You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: ideal_region_list.m
    path of file: ./repos/libDirectional/lib/external/eq_sphere_partitions/eq_partitions/private
    
    the code of the file until where you have to start completion: function r_regions = ideal_region_list(dim,N,c_polar,n_collars)
%IDEAL_REGION_LIST The ideal real number of regions in each zone
%
% List the ideal real number of regions in each collar, plus the polar caps.
%
% Given dim, N, c_polar and n_collars, determine r_regions,

    
function r_regions = ideal_region_list(dim,N,c_polar,n_collars)
%IDEAL_REGION_LIST The ideal real number of regions in each zone
%
% List the ideal real number of regions in each collar, plus the polar caps.
%
% Given dim, N, c_polar and n_collars, determine r_regions,
% a list of the ideal real number of regions in each collar,
% plus the polar caps.
% The number of elements is n_collars+2.
% r_regions[1] is 1.
% r_regions[n_collars+2] is 1.
% The sum of r_regions is N.
%
% r_regions = ideal_region_list(dim,N,c_polar,n_collars);

% Copyright 2004-2005 Paul Leopardi for the University of New South Wales.
% $Revision 1.10 $ $Date 2005-06-01 $
% Documentation files renamed
% $Revision 1.00 $ $Date 2005-02-12 $
%
% For licensing, see COPYING.
% For references, see AUTHORS.
% For revision history, see CHANGELOG.

r_regions = zeros(1,2+n_collars);
r_regions(1) = 1;
if n_collars > 0
    %
    % Based on n_collars and c_polar, determine a_fitting,
    % the collar angle such that n_collars collars fit between the polar caps.
    %
    a_fitting = (pi-2*c_polar)/n_collars;
    ideal_region_area = area_of_ideal_region(dim,N);    
    for collar_n = 1:n_collars
        ideal_collar_area = area_of_collar(dim, c_polar+(collar_n-1)*a_fitting, c_polar+collar_n*a_fitting);
        r_regions(1+collar_n) = ideal_collar_area / ideal_region_area;
    end