A GEOMETRIC LOOK AT CORNER CUTTING

In this paper we consider corner cutting and convexity preserving inte rpolatory refinement schemes in the plane and on the sphere. Using wel l-known facts from projective geometry we present a unified approach t o such schemes and geometric derivations of simple conditions which gu arantee that a scheme generates C-1-curves, Our results generalize all of the results known so far and provide the ground for a new convexit y preserving C-1-interpolation scheme with a simple direct shape handl e. (C) 1997 Elsevier Science B.V.