🚀 go-pugleaf

In article <35DFD6E7.F2A5DA30@xs4all.nl>, Remco de Korte <remcodek@xs4all.nl> writes:
> Matthias Weiss wrote:

> When the radius is variable as well as the angle between the two lines
> connecting the center of the circle with both points the length of the
> arc can be a constant.
> I was just suggesting circles because I think it's the most
> straigtforward solution. It could also be a parabole or something like
> that but I'm afraid that'll get far to complicated for what I want and
> besides you'd have more then one (actually two) solutions.
> (With a circle you'd have only two - if any).
> 

If I have well understood, you want to find the radius or, better, the equation of the circle that match the tube joining both points ?

Let d be the distance between the two points, L the length of the tube, R the radius of the circle and A the angle between the two lines connecting the center of the circle with both points.

We have      L = A.R            
   and       sin(A) = d/(2.R)  

So R is defined by:  R = d/(2.sin(L/R))  (1)
and A is defined by: A = 2.L.sin(A)/d    (2)

With the radius and the coordinates of both points, it's easy to find the equation of the circle. The only problem is that (1) and (2) are reflexive. But I think it's possible to solve them by giving any initial value to R or A and by applying (1) or (2)  until R or A values don't move too much. Just try it...

Sebastien Ferre