  In the geometric data model for spatio-temporal data, introduced by Chomicki
and Revesz, spatio-temporal data are modelled as a finite collection of
triangles that are transformed by time-dependent affinities of the plane. To
facilitate querying and animation of spatio-temporal data, we present a normal
form for data in the geometric data model. We propose an algorithm for
constructing this normal form via a spatio-temporal triangulation of geometric
data objects. This triangulation algorithm generates new geometric data objects
that partition the given objects both in space and in time. A particular
property of the proposed partition is that it is invariant under time-dependent
affine transformations, and hence independent of the particular choice of
coordinate system used to describe he spatio-temporal data in. We can show that
our algorithm works correctly and has a polynomial time complexity (of
reasonably low degree in the number of input triangles and the maximal degree
of the polynomial functions that describe the transformation functions). We
also discuss several possible applications of this spatio-temporal
triangulation.
