From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci)
Subject: Re: Fitting a cylinder to a set of 3-D points
Date: 16 Feb 1999 13:19:23 GMT
Newsgroups: sci.math.num-analysis
To: kluskens@crystal.nrl.navy.mil (Michael Kluskens)

In article <kluskens-1202991632330001@nazgul.nrl.navy.mil>,
 kluskens@crystal.nrl.navy.mil (Michael Kluskens) writes:
|> I need an algorithm to fit a cylinder to a set of 3-D points.  Anyone got
|> one already or good ideas.  I have some ideas I'm going to try out as soon
|> as possible.
|> 
netlib/odrpack is a solution for your problem. see also 
http://plato.la.asu.edu/guide.html 
for a gui. 
however, this is a computational expensive approach. for a cylinder along  
the z-axis fitting a circle to the (x,y) -data of your points would be sufficient
and this is quite simple:
minimize 
sum_i {(x_i-x0)^2+(y_i-y0)^2-r2}^2 
with respect to x0,y0,r2=(r^2), using a standard nonlinear
least squares code (e.g. minpack in netlib or nlscon from elib.
 for a cylinder in general position we
need also to find its axis of symmetry. this amounts in a linear transformation
of 3-space, which could be added easily to the model above. 
if however you think about
an elliptical cylinder, things become much more complicated and in this case
i would prefer using odrpack. 
hope this helps
peter