Bounded curvature triangle mesh subdivision with the convex hull property

The masks for Loop’s triangle subdivision surface algorithm are modified resulting in surfaces with bounded curvature and the convex hull property. New edge masks are generated using a cubic polynomial mask equation whose Chebyshev 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. We observe that controlling the root structure of the mask equation is important for deriving subdivision masks with non-negative weights.