Re: Intersection line and its error of two best fitting planes

[lynx . abraxas]

Dear Leo!


Many thanks for Your reply.

On 14/05/10 21:25:46, Leo Butler wrote:
> < 2010/5/14 <address@hidden>
> <       I have two sets of measured points (in 3D). Points of each set are 
> supposed to
> <       sit on a plane.
> <       Now I want to find the intersection line and its  directional  and  
> positional
> <       error.
> < The best fitting plane could be found with linear regression. The plane is 
> in vector 'B', errors etc can be found in variables 'Residuals' and 'STATS'
>  
> It looks like a linear regression problem, but it's not.
> An affine plane P in R^3 is determined by a unit normal n and
> a constant c such that


I need some time to catch up on this with some math books;-) And to understand
Your octave code.
For that: Waht would be the name  of  the  method  You  use  for  solving  the
problem?
Also I wonder what is a? It's not defined in Your code.


Is the resulting plane the same for both methods and only the error differ?
Looking  at  the nice visualization of Stefans solution, I'd say it looks well
fitted!

Still I'm not sure how the error of the planes (what ever method  used)  would
go  into  the  error  of  the orientation and displacement of the intersection
line.

As a physicist I just had the idea of doing it like this:

1. Take just three points of each set to define two planes (without error).
2. Find the intersection line (without error) of these two planes.
3. Do this for all possible combinations of three points of each set
4. Calculate a mean direction vector of the intersection line by adding up all
normalized direction vectors from the iteration.
5. Divide  the  mean  direction  vector by the number of vectors added and the
inverse of its lenght should be a measure of its error.
6. Do the same for the displacement vector.

But I'm not sure if this procedure is correct to determin  the  error  of  the
orientation and displacement vector.

Anyway,  would  this whole procedure be an appropriate way at all to solve the
problem?

Many thank for Your help!
Lynx