Rotate 3-D Point Cloud Using Rigid Transformation

Hi! I need to rotate a point cloud (or .txt file of the type rx3) by a certain angle theta with respect to the x-axis (or y- or z-axis) while keeping its center of gravity G (already calculated) fixed.

I am using the rotation matrix but I am unclear how to keep the center of gravity fixed and rotate only with respect to a given axis.

angle = 180;
angle_rad = deg2rad(angle);
rot_matrix = [ cos(angle_rad)    sin(angle_rad)     0       0  ; ...
              -sin(angle_rad)    cos(angle_rad)     0       0  ; ...
                    0                   0           1       0  ; ...
                    0                   0           0       1  ];

I had initially tried using this code taken from this link but MatLab reports this error: "Unrecognized function or variable 'rigidtform3d'."

ptCloud = pcread('teapot.ply');
figure
pcshow(ptCloud)
xlabel('X')
ylabel('Y')
zlabel('Z')

rotationAngles = [0 0 45];
translation = [0 0 0];
tform = rigidtform3d(rotationAngles,translation)

ptCloudOut = pctransform(ptCloud,tform);
figure
pcshow(ptCloudOut)
xlabel('X')
ylabel('Y')
zlabel('Z')

Thanks to those who can answer me!

p.s. Otherwise if someone can send me this function ("rigidtform3d") since it's like I don't have it!

Answer 1

[Matt J]

Using AxelRot from this File Exchange download,

https://www.mathworks.com/matlabcentral/fileexchange/30864-3d-rotation-about-shifted-axis?s_tid=srchtitle

axisVector=[0,0,1]; %rotation about z-axis

xyz=AxelRot(ptCloud.Location',angle, axisVector, mean(ptCloud.Location,1) )';

ptCouldOut=pointCloud(xyz);

Answer 2

[Bora Eryilmaz]

• First translate the point cloud to the origin using a translation of -G.
• Rotate the point cloud around an axis.
• Translate it back to its center of gravity using a translation of G.

Answer 3

[Torsten]

angle = 180;
angle_rad = deg2rad(angle);
rot_matrix = [ cos(angle_rad)    -sin(angle_rad)    0   ; ...
               sin(angle_rad)    cos(angle_rad)     0  ; ...
               0                   0           1  ];
ptCloud = pcread('teapot.ply')

ptCloud = 
  pointCloud with properties:

     Location: [41472×3 single]
        Count: 41472
      XLimits: [-3 3.4340]
      YLimits: [-2 2]
      ZLimits: [0 3.1500]
        Color: []
       Normal: []
    Intensity: []

gc = mean(ptCloud.Location,1)

gc = 1×3

0.0372 0.0000 1.7251

figure
pcshow(ptCloud)
xlabel('X')
ylabel('Y')
zlabel('Z')

gc = mean(ptCloud.Location,1)

gc = 1×3

0.0372 0.0000 1.7251

ptCloudOut = ptCloud.Location - gc;
ptCloudOut = (rot_matrix*ptCloudOut.').';
ptCloudOut = ptCloudOut + gc;
gc_transformed = mean(ptCloudOut,1)

gc_transformed = 1×3

0.0372 -0.0000 1.7251

figure
pcshow(ptCloudOut)
xlabel('X')
ylabel('Y')
zlabel('Z')