A geometric look at corner cutting

In this paper we consider conrner cutting and convexity preserving interpolatory refinement schemes in the plane and on the sphere. Using well-known facts from projective geometry we present a unified approach to such schemes and geometric derivations of simple conditions which guarantee that a scheme generates C¹-curves. Our results generalize all of the results known so far and provide the ground for a new convexity preserving C¹-interpolation scheme with a simple direct shape handle.