How Do I Move a Set of (x,y,z) Points so they Align with the X-Y Plane?

Hi all,

I have a large set of (x,y,z) data points creating a “bumpy” (non-flat) surface that I am trying to get to “flatten out” onto the x-y plane without losing any integrity of the surface features.

I tried following the suggestion here http://www.mathworks.com/matlabcentral/answers/66051-how-do-i-move-a-cloud-of-points-in-3d-so-that-they-are-centered-along-the-x-axis, but the asker was specific to ask for their data to follow along the x axis. I am trying to get my data to fall along the x-y plane in whatever angle it originates at. It does not necessarily need to be centered at zero or anything (in my example it is, but I would not like it to), just flattened to the x-y plane using only the given (x,y,z) data.

With the help of the above suggestion, I’ve tried this code:

XYZ = [11 11 11
       12 12 13
       13 13 12
       14 14 15
       15 15 17
       16 16 17
       17 17 18
       18 18 18
       19 19 20
       10 12 12
       11 13 11
       12 14 13
       13 15 14
       14 16 19
       15 17 13
       16 18 15
       17 19 18
       18 20 17
       12 10 11
       13 11 13
       14 12 14
       15 13 12
       16 14 17
       17 15 19
       18 16 18
       19 17 15
       20 18 19];

X = XYZ(:,1);
Y = XYZ(:,2);
Z = XYZ(:,3);

% Plot the raw data
scatter3(X,Y,Z,'b','LineWidth',5) % blue dots
xlabel('X-Axis','FontSize',14,'FontWeight','bold')
ylabel('Y-Axis','FontSize',14,'FontWeight','bold')
zlabel('Z-Axis','FontSize',14,'FontWeight','bold')

xyz0=mean(XYZ);
A=bsxfun(@minus,XYZ,xyz0); % center the data at zero

% Find the direction of most variance using SVD and rotate the data to make 
% that the x-axis

[U,S,V]=svd(A,0);
A_rot = A*V; % V(:,1) is the direction of most variance
hold on
scatter3(A_rot(:,1),A_rot(:,2),A_rot(:,3),'g','LineWidth',5); % green dots

This code centers the data at (0,0,0), flattens it out, and rotates it in the direction of most variance (close to the x-axis) while making use of the svd function. I’m looking to see if I can keep the plot in the same position at its same x-y position, but flatten it down from its z position. I don’t believe I can simply adjust the data by a specific angle, because other surfaces may not be at a nice easy angle and I will not always know what the angle is. It simply needs to be moved down with the same surface features into the x-y plane.

If anybody can help me out on this, it would be very much appreciated, and thank you in advance.