Combine 3 matrices (3D)

Hello all,

I have 3 matrices A, B, C, each has a size of 200x50x50. They are coordinates (X, Y, Z) of points that represent a cube. What I want to do is to obtain a matrix from which if I type the following command D(1, 4, 3), I will access the 1st element in the X dimension, the 4th element in the Y dimension, and the 3rd element in the Z dimension, which should give me the following answer (but this will change in my real case since the points are coordinates):

ans = [1, 4, 3]

For example my A matrix which represents the coordinates in the X axis is as follow:

1, 2, 3, 4, 5, 6, 7, 8, 9, ...
1, 2, 3, 4, 5, 6, 7, 8, 9, ...
1, 2, 3, 4, 5, 6, 7, 8, 9, ...
and so on, with the same numbers for every layer (Z dimension)

My B matrix which represents the coordinates in the Y axis is as follow:

1, 1, 1, 1, 1, 1, 1, 1, 1, ...
2, 2, 2, 2, 2, 2, 2, 2, 2, ...
3, 3, 3, 3, 3, 3, 3, 3, 3, ...
and so on, with also the same numbers for every layer (in the Z dimension)

And my C matrix has the same value for a whole layer, to represent the Z dimension:

1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
then second layer will be filled with twos, the 3rd layer with threes, and so on

So how can I combine these 3 matrices to obtain a single matrix that will give me the coordinates?

Thanks in advance

Answer 1

[Thorsten]

It is not entirely clear to me what you are asking for.

1. So far you have just coordinates for X, Y, Z, presumably generated with meshgrid. But you do not have a value for certain combination of these coordinates, like D(1,4,3). So you have to figure out how X,Y and Z should be combined to yield your D, like, for example

D = X + 2*Y + Z.^2;

2. If you want a single linear index into your 3D cube, that is a different thing. You can obtain this using

ind = sub2ind(size(X), X, Y, Z)

[Matt]

Sorry my English is not that good. All coordinates are known (X, Y, Z).

Let us assume we have a cube (all dimensions given in meters). I have 8 points (1 at each corner).

The A matrix contains X coordinates. So for example it will be:

1, 1.5
1, 1.5

The B matrix contains the Y coordinates:

1, 1
1.5, 1.5

So what we have at the moment is a cube whose bottom left corner is at (1, 1) meters, and top right corner at (1.5, 1.5) meters.

The C matrix will define the coordinates in the Z dimension:

1, 1
1, 1
1st layer

1.5, 1.5
1.5, 1.5
(2nd layer)

So for example if I want to access the coordinates of the bottom left corner of the "first face", I want to just type in:

D(1, 1, 1)

And the result should be:

ans = [1, 1, 1] meters (unit is just to clarify)

If I want to access the top right corner of the same face, I want to type:

D(2, 2, 1)

And the result should be:

ans = [1.5, 1.5, 1] meters

But if I want to access the same top right corner, but on the other face, I want to type:

D(2, 2, 2)

And the result should be:

ans = [1.5, 1.5, 1.5] meters

My question is: how can I make such D matrix?

I hope it is better now.

[Thorsten]

I see. You mean something like

x = [1 1.5];
y = x; z = x;
[A B C] = meshgrid(x,y,z);
D = cat(4, A, B, C);

You can then access, e.g.,

D(1,1,1,:)
D(2,2,2,:)

Note that D has 2*n^3 elements, if n is the number of different elements in A,B, and C. That seems to be an inefficient way to organize your data; the same information is already in your n values.

Instead of explicitely store the data in a huge 4D matrix, you could write an anonymous function

 fD = @(i1, i2, i3) [x(i1) y(i2) z(i3)]

 fD(1,1,1)
 fD(2,2,2)

[Matt]

Thank you for your answer. I will give it a try. I think I have to go the 4D route since I have to check at every time step if the Z coordinate of every point is below a threshold, so having all the Z coordinates stored at one place will help me a lot in that rather than having to call the function (I think).

The issue for me then is to rotate that 4D matrice and compute the new points position but I fail to succeed in that yet.