A geometric look at corner cutting Original Research Article

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.