Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature

Curvature Smoothness of Subdivision Surfaces

We examine the smoothness properties of the principal curvatures of subdivision surfaces near extraordinary points. In particular we give an estimate of their Lp class based on the eigen structure of the subdivision matrix. As a result we can show that the popular Loop and Catmull-Clark schemes (among many others) have square integrable principal curvatures justifying their use as shape functio...

Curvature integrability of subdivision surfaces

We examine the smoothness properties of the principal curvatures of subdivision surfaces near irregular points. In particular we give an estimate of their Lp class based on the eigenstructure of the subdivision matrix. As a result we can show that the popular Loop and Catmull-Clark schemes (among many others) have square integrable principal curvatures enabling their use as shape functions in F...

Gaussian and Mean Curvature of Subdivision Surfaces

By explicitly deriving the curvature of subdivision surfaces in the extraordinary points, we give an alternative, more direct account of the criteria necessary and sufficient for achieving curvature continuity than earlier approaches that locally parametrize the surface by eigenfunctions. The approach allows us to rederive and thus survey the important lower bound results on piecewise polynomia...

Surfaces of Constant Mean Curvature

New Constant Mean Curvature Surfaces

We use the DPW construction [5] to present three new classes of immersed CMC cylinders, each of which includes surfaces with umbilics. The first class consists of cylinders with one end asymptotic to a Delaunay surface. The second class presents surfaces with a closed planar geodesic. In the third class each surface has a closed curve of points with a common tangent plane. An appendix, by the t...