Setting up Matrix in a Different way

I have a Matrices as:

A=[1 10 12;2 12 3; 3 15 4; 4 16 7; 5 18 9; 6 10 10; 7 12 9; 9 5 6];

B=[3 9 8; 4 8 3; 5 2 5; 7 10 2; 8 9 7; 9 12 10; 10 5 6];

Where Colum 1 is the index Colum 2 is the x and Colum 3 is the y. I would like to match each index of the 2 matrices and set the x and y values in Matirx C. Here Colum 1 is the A matrix values and Colum 2 is the B matrix values that is negative

The solution should be something like this:

C=[10 0;12 0; 12 0; 3 0; 15 -9; 4 -8;16 -8; 7 -3; 18 -2; 9 -5; 10 0; 10 0; 12 -10; 9 -2;0 -9; 0 -7;5 -12; 6 -10; 0 -5;0 -6] 

How would I do this?

[KSSV]

It is not clear how you framed C.

[A]

the A matrix is [index xa ya] and the B matirx is [index xb yb] so the C matirx should be like [xa -xb; ya -yb]

[Stephen23]

@AB: why does your example D matrix have the follow rows occuring only once:

0    -9
0    -7

even though the corresponding row occurs twice in B:

8     9     7
8     9     7

What is the rule for ignoring one of those rows of B ?

[A]

@Stephen Sorry that was a mistake, I fixed it

Answer 1

[the cyclist]

This does what you want via a straightforward loop. I expect there is a slicker way to do this.

A=[1 10 12;
   2 12  3;
   3 15  4;
   4 16  7;
   5 18  9;
   6 10 10;
   7 12  9;
   9  5  6];

B=[3  9  8;
   4  8  3;
   5  2  5;
   7 10  2;
   8  9  7;
   9 12 10;
   10 5  6];

AB1 = union(A(:,1),B(:,1));
C1  = [AB1';AB1'];

C = [C1(:),zeros(numel(C1),2)];

for nc = 1:size(C,1)
    
    if any(A(:,1)==nc)
        C([2*nc-1:2*nc],2) = A(A(:,1)==nc,2:3)';
    end
    if any(B(:,1)==nc)
        C([2*nc-1:2*nc],3) = -B(B(:,1)==nc,2:3)';
    end
    
end

C(:,1) = []

C = 20×2

10 0 12 0 12 0 3 0 15 -9 4 -8 16 -8 7 -3 18 -2 9 -5

[A]

Thank you so much!!!