rotate 3D plane to a new 2d coordinate system

Hello, I have been looking for this relatively simple issue but I haven't found a simple solution.

I have extracted a plane in 3D from a visualization software, so I have a matrix of coordinates: Coor_3D= [x1 x2 x3];.

As all the points are lying on the same plane, I was wondering how can I transform the above matrix to obtain a simple one in 2D, i.e = Coor_2D=[x1' x2' 0];

Thanks

Answer 1

[Matt J]

Once you decide on a target plane, find the axis where the targe tplane intersects your current plane. Then rotate around that axis using

http://www.mathworks.com/matlabcentral/fileexchange/30864-3d-rotation-about-shifted-axis

Answer 2

[Elena Figal]

Hello, I tried to recover the original 3D points from the transformation by using the same matrix T and a set of 2D points with a rows of zero and a row of 1, but my new 3D points are different from the originals, could you please help me?

[Johannes]

I want to know the same: Please open a new issue and let's see if someone finds the answer. Please let me know if you find something.

I am this far now:

Matt kindig does:

 T = [unitx(:), unity(:), unitz(:), origin(:); 0 0 0 1];
 C = [pnts, ones(N,1)]
 Coor_2D = T \ C'

To recover pnts out of Coor_2D, you have to solve the equation for C and then extract pnts. I think it should be:

 C = (T*Coor_2D)'

But this does not result in the correct points...any other idea?

Edit: I found the solution!

My mathematical solution was right, you just have to handle Coor_2D correctly to transform it backwards. Here's the code. You just need 2d-points (twoDpnts), the Transformation T and a row of zeros (zeros(size(twoDpnts,1)) and a row of ones (ones(size(twoDpnts,1),1)).

    Coor_2D_backwards = [twoDpnts zeros(size(twoDpnts,1),1) ones(size(twoDpnts,1),1)]'

    C = (T*Coor_2D_backwards)'

    pnts = C(:,1:3)

Best regards