Mesh Subdivision

Goals of mesh subdivision:

• Finer control for editing processes
• Required for finite element methods

Terminology:

• Refinement is a topological operation, does not change the geometry (new vertices lie on the surface of the original mesh)
• Subdivision combines refinement with a geometric operation (eg. smoothing)

Uniform refinement

Rivera split

Dyadical split

$\sqrt{3}$ split

Adaptive refinement

Red-Green triangulation

Adaptive $\sqrt{3}$-Refinement

Curvature-continuous Subdivision

Loop subdivision

$\sqrt{3}$-Subdivision