  We describe a new approach to fit the polyhedron describing a 3D building
model to the point cloud of a Digital Elevation Model (DEM). We introduce a new
kinetic framework that hides to its user the combinatorial complexity of
determining or maintaining the polyhedron topology, allowing the design of a
simple variational optimization. This new kinetic framework allows the
manipulation of a bounded polyhedron with simple faces by specifying the target
plane equations of each of its faces. It proceeds by evolving continuously from
the polyhedron defined by its initial topology and its initial plane equations
to a polyhedron that is as topologically close as possible to the initial
polyhedron but with the new plane equations. This kinetic framework handles
internally the necessary topological changes that may be required to keep the
faces simple and the polyhedron bounded. For each intermediate configurations
where the polyhedron looses the simplicity of its faces or its boundedness, the
simplest topological modification that is able to reestablish the simplicity
and the boundedness is performed.
