Abstract: 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.