So basically I need to calculate this
where L is defined as
I decided to go for (Wikipedia link below, I assume notation is reasonably understandable)
but, no matter how shameful that is, I am not sure how to quickly define a projection (of the curve) to Oxy plane...
P.S. Moreover, since all this means some specific circulation, how differently should L be described if I wanted it to go the other way (and get the opposite value)?