Ternary blending operations

We discuss new analytical formulations for localized and controllable blending operations in the function- based solid modeling. The blending set operations are defined using R-functions and displacement func- tions with the localized area of influence. The shape and location of the blend are controlled by an ad- ditional bounding solid thus turning the operation into a ternary one. We also describe a new approach to solving the problem of shape metamorphosis be- tween k-dimensional shapes by applying space-time bounded blending to the specially constructed (k+1)- dimensional half-cylinders and making cross-sections for getting intermediate shapes under the transforma- tion.