Interpolatory Subdivision Surface With Non-uniform Parametrization

Non-uniform rational B-spline and subdivsion surfaces are two of the most popular techniques in geometric modeling for freedom surfaces, which have be-come prevailing standards respectively for industrial and animation. In pursuit for compatible representation, the incorporation of non-uniform parameteriza-tion with subdivision surfaces has recently become an engaging research focus.[1-3]has find a serious of non-uniform approximate subdivision scheme. Howev-er,there are only researches of non-uniform subdivsion curve and tension-product on interpolatory subdivision schemes. In this paper,we will bring out a new in-terpolatory subdivision scheme for arbitrary topology mesh. We’ll find a new relationship between non-uniform four point subdivision scheme and non-uniform B-spline refinement rule. With the help of the new ralationship, we’ll derive a new interpolatory subdivision schemes from a new approximating one. When all the knot intervals are equal,the new scheme is the same as [12], else when there are no irregular points in the mesh,it becomes the tension-product of non-uniform four point subdivision schemes. The scheme is at least Gl continuity provided by numerical examples. This scheme has brought in knot interval,which makes it compatible with NURBS, and provides the mesh more freedom.For the highly non-uniform initial mesh, the new non-uniform scheme will get better results than the uniform ones.