function out = rotate_z(X,phi)
%
%
% This function rotates a set of points around the z-axis by phi degrees.
% The x,y,z coordinates of the points are given in X.
%
% Peter Schall, 2003.
%
%
phi = phi*pi/180;
% Center the set of points
x0 = max(X(:,1)) / 2;
y0 = max(X(:,2)) / 2;
X(:,1) = X(:,1) - x0;
X(:,2) = X(:,2) - y0;
% Define Rotation matrix
M = [cos(phi) sin(phi) 0; -sin(phi) cos(phi) 0; 0 0 1];
% Rotate
X = X * M;
% Displace back
xmin = min(X(:,1));
ymin = min(X(:,2));
X(:,1) = X(:,1) - xmin + 1;
X(:,2) = X(:,2) - ymin + 1;
out = X;