Continuity of non-uniform recursive subdivision surfaces

摘要

Since Doo-Sabin and Catmull-Clark surfaces were proposed in 1978,eigenstructure, con- vergence and continuity analyses of stationarysubdivision have been performed very well, but it has been verydifficult to prove the convergence and continuity of non-uniformrecursive subdivision sur- faces (NURSSes, for short) of arbitrarytopology. In fact, so far a problem whether or not there exists thelimit surface as well as G~1 continuity of a non-uniformCatmull-clark subdivision has not been solved yet. Here the conceptof equivalent knot spacing is introduced.