Combine 3 matrices (3D)

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Matt 2015-10-13

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https://ww2.mathworks.cn/matlabcentral/answers/248344-combine-3-matrices-3d

编辑： Matt 2015-10-14

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

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Answer 1

Thorsten 2015-10-13

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编辑：Thorsten 2015-10-13

在 MATLAB Online 中打开

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)

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Matt 2015-10-13

编辑：Matt 2015-10-13

在 MATLAB Online 中打开

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 2015-10-13

编辑：Thorsten 2015-10-13

在 MATLAB Online 中打开

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 2015-10-14

编辑：Matt 2015-10-14

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.

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