Implicit Set Blends with Solid-Bounded Blending Regions for Function Representation

In Function representation of implicit surface, a complex implicit solid is constructed like block building from primitive solids via implicit Boolean set blends, including union, intersection and difference blends. Set blends can smooth out sharp corners and edges with transition surfaces automatically generated from the intersecting curves between the level surfaces in the blending regions of blended primitives. In existing blends, the shapes of the level surfaces in the blending regions are always like those of blended primitives proportionally. Contrary to existing blends, this paper develops new set blends with solid-bounded blending regions, that is, each primitive can be assigned a bounding solid to totally change the shapes of the level surfaces in its blending regions. Consequently, by choosing suitable bounding solids these newly proposed blends offer new modeling functions: a. bulge elimination on sequential unions of intersecting or connecting cylinders with less computing complexity than other gradient-based methods, b. changing the shape of the contour of a blend's transition by the chosen bounding solid, and c. Partial blending of a primitive, that is, blend can occur only on parts of a primitive.