Topological and geometric properties of interval solid models

A solid is a connected orientable compact subset of R-3 which is a 3-manifold with boundary. Moreover, its boundary consists of finitely many components, each of which is a subset of the union of finitely many almost smooth surfaces. Motivated by numerical robustness issues, we consider a finite collection of boxes, with faces parallel to the coordinate planes, which covers the boundary of the solid itself. An interval solid is the union of this collection and the solid. In this paper we develop sufficient conditions on the collection of the boxes and a 3-manifold, so that the union of the collection and the manifold is homeomorphic: to the manifold itself. Finally, we outline an approach for constructing an interval solid, using interval arithmetic, homeomorphic to the solid. (C) 2001 Academic Press.