Geometric Modeling is central to many CAD systems, even though the modelstraditionally employed do not satisfy all applications. Scientic applications need to dealwith ob jects made of dierent materials, with distinct properties. Contact relationshipsare crucial in kinematics, assembly planning, robotic, and geology.In this context, it is necessary to model aggregates of ob jects (including solidswith lower dimensional parts), keeping track of the adjacency relationships among theseob jects. This suggests the creation of a development environment where the applicationscan share not only data but also algorithms that process and transform these data. Theway to handle such problems is by supporting arbitrary space subdivisions, instead ofthe classical subdivision in three regions (interior, boundary, and exterior of a solidob ject).Planar subdivisions are simpler, but also important, mainly in geology and cartography. The creation of a planar subdivision diers from the creation of a spatialsubdivision, specially by the interaction with the user (by the modeling process).The aim of this work is to deal with the problem of creating, combining, and maintaining, in real time, subdivisions of the two- and three-dimensional Euclidean space.The main goal is devising a methodology that permits the construction of subdivisionswhich are topologically and geometrically consistent. This methodology is determinedby a modeling process, a mathematical model, and a representation scheme. To achievethis, some extensions were added to the concept of selective geometric complex, creating the basis for a exible scheme that eliminates several restrictions imposed by traditionalmodeling.The proposed representation scheme maintains an explicit boundary representationand allows one to add boolean operations without any additional restriction (furthermore, it enables the implementation of efficient geometrical algorithms). This provides apowerful set of modeling tools that can be used as the base for the creation of an interactive construction language for space subdivisions. The construction of basic operationswhich allow the insertion of a surface patch or a curve segment in a given subdivisionin linear time, is also described in detail. This means that a complete subdivision canbe built in quadratic time with the number of subdivision s elements.