function r = latticepointsaroundorigin(num)
% r = latticepointssorted(n) retruns a list of lattice points,
% in the order of  distance from the origin and polar angle.
% Uncomment the last three lines to show the locations of the points.
% (ja.doukaku.org Q65)
rg = ceil(sqrt(num/pi));
[x y] = meshgrid(-rg:rg);
pts = [x(:) y(:) sqrt(x(:).^2+y(:).^2) atan2(-y(:),-x(:))];
r = sortrows(pts, [3,4]);
r = r(1:num,1:2);
% figure
% axis([-rg rg -rg rg])
% text(r(:,1),r(:,2),num2cell(1:num))