  Polytope complexes are the generalisation of polygon meshes in
geo-information systems (GIS) to arbitrary dimension, and a natural concept for
accessing spatio-temporal information. Complexes of each dimension have a
straight-forward dimension-independent database representation called
"Relational Complex". Accordingly, complex overlay is the corresponding
generalisation of map overlay in GIS to arbitrary dimension. Such overlay can
be computed by partitioning the cells into simplices, intersecting these and
finally combine their intersections into the resulting overlay complex. Simplex
partitioning, however, can expensive in dimension higher than 2. In the case of
polytope complex overlay /signed/ simplicial decomposition is an alternative.
This paper presents a purely combinatoric polytope complex decomposition which
ignores geometry. In particular, this method is also a decomposition method for
/non-convex/ polytopes. Geometric n-D-simplex intersection is then done by a
simplified active-set-method---a well-known numerical optimisation method.
"Summing" up the simplex intersections then yields the desired overlay complex.
