In this paper we give an elementary proof that polynomial curves are the only differentiable curves which permit subdivision by simple linear techniques. Subdivision methods for rational polynomial curves are also discussed. © 1984.
Goldman, R. N., & Heath, D. C. (1984). Linear subdivision is strictly a polynomial phenomenon. Computer Aided Geometric Design, 1(3), 269–278. https://doi.org/10.1016/0167-8396(84)90013-X