Construction of quadrilateral subdivision surfaces with prescribed G1G1 boundary conditions

We present a scheme that combines the subdivision technique and the geometric partial differential equations method which provides us an efficient algorithm for designing high-quality surfaces with arbitrary topology structure. We use several fourth-order geometric partial differential equations to construct Catmull–Clark’s subdivision surfaces with prescribed G1G1 boundary conditions where a mixed finite element method is based on the modified Catmull–Clark’s subdivision scheme. Our approach can uniformly handle surface construction both with specified boundary normals and with interior sharp edges, which is a powerful tool for designing the shape of surfaces.

► Catmull–Clark’s subdivision surface patches with given G1G1 boundary conditions.
► Three fourth-order evolutionary geometric partial differential equations.
► Mixed finite element method in the modified Catmull–Clark’s subdivision function space.