Generalized functional and decorative filleting and blending operations

The use of blending and filleting operations in solid modeling and computer-aided geometric design is well established. The question of filling a gap between two (or more) surface boundaries or rounding a sharp edge has been extensively investigated. The vast majority of the prior work on blending and filleting concentrated on a wide variety of fitting schemes as well as attempts to establish and guarantee better continuity conditions. This work extends the notion of filleting and blending modeling tools and elevates them into shaping operations that are either functional or ornamental in nature. The extended shaping operations can be conducted between two boundaries of two adjacent surfaces, much like traditional blending or filleting methods. Furthermore, the presented extended forms can also be applied to the interior of a single surface, guided by arbitrary parametric curves in the domain of the patch.