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New analytical formulations of bounded blending operations can enhance function-based constructive shape modeling. In this article, we introduce bounded-blending operations that we define using R-functions and displacement functions with the localized area of influence. We define the shape and location of the blend by control points on the surfaces of two solids or by an additional bounding solid. We can apply our proposed blending using a bounding solid to a single selected edge or vertex. We also introduce new multiple blends and a partial edge blend. Our description supports set-theoretic operations on blends and blends on blends - that is, recursive blends. In this sense, our proposed operations could replace pure set-theoretic operations in the construction of a solid without rebuilding the entire construction tree data structure. Our proposed blending method can have application in interactive design.