I understand the mathematics of this shape and I want to use OpenGL to display it. How does one display something other than a sphere or cylinder ? I’ve been studying the “OpenGL SuperBible” , but am not sure how to define the shape for use in OpenGL. Once I know this I think I can figure out how to display it.
Any help geatly appreciated.

you gotta point your vertexes to the positions you want in a opengl window you created it is like this the numbers represent the axis so the first is x axis (0.0) the second number is y axis(0.0) and the third is the z axis(0.0) and you have to guess because no one made a standard graph that i can find that allows you to know where to point without all that crappy effort people enforce but um yea theres my two sense the axis are only there single axis the dot doesn’t separate different axises btw

OpenGL doesn’t have sphere or cylinder primitives (it’s not a raytracer where those are common). The supported primitives are basically triangles, lines and points (with some variations).
So to render a sphere you need to approximate it with a triangle mesh and that method is also what you’d use to render a paraboloid: you calculate points on the surface in a more or less regular pattern and connect them to form triangles.
Haven’t tried it but searching for “paraboloid triangulation” or similar should turn up something useful.