  We trace movements of certain points in space-time along their corresponding
continuous path. We partition the space at every moment of time using
alpha-Complexes, Voronoi medusa is then the collection or union of restricted
Voronoi cells at every moment in time. We can imagine them as a four
dimensional structure formed when three dimensional restricted Voronoi cells
sweeps continuously through the extra dimension of time. Similarly Delaunay
medusa is the collection of the corresponding Delaunay triangulations at each
moment in time. In this article we prove that these two structures are
homotopic.
