🚀 go-pugleaf

Sebastien Ferre wrote:
> 
> 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

Thanks, that should do it.

:)

Remco de Korte
http://www.xs4all.nl/~remcodek/softmach.html