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One essential interpolation constraint on subdivision surfaces is curve interpolation. Subdivision surfaces through predefined meshes of curves can now be generated using either variations of existing subdivision schemes or (in our case) polygonal complexes. This paper goes one step further; given a sequence of cross sectional curves (ci), each defined by a uniform cubic B-spline control polygon (cpi), we present a technique for generating a lofted subdivision surface through these curves. The advantages of using polygonal complexes coupled with subdivision surfaces are that curves do not have to be compatible and that it is possible to locally control the cross curvature of a given cross section.