Saba, T. Schneider, K. Hormann, R. Scateni.
Curvature-based blending of closed planar curves.
Graphical Models, 76(5):263-272 (GMP 2014, Singapore, SN).
Elsevier, September 2014.