Blend localization (left), multiple blending (middle), and blend on blend (right).

Pasko G., Pasko A., Kunii T.L., Bounded blending for function-based shape modeling,
IEEE Computer Graphics and Applications, vol. 25, No. 2, 2005, pp. 36-45.
Electronic pre-final version: PDF (430K)

We propose new analytical formulations of bounded blending operations for the function-based constructive shape modeling. The blending set operations are defined using R-functions and displacement functions with the localized area of influence. The shape and location of the blend is defined by control points on the surfaces of two solids or by an additional arbitrary bounding solid also defined by a real-valued function. The proposed blending using a bounding solid can be applied to a single selected edge, a vertex, or another blend. We introduce new types of blends such as a multiple blend with the disconnected bounding solid and a partial edge blend. We show that the proposed operations can replace pure set-theoretic operations in the solid model without rebuilding the entire construction tree data structure. The proposed blending is shown to have versatile applications in interactive design. Influence of all parameters on the blend shape and location is illustrated.