VERY quick and dirty math visualizationg using Jmol and the pmesh command --- VERY CRUDE -- I wrote this page in about 30 minutes! (not closing the surface, for example)
This is 10,000 points (100x100)
-- Bob Hanson
Based on http://www.javaview.de/demo/PaParmSurface.html

fx = "2./(1.+Math.pow(u*sin(v),2))*sqrt(1.+u*u)*sin(v)*cos(u-atan(u))" fy = "2./(1.+Math.pow(u*sin(v),2))*sqrt(1.+u*u)*sin(v)*sin(u-atan(u))" fz = "log(tan(v/2.))+2./(1.+Math.pow(u*sin(v),2))*cos(v)" umin = -4.5 umax = 4.5 vmin = 0.05 vmax = 3.09159 nu = 100 nv = 100 ustep = (umax-umin)/nu vstep = (vmax-vmin)/nv