One half of these surfaces (cut in the middle) converge to the Pseudosphere
K = -1
are explicit and well known. To deform these surfaces, keeping K = -1, it is more
convenient to construct these surfaces from solutions of the Sine-Gordon equation (SGE).
For surfaces of revolution these SGE solutions can be obtained from the ODE
q''(u) = sin(q(u)), with symmetric solutions defined by initial conditions q(0) = h > 0 and
q'(0) = 0. Then one can do the same as in the classical Dini deformation: define
new solutions qn(u,v) := q(cosh(d)*u + sinh(d)*v), with d the Dini parameter. The
animation shows these surfaces. Most of them have self intersections, but some have
screw motion symmetry - see the last image of the animation.
