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: eq_point_set_polar_symm.m
    path of file: ./repos/libDirectional/lib/external/eq_sphere_partitions/eq_partitions
    
    the code of the file until where you have to start completion: function points_s = eq_point_set_polar_symm(dim, N, deleteHalf, varargin)
%EQ_POINT_SET_POLAR Center points of regions of an EQ partition
%
%Syntax
% points_s = eq_point_set_polar(dim,N,options);
%
%Description
% POINTS_S = EQ_POINT_SET_POLAR(dim,N) does the following:
% 1) uses the recursive zonal equal area sphere partitioning algorithm to
% partition S^dim (the unit sphere in dim+1 dimensional space) into N regions
% of equal area and small diameter, and
% 2) sets POINTS_S to be an array of size (dim by N), containing the center
% points of each region. Each column of POINTS_S represents a point of S^dim,
% in spherical polar coordinates.
%
% The arguments dim and N must be positive integers.
%
% POINTS_S = EQ_POINT_SET_POLAR(dim,N,'offset','extra') uses experimental extra
% offsets for S^2 and S^3 to try to minimize energy. If dim > 3, extra offsets
% are not used.
%
% POINTS_S = EQ_POINT_SET_POLAR(dim,N,extra_offset) uses experimental extra

    
function points_s = eq_point_set_polar_symm(dim, N, deleteHalf, varargin)
%EQ_POINT_SET_POLAR Center points of regions of an EQ partition
%
%Syntax
% points_s = eq_point_set_polar(dim,N,options);
%
%Description
% POINTS_S = EQ_POINT_SET_POLAR(dim,N) does the following:
% 1) uses the recursive zonal equal area sphere partitioning algorithm to
% partition S^dim (the unit sphere in dim+1 dimensional space) into N regions
% of equal area and small diameter, and
% 2) sets POINTS_S to be an array of size (dim by N), containing the center
% points of each region. Each column of POINTS_S represents a point of S^dim,
% in spherical polar coordinates.
%
% The arguments dim and N must be positive integers.
%
% POINTS_S = EQ_POINT_SET_POLAR(dim,N,'offset','extra') uses experimental extra
% offsets for S^2 and S^3 to try to minimize energy. If dim > 3, extra offsets
% are not used.
%
% POINTS_S = EQ_POINT_SET_POLAR(dim,N,extra_offset) uses experimental extra
% offsets if extra_offset is true or non-zero.
%
%Notes
% Each region is defined as a product of intervals in spherical polar
% coordinates. The center point of a region is defined via the center points
% of each interval, with the exception of spherical caps and their descend