Tilted 3D model orientation

The code I am writing opens an interface into which I can upload 3D models. The easiest way to describe the models is as stick-shaped, so much longer on one plane that the others. I am trying to write a script that will orientate each 3D model however, I am struggling a bit because the models are uploaded in different original orientations. So I need to write a script that will put all the models into the same general position on x, y, and z axes before the rest of the orientation program can run. Ideally being parallel to the x-axis. I've put the script that I was trying to use below but I'm not sure if its the best solution.

Any help would be greatly appreciated!

function [x, y, z] = correctZTilt(oc)
% oc - original coordinates
%Find centroid of the model
centroid = mean(oc, 1);
%Step 1: Align the centroid with the x-z plane
angle_x_tilt = atan2(centroid(2), centroid(3)); % Angle to align the centroid with the x-z plane
R_align_xz = [1, 0, 0;
    0, cos(angle_x_tilt), -sin(angle_x_tilt);
    0, sin(angle_x_tilt), cos(angle_x_tilt)];
aligned_oc = (R_align_xz * oc')';
%Step 2: Align the primary axis of the model with the x-axis
% Assuming that the primary axis of the model is the z-axis
angle_y_tilt = -atan2(centroid(1), centroid(3)); % Angle to align the centroid with the x-axis
R_align_x = [cos(angle_y_tilt), 0, sin(angle_y_tilt);
    0, 1, 0;
    -sin(angle_y_tilt), 0, cos(angle_y_tilt)];
rotated_oc = (R_align_x * aligned_oc')';
%Extract the coordinates after correction
x = rotated_oc(:, 1);
y = rotated_oc(:, 2);
z = rotated_oc(:, 3);
end
% Sample 3D model represented by points
oc = [1, 2, 3;
    4, 5, 6;
    7, 8, 9;
    % Add more points here...
    ];
% Correct the tilt of the  model
[x, y, z] = correctZTilt(oc);

[Bruno Luong]

" but I'm not sure if its the best solution."

First question: Does your function aligns correctly the centroid with x-axis? Meaning does it perform as your expectation?

Beside that I see clearly a problem.

An object orientation has 3 DOFs. Your code estime 2DOFs to align the centroid with x-axis. So there is 1 DOF that is not estimated just by align the centroid with x-axis.

Also rotation about the origin seems kind of arbitrary to me.

[Bruno Luong]

I answer my own question "First question: Does your function aligns correctly the centroid with x-axis? "

The answer is No; I fix the original code to achieve that goal as see below.

My other comments on DOFs still valid. Align centroid with x-axis is not enough to resolve and restore orientation. The (new) points can still freely rotate about the x-axis, and the centroid remains on this axis. This is the missing DOF.

% Sample 3D model represented by points
oc = [1, 2, 3;
      4, 5, 6;
      7, 8, 9;
      % Add more points here...
     ];
% Correct the tilt of the  model
[x, y, z] = correctZTilt(oc);

% Check if the new coordinates has centroid aligne with x-axis
mean(x)

ans = 8.7750

mean(y)

ans = -3.7007e-16

mean(z)

ans = 5.5511e-16

function [x, y, z] = correctZTilt(oc)
    % oc - original coordinates
    %Find centroid of the model
    centroid = mean(oc, 1);
    %Step 1: Align the centroid with the x-z plane
    angle_x_tilt = atan2(centroid(2), centroid(3)); % Angle to align the centroid with the x-z plane
    R_align_xz = [1, 0, 0;
                  0, cos(angle_x_tilt), -sin(angle_x_tilt);
                  0, sin(angle_x_tilt), cos(angle_x_tilt)];
    aligned_oc = (R_align_xz * oc')';

    
    %Step 2: Align the primary axis of the model with the x-axis
    % Assuming that the primary axis of the model is the z-axis

    % These two lines are modified by Bruno Luong
    aligned_centroid = (R_align_xz * centroid')'; 
    angle_y_tilt = atan2(aligned_centroid(3), aligned_centroid(1)); % Angle to align the NE centroid with the x-axis

    R_align_x = [cos(angle_y_tilt), 0, sin(angle_y_tilt);
                 0, 1, 0;
                 -sin(angle_y_tilt), 0, cos(angle_y_tilt)];
    rotated_oc = (R_align_x * aligned_oc')';
    %Extract the coordinates after correction
    x = rotated_oc(:, 1);
    y = rotated_oc(:, 2);
    z = rotated_oc(:, 3);
end

Answer 1

[Star Strider]

The rotate function could be worth exploring.

Example —

[X,Y,Z] = peaks(50);

figure
hs1 = surf(X,Y,Z+10);
hold on
hs2 = surf(X,Y,Z);
hs3 = surf(X,Y,Z-15);
hold off
grid on

rotate(hs1, [1 1 0], 30)
rotate(hs2, [0 1 0.5], 30)
rotate(hs3, [0.5 0 1], 30)

Once the surf plots are formed, they can be shifted or rotated however you want. (It will likely take a bit of experimentation to get them the way you want them.) The (1x3) vectors also do not need to be limited to values of 0 or 1, since they can also be decimal fractions (as illustrated).

.

Answer 2

[Chhayank Srivastava]

Hi, you can look into MATLAB view command

https://www.mathworks.com/help/pde/ug/pde.discretegeometry.rotate.html

https://www.mathworks.com/help/matlab/ref/view.html

https://www.mathworks.com/help/robotics/ref/eul2rotm.html

You can use a rotate and eul2rotm command, followed by view command.

function [x, y, z] = correctZTilt(oc)
    % oc - original coordinates
    %Find centroid of the model
    centroid = mean(oc, 1);
    %Step 1: Align the centroid with the x-z plane
    angle_x_tilt = atan2(centroid(2), centroid(3));
    rotation_matrix =  eul2rotm([angle_x_tilt * 180 / pi,0,0]) %rotation matrix
    point_new = oc + [oc-centroid]* rotation_matrix 

    
    %Extract the coordinates after correction
    x = point_new(:, 1);
    y = point_new(:, 2);
    z = point_new(:, 3);
end
% Sample 3D model represented by points
oc = [1, 2, 3;
      4, 5, 6;
      7, 8, 9;
      % Add more points here...
     ];
% Correct the tilt of the  model
[x, y, z] = correctZTilt(oc);
% View 
view([1,1,1])

Let me know if this works out for you.