Convex Triangular Subdivision Surfaces with Bounded Curvature

The edge masks for Loop’s triangular subdivision surface algorithm are modified resulting in surfaces with bounded curvature and the convex hull property. The new edge masks are derived from a polynomial mask equation whose Chebyshev expansion coefficients are closely related to the eigenvalues of the corresponding subdivision matrix. The mask equation is found to satisfy a set of smoothness constraints on these eigenvalues.