Smoothing of free-form surfaces with Bézier patches

Abstract In this paper, a unified method for smoothing free-form surfaces with Bezier patches is presented. A non-smooth surface consisting of bicubic patches is turned into a G 1 surface by the following process. Trim each patch along user-defined parameter lines using subdivision. Attach eight patches (one to each edge and one to each vertex) to each trimmed patch to blend between it and its neighbor patches. Using this method, solid objects bounded with bicubic Bezier patches can be G 1 smoothed with bicubic patches. The operation is local. It provides designers with the facility to adjust the shape of a smoothed object interactively. The method can also be used for constructing smooth closed surfaces whose modeling is important for CAD/CG (cf. (Barnhill, 1985)).

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