  Motivated by applications in CNC machining, we provide a characterization of
surfaces which are enveloped by a one-parametric family of congruent rotational
cones. As limit cases, we also address developable surfaces and ruled surfaces.
The characterizations are higher order nonlinear PDEs generalizing the ones by
Gauss and Monge for developable surfaces and ruled surfaces, respectively. The
derivation includes results on local approximations of a surface by cones of
revolution, which are expressed by contact order in the space of planes. These
results are themselves of interest in geometric computing, for example in
cutter selection and positioning for flank CNC machining.
