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 being 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. An interval solid is the union of this collection and the solid. In this paper we study the topology of a 3-manifold, when its boundary is covered by such a collection of boxes. We develop sufficient conditions on the collection of the boxes and the manifold, so that the union of the collection and the manifold is homeomorphic to the manifold itself. In particular, we apply this procedure to a solid and the associated interval solid. Finally, we present a method of constructing an interval solid, using interval arithmetic, homeomorphic to the solid.