How to convert local coordinate to Global Coordinate of a 3d plane?

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Swati Jain 2017-10-26

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https://ww2.mathworks.cn/matlabcentral/answers/363313-how-to-convert-local-coordinate-to-global-coordinate-of-a-3d-plane

编辑： Swati Jain 2017-10-26

Hi,

I have a 3d plane with equation: z+0.898x-0.443y=452, I got this equation by plane fit. This plane is inclined at a crazy angle and I want to make one of the point to origin and then make it flat and coincide it one of the axis (mostly x or y). My approach for doing this is first to translate one of the corner point to origin (which is working well I think) and then rotate plane about x-axis to make it parallel to xy-plane. and then give it one more rotation depending on situation.

For rotation, I find direction cosines of the plane and then rotate it by applying rotation matrix about x-axis. But its not working well. Could any one suggest what I am doing wrong or is there any better approach to do this. Figures of my original plane, translated plane and rotated plane about x and y axis are attached. My code is given below:

    arr = step_mask('Sigle_Step_Aug23-2017.xlsx','Sheet1', 'A:C');
    x=arr(:,1); y=arr(:,2); z=arr(:,3);
    % plane fitting
    [xnum,ynum]=size(arr);
    B = [arr(:,1:2), ones(xnum,1)] \ arr(:,3);
    a=B(1); 
    b=B(2);
    d=B(3);
    Z=a*x+b*y+d;
    [row,col]=size(Z);
    c=1;
    dist=sqrt(a^2+b^2+c^2);
    % calculation of direction cosines
    l=-a/dist; %cx
    m=-b/dist; %cy
    n=c/dist;% cz
    % calculation of angle 
    alfa=acosd(l); % w.r.t x-axis
    beta=acosd(m); %w.r.t. y-axis
    gamma=acosd(n); %w.r.t. z-axis
    A=zeros(row,3);
    A(:,1)=x;
    A(:,2)=y;
    A(:,3)=Z;
    % Translation Matrix
    A_trans=zeros(4,row);
    tx=12.87606300000000025818280846579; ty=28.084973999999998994780980865471; tz=-450.70078850208750509409583173692;
    T=[1 0 0 tx; 0 1 0 ty; 0 0 1 tz; 0 0 0 1];
    R1=[1 0 0 0; 0 cos_alfa -sin_alfa 0; 0 sin_alfa cos_alfa 0; 0 0 0 1];
    %rotation about x-axis
    R1=[1 0 0 0; 0 cosd(-alfa) -sind(-alfa) 0; 0 sind(-alfa) cosd(-alfa) 0; 0 0 0 1];
    % rotation about y-axis
    R2=[cosd(beta) 0 sind(beta) 0; 0 1 0 0; -sind(beta) 0 cosd(beta) 0; 0 0 0 1];
    for i=1:row
     %A_trans(:,i)=T*R1*[A(i,1);A(i,2);A(i,3);1];
     A_trans(:,i)=T*R1*R2*[A(i,1);A(i,2);A(i,3);1];
    end
    figure;
    plot3(A_trans(1,:),A_trans(2,:),A_trans(3,:),'.b'); grid on;
    xlabel('x-axis'); ylabel('y-axis'); zlabel('z-axis');
    set(gca, 'FontName', 'Arial');
    set(gca, 'FontSize', 12);
    title('Translated Plot', 'fontsize', 20);