Mid-edge subdivision
= Mid-edge subdivision
Mid-edge subdivision replaces each mesh edge by its midpoint, joins successive midpoints around every old face, and joins successive midpoints around every old vertex. For an interior <manifold> mesh, each new vertex has valence four. Each geometric update is a <convex combination>, so every refined control point remains in the <convex hull> of the original control mesh. The regular limit is associated with the <quadratic four-direction box spline>.