Relative blending

Solid models may be blended through filleting or rounding operations that typically replace the vicinity of concave or convex edges by blends that smoothly connect to the rest of the solid’s boundary. Circular blends, which are popular in manufacturing, are each the subset of a canal surface that bounds the region swept by a ball of constant or varying radius as it rolls on the solid while maintaining two tangential contacts. We propose to use a second solid to control the radius variation. This new formulation supports global blending (simultaneous rounding and filleting) operations and yields a simple set-theoretic formulation of the relative blending RB(A) of a solid A given a control solid B. We propose user-interface options, describe practical implementations, and show results in 2 and 3 dimensions.