mirror of https://github.com/CGAL/cgal
19 lines
1.2 KiB
TeX
19 lines
1.2 KiB
TeX
This \cgal\ package provides functions to compute global informations
|
|
on the shape of a set of 2D or 3D objects such as points. It provides the computation of bounding boxes, centroids of point sets, barycenters of weighted point sets, as well as linear least squares fitting.
|
|
|
|
Linear least squares fitting approximates a set of objects by a linear
|
|
sub-space such as a line or a plane. Formally, given a set of points in $R^d$, linear least squares fitting amounts
|
|
to find the linear sub-space of $R^d$ which minimizes the sum of squared
|
|
distances from the points to their projection onto this linear sub-space. This
|
|
problem is equivalent to search for the linear sub-space which maximizes the
|
|
variance of projected points, the latter being obtained by eigen decomposition
|
|
of the covariance matrix. Eigenvectors corresponding to large eigenvalues are
|
|
the directions in which the data has strong component, or equivalently large
|
|
variance. If eigenvalues are the same there is no preferable sub-space.
|
|
This package implements the linear least squares fitting for
|
|
several objects of a \cgal\ 2D or 3D kernel: the best fit 2D line for 2D
|
|
point sets, and the best fit 3D line or plane for point and
|
|
triangle sets. The object sets are specified by iterator ranges of
|
|
containers.
|
|
|