Mesh Subdivision

Goals of mesh subdivision:

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


  • 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


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