The new polygon with light vertices has twice as many vertices. Repeating this process yields denser and denser polygons. The limit of this process is a smooth curve. In fact, this curve is the quadratic B-spline defined by the dark vertices. The operation of replicating and averaging is referred to as subdivision .
Subdivision is a geometric transformation that maps polygons into more densely faceted polygons.
Surface subdivision methods map polyhedra into polyhedra. Hoppe, DeRose, et al. build a variant of Loop's method that can be used to define surfaces with distinct vertices and sharp, curved edges. Each vertex of the initial polyhedron is tagged as lying on a vertex, edge, or face of the limit object. Distinct averaging masks are then used for vertices of each type to produce a new, more densely faceted polyhedron whose vertices are also tagged. The limit of this process is an object with smooth, curved faces and smooth, sharp edges.