A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
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Subdivision surfaces are smooth surfaces generated from polyhedral models. The three most popular subdivision methods (Modified Butterfly, Loop, and Catmull-Clark) are compared in this project by the smooth surfaces they generate from the same initial meshes. Subdivision methods can be classified by 3 independent characteristics: their fidelity to the data points (approximating vs. interpolating), type of input mesh (triangular vs. quadrilateral), and type of refinement rule (vertex insertion vs. corner-cutting). All 3 methods that we study use vertex insertion. The Modified Butterfly scheme [2] uses interpolation on a triangular mesh, the Loop scheme [3] uses approximation on a triangular mesh, and the Catmull-Clark scheme [1] uses approximation on a quadrilateral mesh. The different effect of the three schemes comes from the different subdivision masks used (Fig. 1).