Rounding and Blending of Solids by a Real Elimination Method

Given a semialgebraic description of an object in real 3-space, we compute a semialgebraic description of the rounded or blended object using circular constant radius rounding and blending. Our approach uses a real elimination method that can handle polynomial inequalities both in the input and in the output. We discuss the general properties of constant radius rounding of objects from inside and from outside and of constant radius blending of composite objects for arbitrary closed semialgebraic sets in real n-space. We show that rounding and blending can be reduced to an iterated formation of certain offsets. Our method is implemented based on the REDUCE package REDLOG. First computational experiments are very promising.