rotation matrix 3D point data

Let' say , I have the 3d point data in format [xi yi zi] of 176 point as show in attachment file test.txt. The 3d point data is as below figure (shown in OXY plane):

Now, I want to find rotate the data around axis OZ , and 1 edge of the rectangle // Ox, the other //Oy as the below image. How to find new coordinate?

Answer 1

[ha ha]

FINAL ANSWER:

%%Load input 3D data
clear;clc;filename = 'test.txt'; inputfile = importfile(filename);
P = inputfile(:,1:3);%get data=coordinate(x,y,z) from set of data 
x = P(:,1) ; y = P(:,2) ;z = P(:,3) ; % get (x,y,z) coordinate  
x0 = x-mean(x) ; y0 = y-mean(y) ; z0 = z-mean(z) ; % remove mean 
P1 = [x0 y0 z0] ; %this step to bring the coord of P near to the origin. The new coord will be created
scatter3(P1(:,1),P1(:,2),P1(:,3),'b.');%plot new coord of P1
HA=[min(P1(:,1)) min(P1(:,2)) max(P1(:,3))+1];%just for better visualaztion
hold on;scatter3(HA(:,1),HA(:,2),HA(:,3),'g.');%just for better visualaztion
%%Finding  principal vector of 3D data P
PCA=pca(P);
e1=PCA(:,1)'; e2=PCA(:,2)' ;e3=PCA(:,3)';  % 3 principal vector(3 eigenvector) of "input data"
n1=[1 0 0]  ; n2=[0 1 0]   ; n3=[0 0 1];   % 3 unit vector Ox,Oy,Oz

transformation matrix from "e" space to "n" space

R=[e2;e1;e3];  % rotation matrix , match with xyz (e1//n2, e2//n1, e3//n3)
% R=[e1;e2;e3];  % rotation matrix , match with xyz (e1//n1, e2//n2, e3//n3) 
% R=[e3;e2;e1]; % If  e1//n3, e2//n2, e3//n1
%%Finding the new rotate data
newdata1=(R*P1')';%new data corresponding to P1 coordinate
hold on; scatter3(newdata1(:,1),newdata1(:,2),newdata1(:,3),'r.');
newdata=[newdata1(:,1)+mean(x),newdata1(:,2)+mean(y),newdata1(:,3)+mean(z)];
%%Plot the original & rotation 3D data
figure;scatter3(P(:,1),P(:,2),P(:,3),'b.');
hold on;scatter3(newdata(:,1),newdata(:,2),newdata(:,3),'r.');
HA=[min(P(:,1)) min(P(:,2)) max(P(:,3))+1];%just for better visualaztion
hold on;scatter3(HA(:,1),HA(:,2),HA(:,3),'g.');%just for better visualaztion
legend('original data(P)','rotated data(newdata)');title({'Plot the rotation matrix 3D point data';'(FINAL RESULT)'});

Answer 2

[KSSV]

You need to rotate your data by certain angle to achieve what you shown. You need to know Affine transformations. Check the below code.

coor = load('test.txt') ;
x = coor(:,1) ; y = coor(:,2) ; % (x,y) points  
x0 = x-mean(x) ; y0 = y-mean(y) ; % remove mean 
A = [x0 y0 ones(size(x))] ;  
th = 38 ;  % angle in degrees by which data is rotated 
T = [cosd(th) sind(th) 0 ; -sind(th) cosd(th) 0 ; 0 0 1] ;  % TRansformation matrix 
At = A*T ;  % rotate the dat 
At = [At(:,1)+mean(x) At(:,2)+mean(y)] ;  % Add mean to At

plot(x,y,'.r') ;
hold on
plot(At(:,1),At(:,2),'.b') ;

[Jan]

Where does the value of 38 deg come from?

[ha ha]

Where 38 degree come from? And, why you use only x,y coordinate. My data is 3D coordinate(in the question i just show the XY view)

[Jan]

@ha ha: Showing a 2D view was confusing. But the problem can be reduced to 2D easily by finding the plane nearest to all points at first and use e.g. fitgeotrans on the points projected into this plane.

[ha ha]

ok. agree, but where 38 degree come from? I guess this is the angle between rectangle & Oy?