rotation matrix 3D point data

34 views (last 30 days)
ha ha on 11 May 2018
Edited: ha ha on 24 Nov 2018
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?

ha ha on 11 May 2018
Edited: ha ha on 11 May 2018
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)'});

KSSV on 11 May 2018
You need to rotate your data by certain angle to achieve what you shown. You need to know Affine transformations. Check the below code.
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') ;
ha ha on 11 May 2018
ok. agree, but where 38 degree come from? I guess this is the angle between rectangle & Oy?