Does anyone know how i could divide a segment in a specified number of sub-segments, so that they do have random lenghts but also have a min and max possible length?
That exactly correct. u and v are simply the two-dimensional variants of t. In fact, u and v are only called u and v by users, programmers tend to prefer s and t.
It is actually quite expensive (CPU cycle wise) to calculate an exact length along a curve. This is why almost no SDK functions use length based parameters.
While I understand the distinction between the length along the curve and the curve parameter, I've found t values extremely easy to work with. It took a while to sink in, but now I find it very intuitive to treat surfaces and curves as 2 and 1 dimensional intervals respectively.
I'm wishing I had some component, similar to subsurface, that could extract a subcurve based on supplied intervals. I think such a component would have been very helpful with this particular discussion. Currently, seems that I would have to shatter a curve, and then select out each portion.