Refinement Schemes
Subdivision surface refinement schemes can be broadly classified into two categories: interpolating and approximating. Interpolating schemes are required to match the original position of vertices in the original mesh. Approximating schemes are not; they can and will adjust these positions as needed. In general, approximating schemes have greater smoothness, but editing applications that allow users to set exact surface constraints require an optimization step. This is analogous to spline surfaces and curves, where Bézier splines are required to interpolate certain control points (namely the two end-points), while B-splines are not.
There is another division in subdivision surface schemes as well, the type of polygon that they operate on. Some function for quadrilaterals (quads), while others operate on triangles.
Read more about this topic: Subdivision Surface
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