Re: best line through a set of 3D points

*To*: mathgroup at smc.vnet.net*Subject*: [mg18387] Re: best line through a set of 3D points*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Wed, 7 Jul 1999 00:10:55 -0400*Organization*: Universitaet Leipzig*References*: <7lcfio$1kv@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, at first make some data data=Table[{t+0.2*Random[],2t+0.3*Random[],t/2+0.1*Random[]},{t,1,10,0.1}]; and then fit the components of the vector to linear functions pf=Fit[#,{1,t},t] & /@ Transpose[data] Hope that helps Jens Maarten.vanderBurgt at icos.be wrote: > > Dear all, > > This is not strictly a mathematica question but someone might have a > solution in the form of a mathematica function or so. > > I have a set of 3d points, DATA = {{x1,y1,z1},{x2,y2,z3},...}, roughly > occupying a sigar shaped volume in the 3D space. > I want to find the line that best fits these points. > > I tried a least squares approach: I assumed the line was going through the > average off all the points in DATA and then I tried to find a vector in the > direction of the line by minimizing the sum of the squares of the distances > from the points to the line. > For some reason I end up with a set of 3 equations which only solution is > (0,0,0). There is probably some sensible reason for this but I did not > manage to figure out why. Maybe someone else knows? > thanks a lot > > Maarten