CGAL users discussion list

[Pierre Alliez <>]

hi Gerd,

the documentation of the PCA component (user manual) says:
Given a set of objects, linear least squares fitting amounts to finding the linear sub-space which minimizes the sum of squared distances from all points composing the objects of the set, to their projection onto this linear sub-space. Such linear sub-space is obtained by so-called principal component analysis (PCA). PCA is defined as a transformation that transforms the objects to a new coordinate system such that the greatest variance by orthogonal projection of the objects comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on.

pierre

Pierre Alliez
INRIA Sophia Antipolis - Mediterranee 
Project-team GEOMETRICA 
http://www-sop.inria.fr/members/Pierre.Alliez/
Tel: +33 4 92 38 76 77
Fax: +33 4 97 15 53 95

ganders a écrit :

Dear CGAL-team,

I am searching for a method that calculates a fitting line in terms of a
total-least-squares (TLS) approach for 3D points. As input I would like to
provide a matrix with the x/y/z coordinates and as output I would like to
receive two points describing the straight line. It looks that
linear_least_squares_fitting_3 is exactly that what I am looking for. But I
am not sure if it really calculates the TLS or the different
linear-least-squares (LLS) solution. May I ask you to tell me what approach
is implemented (TLS or LLS)? Thanks a lot in advance.

Cheers,
Gerd