Construction of quadrilateral subdivision surfaces with prescribed G1 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 G^1 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.

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