Editing Subdivision surface (section)

===Interpolating schemes===
After subdivision, the control points of the original mesh and the newly generated control points are interpolated on the limit surface. The earliest work was so-called "[[butterfly scheme]]" by Dyn, Levin and Gregory (1990), who extended the four-point interpolatory subdivision scheme for curves to a subdivision scheme for surface. Zorin, Schröder and Sweldens (1996) noticed that the butterfly scheme cannot generate smooth surfaces for irregular triangle meshes and thus modified this scheme. Kobbelt (1996) further generalized the four-point interpolatory subdivision scheme for curves to the tensor product subdivision scheme for surfaces. In 1991, Nasri proposed a scheme for interpolating Doo-Sabin;<ref>Nasri, A. H. Surface interpolation on irregular networks with normal conditions. Computer Aided Geometric Design 8 (1991), 89–96.</ref> while in 1993 Halstead, Kass, and DeRose proposed one for Catmull-Clark.<ref>Halstead, M., Kass, M., and DeRose, T. Efficient, Fair Interpolation Using Catmull-Clark Surfaces. In Computer Graphics Proceedings (1993), Annual Conference Series, ACM Siggraph</ref>
<!-- * [[Doo-Sabin subdivision surface|Doo-Sabin]], Quads - generalization of bi-quadratic uniform [[B-spline]]s -->
* [[Butterfly subdivision surfaces|Butterfly]] (1990), Triangles – named after the scheme's shape
* [[Midedge|Modified Butterfly]] (1996), Quads<ref>{{Cite journal|last=Zorin|first=Denis|last2=Schröder|first2=Peter|last3=Sweldens|first3=Wim|year=1996|title=Interpolating Subdivision for Meshes with Arbitrary Topology|url=https://cims.nyu.edu/gcl/papers/zorin1996ism.pdf|journal=Department of Computer Science, California Institute of Technology, Pasadena, CA 91125}}</ref> – designed to overcome artifacts generated by irregular topology
* [[Kobbelt]] (1996), Quads – a variational subdivision method that tries to overcome uniform subdivision drawbacks