An Algebraic Approach to Offsetting and Blending of Solids

We propose to broaden the framework of CSG to a representation of solids as boolean combinations of polynomial equations and inequalities describing regular closed semialgebraic sets of points in 3-space. As intermediate results of our operations we admit arbitrary semialgebraic sets. This allows to overcome well-known problems with the computation of blendings via offsets. The operations commonly encountered in solid modelers plus offsetting and constant radius blending can be reduced to quantifier elimination problems, which can be solved by exact symbolic methods. We discuss the general properties of such offsets and blendings for arbitrary regular closed semialgebraic sets in real n-space. Our computational examples demonstrate the capabilities of the REDLOG package for the discussed operations on solids within our framework.