NAME

Math::Vector::BestRotation - best rotation to match to vector sets

INHERITANCE

VERSION

Version 0.005

SYNOPSIS

use Math::Vector::BestRotation;

my $foo = Math::Vector::BestRotation->new();

DESCRIPTION

INTERFACE

Constructors

new

Usage   : Math::Vector::BestRotation->new(%args)
Function: creates a new Math::Vector::BestRotation object
Returns : a Math::Vector::BestRotation object
Args    : initial attribute values as named parameters

Creates a new Math::Vector::BestRotation object and calls init(%args). If you subclass Math::Vector::BestRotation overload init, not new.

init

Usage   : only called by new
Function: initializes attributes
Returns : nothing
Args    : initial attribute values as named parameters

If you overload init, your method should also call this one. It provides the following functions:

• For each given argument (which has not been deleted by the previous actions) it calls the accessor with the same name to initialize the attribute. If such an accessor does not exist a warning is printed and the argument is ignored.

Public Attributes

matrix_r

This attributes holds a matrix built from the pairs of vectors and used to compute the desired orthogonal map. It is called R in the documentation and the underlying Research papers. The accessor is readonly. At startup, matrix_r is initialized with zeros.

Note that the matrix is stored internally as an array to speed up data acquisition. When you call the accessor a Math::MatrixReal object is created. This implies that such an object is not updated as you add more vector pairs. You have to call the accessor again to get a new object. Accordingly, changing of your retrieved matrix does not alter the underlying matrix stored in the Math::Vector::BestRotation object.

Methods for Users

add_pair

Usage   : $obj->add_pair([1, 2, 3], [0, 7, 5])
Function: updates matrix_r
Returns : nothing
Args    : a pair of vectors, each as an ARRAY reference

The orthogonal map computed by this module will try to map the first vector onto the second. This method uses the new vector pair to update the matrix R which is later used to compute the best map. The vectors are discarded afterwards and can therefore not be removed once they have been added.

In some applications, very many vector pairs will be added making this the rate limiting step of the calculation. Therefore, no convenience functionality is offered. For example, the method strictly requires ARRAY references. If your vectors are stored e.g. as Math::VectorReal objects you have to turn them into ARRAY references yourself. Furthermore, no error checking whatsoever is performed. The method expects you to provide valid data.

best_orthogonal

Usage   : $matrix = $obj->best_orthogonal
Function: computes the best orthogonal map between the vector sets
Returns : a Math::MatrixReal object
Args    : none

Computes the best orthogonal map between the two vector sets, i.e. the orthogonal map that minimizes the sum of the squared distances between the image of the first vector of each pair and the corresponding second vector. This map can be either a rotation or a rotation followed by a reflection.

The representing matrix of the found map is returned in form of a Math::MatrixReal object.

best_rotation

Usage   : $matrix = $obj->best_rotation
Function: computes the best rotation between the vector sets
Returns : a Math::MatrixReal object
Args    : none

This is identical to best_orthogonal except that it finds the best special orthogonal map (this means that the determinant is +1, i.e. the map is a true rotation).

The method computes the best rotation between the two vector sets, i.e. the rotation that minimizes the sum of the squared distances between the image of the first vector of each pair and the corresponding second vector.

The representing matrix of the found map is returned in form of a Math::MatrixReal object.

best_flipped_rotation

Usage   : $matrix = $obj->best_flipped_rotation
Function: computes the best rotation combined with a reflection
Returns : a Math::MatrixReal object
Args    : none

This is identical to best_orthogonal except that it finds the best orthogonal map with determinant is -1. I do not know why one would want that, but the method is included for completeness.

The representing matrix of the found map is returned in form of a Math::MatrixReal object.

clear

Usage   : $obj->clear
Function: resets the object
Returns : nothing
Args    : none

This method resets matrix_r to the null matrix (all entries equal zero). This enables you to start from scratch with two new vector sets without destroying the object.

DIAGNOSTICS

Exceptions

Warnings

BUGS AND LIMITATIONS

No bugs have been reported, but the code should be considered as beta quality.

Please report any bugs or feature requests to bug-math-vector-bestrotation at rt.cpan.org, or through the web interface at http://rt.cpan.org/NoAuth/ReportBug.html?Queue=Math-Vector-BestRotation. I will be notified, and then you will automatically be notified of progress on your bug as I make changes.

AUTHOR

Lutz Gehlen, <perl at lutzgehlen.de>

ACKNOWLEDGEMENTS

The algorithm implemented here is based on two research papers by Wolfgang Kabsch, Max-Planck-Institut für Medizinische Forschung, Heidelberg, Germany:

[1] Kabsch, W. (1976). A solution for the best rotation to relate two sets of vectors. Acta Cryst., A32, 922

[2] Kabsch, W. (1978). A discussion of the solution for the best rotation to relate two sets of vectors. Acta Cryst., A34, 827-828

LICENSE AND COPYRIGHT

Copyright 2010 Lutz Gehlen.

This program is free software; you can redistribute it and/or modify it under the terms of either: the GNU General Public License as published by the Free Software Foundation; or the Artistic License.

See http://dev.perl.org/licenses/ for more information.

cpanm Math::Vector::BestRotation

perl -MCPAN -e shell
install Math::Vector::BestRotation