How can I transform 3D position coordinates from a global to a local coordinate sytem?

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Jennifer Davies 2017-2-7

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https://ww2.mathworks.cn/matlabcentral/answers/323793-how-can-i-transform-3d-position-coordinates-from-a-global-to-a-local-coordinate-sytem

评论： Jayaram Theegala 2017-2-17

I'm stuck trying to transform 3D position coordinates from a global to a local coordinate system. My current code is below, but is incorrect and I don't know where the error is. Any help would be much appreciated.

%Marker coordinates in GCS
Marker1_GCS=[-941,549,1006];
Marker2_GCS=[-939,294,990];
Marker3_GCS=[-1127,461,1018];
Marker4_GCS=[-1127,375,1017];
%Define origin of LCS as between markers 3 and 4
origin_LCS=mean([Marker3_GCS;Marker4_GCS]);
%Define the y axis as from origin to the mean of markers 1 and 2
V=mean([Marker1_GCS;Marker2_GCS])-origin_LCS;
%The unit vector on the y axis is V/length(V) in the GCS
Y=V/sqrt((V(1)^2)+(V(2)^2)+(V(3)^2));
%Define a vector U from Marker 1 to Marker 2 as the plane of the x-axis
U=Marker2_GCS-Marker1_GCS;
%The unit vector on the Uu axis is U/length(U) in the GCS
Uu=U/sqrt((U(1)^2)+(U(2)^2)+(U(3)^2));
%Define the direction of the z axis (W) by the vector cross product of Uu and Y
W=cross(Uu,Y);
%The unit vector on the Z axis is W/length(W) in the GCS
Z=W/sqrt((W(1)^2)+(W(2)^2)+(W(3)^2));
%Define the direction of the x axis by the vector cross product of Y and Z
X=cross(Y,Z);
%Put these variables together into the transformation matrix.
%This is the transformation matrix to get from the global CS to the local pelvis coordinate system (Tgl)  
%Tgl is arranged:
%  Xx  Yx  Zx  Ox
%  Xy  Yy  Zy  Oy
%  Xz  Yz  Zz  Oz
%  0   0   0   1
Tgl=[X' Y' Z' origin_LCS';0 0 0 1];
%Calculate marker coordinates in LCS
Marker1_LCS=(Tgl*[Marker1_GCS';1])';
Marker2_LCS=(Tgl*[Marker2_GCS';1])';
Marker3_LCS=(Tgl*[Marker3_GCS';1])';
Marker4_LCS=(Tgl*[Marker4_GCS';1])';

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Jayaram Theegala 2017-2-17

If you want to transform your coordinates from global to local coordinate system, you can consider using MATLAB's "global2localcoord" function. For more information about this function, click on the following URL:

https://www.mathworks.com/help/phased/ref/global2localcoord.html

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