angle2dcm: How to reference direction cosine matrix output?

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Kurt 2023-3-29

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编辑： Kurt 2023-4-3

I have seen lots of discussion on how to call angle2dcm, but almost none on how to use it to transform the coordinates of an object.

Here is my sample code. I create an ellipse in 3D and apply pitch, roll and yaw angles to it. How do I pry the results out of angle2dcm?

function tilt_ellipse()
    xc = 50;
    yc = 50;
    zc = 50;
    a = 25;
    b = 50;
    m = 1000;
    x = zeros(m,1);
    y = zeros(m,1);
    z = zeros(m,1);
    dtor = 0.01745      % degrees to radians
    theta = linspace(0,2*pi,m);
    
    for k = 1:m     % define ellipse
        x(k) = a * cos(theta(k));
        y(k) = b * sin(theta(k));
    end
    
    pitch = input('Enter the pitch in degrees');
    roll = input('Enter the roll in degrees');
    yaw = input('Enter the yaw in degrees');
    
    dcm = angle2dcm(pitch * dtor, roll * dtor, yaw * dtor, "ZYX");  % is this the correct rotation order?
    
    xr = ?      % how do I get the vector rotations?
    yr = ?
    zr = ?
    
    plot3(xr+xc, yr+yc, zr+zc);
    grid on;
    hold on;
    axis equal;
end

This should work for any object that I apply the transformations to (vector, ellipse, cone, etc.)

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Kurt 2023-3-30

This code is an extension of the 2D example referenced here, which uses a cosine matrix for transformation. I'm looking for the generalized 3D solution using angle2dcm().

https://www.mathworks.com/matlabcentral/answers/342148-how-can-i-rotate-an-ellipse?s_tid=answers_rc1-2_p2_MLT

Kurt 2023-3-31

在 MATLAB Online 中打开

Hint: If pitch, roll and yaw are zero, I get the identity matrix:

[1 0 0
 0 1 0
 0 0 1]

Is this a clue as to where I find my results? i.e., m[(1,1), (2,2), (3,3)]?

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Answer 1

James Tursa 2023-3-31

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1937434-angle2dcm-how-to-reference-direction-cosine-matrix-output#answer_1206074

编辑：James Tursa 2023-3-31

在 MATLAB Online 中打开

Does this do what you want:

x = zeros(1,m); % reorder these to row vectors
y = zeros(1,m);
z = zeros(1,m);
:
xyz = [x;y;z]; % matrix with column vectors of (x,y,z) points
xyzr = dcm * xyz; % rotate them
xr = xyzr(1,:); % pick off x,y,z components
yr = xyzr(2,:);
zr = xyzr(3,:);

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Kurt 2023-3-31

编辑：Kurt 2023-4-3

That worked. Thanks!

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angle2dcm: How to reference direction cosine matrix output?

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