MATLAB: Converting 3D to 2D cloud of points

2d3ddimensionrotationtranslation

I am trying to convert a set of data which is a cloud of points from 3D to 2D, I am using this code:
% Function from 3D to 2D
function [D,R,T]=dimred(X)
  T = repmat(mean(X),[size(X,1),1]);
  XX = X-T;
  [R,N]=eig(XX'*XX);
  D=XX*R;
  D=D(:,2:end);
  Q=[zeros(size(D,2),1) eye(size(D,2))];
  R=Q*R';
return
% 3D to 2D
[nodes_2D,R,T]=dimred(newnodes1) % R = rot matrix, T = Translation matrix
The data correctly converts to 2D, in this case, looking at the image the 3D points are rotated to the left, but for a different cloud of points it rotates it to the right. My question is the next, is there any way of forcing to apply the rotation always in the same direction? (without manually reversing the 2D red plot).
I have attached the figure and the .mat containing the cloud of points in 3D.
Thank you for any help.

Best Answer

This uses AxelRot (Download),
normal=null(XX);
normal=normal(:,end)*sign(normal(1,end));
rotaxis=-cross([0,0,1].',normal);
theta=asind(norm(rotaxis));
[D,R,~] = AxelRot(XX.', theta, rotaxis, []);
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