**Patching Catmull-Clark Meshes**

Siggraph 2000

Jörg Peters

**Context:**

**A simple, explicit transformation creates
maximally large, smoothly joining Nurbs patches of degree(3,3) from Catmull-Clark
subdivision meshes. It can be applied after any of the first subdivision
steps and creates patches that are maximally large in the sense that one
patch corresponds to one quadrilateral facet of the initial, coarsest quadrilateral
mesh before subdivision. The patches join C^2 almost everywhere and with
tangent continuity in the immediate neighborhood of extraordinary mesh
nodes, matching the global smoothness of Catmull-Clark limit surfaces.
The transitions between patches are almost all parametric. Named after
the title, the PCCM transformation integrates naturally with array-based
implementations of subdivision surfaces. See the Siggraph talk slides for
remarks on choice of normal, even higher-order saddle points and blend
ratios and smoothed creases.**