Large amount of coordinates transformation in 3D

Hello,

I am trying to perform transformation of large amount of coordinates, but firstly I am doing it on this small example:

I would like to rotate by 10 degrees about y axis x y z coordinates ( size is 8 x 3). How to perform such rotation? I have found rotation matrices but they are 3x3 and if I want to mupliply matrices [3x3] * [8x3] it is not possible.

Therefore I would like to ask you for help.

theta = 10;
A = [0 0 0; 1 1 1; 0 0 1; 1 1 0; 1 0 1; 0 1 0; 0 1 1; 1 0 0];
x = A(:,1);  y = A(:,2);  z  = A(:,3);

RY = [
    cosd(theta)     0     sind(theta)
    0 1 0;
    -sind(theta)     0     cosd(theta)];
ARY = RY*A;

Best regards

Michal

Answer 1

[Chunru]

Transpose A:

theta = 10;
A = [0 0 0; 1 1 1; 0 0 1; 1 1 0; 1 0 1; 0 1 0; 0 1 1; 1 0 0]';
x = A(:,1);  y = A(:,2);  z  = A(:,3);
RY = [
    cosd(theta)     0     sind(theta)
    0 1 0;
    -sind(theta)     0     cosd(theta)];
ARY = RY*A

ARY = 3×8

0 1.1585 0.1736 0.9848 1.1585 0 0.1736 0.9848 0 1.0000 0 1.0000 0 1.0000 1.0000 0 0 0.8112 0.9848 -0.1736 0.8112 0 0.9848 -0.1736

A

A = 3×8

0 1 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0

Answer 2

[Walter Roberson]

theta = 10;
M = makehgtform('yrotate', deg2rad(theta))

M = 4×4

0.9848 0 0.1736 0 0 1.0000 0 0 -0.1736 0 0.9848 0 0 0 0 1.0000

A = [0 0 0; 1 1 1; 0 0 1; 1 1 0; 1 0 1; 0 1 0; 0 1 1; 1 0 0];
x = A(:,1);  y = A(:,2);  z  = A(:,3); 
c = zeros(size(x));

xyzc = [x, y, z, c];
newxyz = xyzc * M

ans = 8×4

0 0 0 0 0.8112 1.0000 1.1585 0 -0.1736 0 0.9848 0 0.9848 1.0000 0.1736 0 0.8112 0 1.1585 0 0 1.0000 0 0 -0.1736 1.0000 0.9848 0 0.9848 0 0.1736 0

newx = newxyz(:,1); newy = newxyz(:,2); newz = newxyz(:,3);

Answer 3

[Remo Pillat]

The other answers are good. One more possibility is to use the so3 object in MATLAB, which represents a 3D rotation matrix and has a lot of built-in functionality for converting between different rotation representations and for applying rotations to vectors. You also don't have to do any explicit transposes, since the transform function handles that internally.

For your example, the code would be fairly simple:

theta = 10;
A = [0 0 0; 1 1 1; 0 0 1; 1 1 0; 1 0 1; 0 1 0; 0 1 1; 1 0 0];

% Create 3D rotation object with rotation around y axis
RY = so3(deg2rad(theta), "roty")

RY = so3
    0.9848         0    0.1736
         0    1.0000         0
   -0.1736         0    0.9848

% Apply rotation to original matrix of vectors
ARY = transform(RY, A)

ARY = 8×3

0 0 0 1.1585 1.0000 0.8112 0.1736 0 0.9848 0.9848 1.0000 -0.1736 1.1585 0 0.8112 0 1.0000 0 0.1736 1.0000 0.9848 0.9848 0 -0.1736

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[Paul]

Hi Remo,

The linked doc page for so3 is incorrect. Compare the the signs of the (2,3) and (3,2) terms for "rotx" to Rx(phi) in the Description.

phi = 45*pi/180;
so3(phi,"rotx")

ans = so3
    1.0000         0         0
         0    0.7071   -0.7071
         0    0.7071    0.7071

Also, using psi for a rotation around y and theta for a rotation around z as on that doc page is nonstandard, is it not?