The development of solid modeling as an industrially viable technology was paced by the development, in the 1970's, of theory and algorithms for boolean operations on solids, i.e. for converting constructive (CSG) representations into boundary representations (B-reps). Theory and algorithms for the inverse conversion, from boundary to CSG (called BCSG), were largely unknown prior to the work of Shapiro and Vossler in 1989-91. Their cell-based methods are mathematically sound and have been implemented experimentally, but several important practical issues remain open. This research addresses those issues through the following goals: (1) development of significantly better algorithms for cell-based BCSG conversion; (2) development of a publicly available implementation of BCSG, initially for a domain of natural quadric surfaces, that is usable with one or more open architecture (i.e. public) B-rep modeling systems; and (3) development of theory and techniques, using new algebraic-patch and constructive-shell representations, to enable BCSG conversion to accommodate freeform solids. This research will re-establish CSG as an industrially viable representation for solids, and will enable fully symmetric dual- representation modeling systems to be built which should be considerably more powerful than today's B-rep-only systems.