A quick note: If you just want a curve which is in the shape of dfyb's rope picture, you'll get it using hyperbolic functions (which are somehow similar or analogious to trigonometric functions.) Don't ask me how, cause I heard this from my math teacher in hi school, and he didn't tell me anything more about hyperbolic functions. If some math guru knows more about using them, I'll be interested to hear and learn
Ooh, math! I can't wait to take a crack at this after my exam today.
Does Drasa's idea meet all the requirements? Because I'm sure that this is the best way go about this rope business. Wikipedia points out that the equation for a catenary is:
But I think we would need a more general form. Maybe
Then you get the two endpoints for the rope, plug them in for x and y to get values for x0 and y0. That leaves a which will basically determine the stiffness of your rope, so you can set it at whatever looks good.