The Separation Problem of Real Function Partitions and its Significance in Solid Modeling 1

Given a set F of real-valued functions from R ³ to R, the separation problem asks for a set of auxiliary functions H that distinguishes the connected components of the cells of the sign-invariant partition of R ³ induced by F. We explain the problem and some of the ways in which it comes up in solid modeling. We also summarize what is known about it in the solid modeling community.