symmetric ranges of curve division on an oloid

Question

taken from wikipedia , I drew an Oloid by using the functions

with

;

;

and

with

;

;

If I use any equal spaced range of t(x) on ; I will end up with an unequal range t(y), which looks like this:

My goal is to have a symmetric, spacing on both of the curves like in this model:

I can only remap the values of t(x).

What function do I need to apply on the range t(x) to get a symmetric curve division also on t(y) ? Any expert out there? Please help.

Best,

Phillip