1. Subdivision Overview Subdivision is a two part process Control Mesh
Topological Split
Averaging
Subdivision is a two part process
Topological split
Local averaging / smoothing

2. Subdivision Overview
Control Mesh
Generation 1
Generation 2
Generation 3
Repeated uniform subdivisions of the control mesh converge to the limit surface
Stationary schemes (averaging mask does not change)
Limit position and normal from eigen-analysis

3. Bspline Surfaces
A single Bspline surface patch is controlled by a regular 4x4 grid of control points

4. Bspline Surfaces
2 adjacent patches share 12 control points and meet with C2 continuity

5. Bspline Surfaces
Requires regular rectangular (toroidal) control mesh to guarantee continuity (all valence-4 vertices!)
Subdivision can be performed by knot insertion (i.e. blossoming)

6. Catmull-Clark Subdivision Surfaces
Smooth surfaces for control meshes of arbitrary topology
Closed control mesh  closed limit surface
Quad mesh generalization of Bsplines
C1 at non-valence-4 vertices,
C2 every where else (Bsplines).
Sharp corners can be tagged:
allows for smooth and sharp features;
allows for non-closed meshes.

7. Catmull-Clark Subdivision
Gen 0
Gen 1
Gen 2
Extraordinary vertices are generated by non-valence-4 vertices & faces in the input mesh.
No further extraordinary vertices are created after the first generation of subdivision.

8. Catmull-Clark Averaging
Vn0
V20
C10
F10
En0
E40
E30
E20
Fn0
F40
F30
F20
C30
C40
Cn0
C20
NEW EDGE POINTS:
NEW FACE POINTS:
SMOOTHED VERTICES:

9. Loop Subdivision Surfaces
Gen 0
Gen 1
Gen 2
NEW EDGE POINTS: