How do 3D coordinates map to a 3D matrix?

The project is about point cloud. Given a large number of 3-D coordinates (x-y-z) with all intensities are the same, say 1 or 255. 

The range of x, y and z shown as follows. 
* -113<x<158;
* -136<y<135 and
* -771<z<-500.
# If i create a 272 by 272 by 272 matrix, how can i map those 3-D coordinates to the matrix? 
  A = zeros(272, 272, 272);
# I know the matrix index starts from 1 in MAT-LAB. Should I create a 3-D grid to do mapping?

[Iain]

What are you trying to achieve?

I wouldn't necessarily put 4 vectors into a 3-D matrix. You can still achieve just about all of the same things easily.

[ting]

I am given a number of 3d data (x y, and z coordinates) ranging from -113<x<158 -136<y<135 -771<z<-500.

Example: (29 -76 -614) (30 -76 -614) (32 -76 -614) (32 -76 -614) (36 -76 -614) (36 -76 -614) I find the max and min values of x y z, i decide to build 272 by 272 by 272 matrix. You can ignore the intensity value, they are the same. Just consider as 3D data. I want to put them into a matrix according to their 3D coordinates and make 8*8*8 small block finally. I am not a good programmer, please also provide some functions or code.

[ting]

BTW,I consider the matrix as 272*272*272 block, i should mention that if that coordinate exists put 1 or 255 in the matrix. Otherwise put 0. Thanks

Answer 1

[Bruno Pop-Stefanov]

I assume in the following piece of code that your 3D points are listed in an N-by-3 vector named 'points'.

% Min and max values
xmin = -113;
xmax = 158;
ymin = -136;
ymax = 135;
zmin = -771;
zmax = -500;

% Initialize output matrix in which a non-zero entry indicates a 3D point exists in the input set
mat = zeros(xmax-xmin+1, ymax-ymin+1, zmax-zmin+1);

% For all 3D points
for p=1:size(points, 1)
    if ( points(p,1)>xmax || points(p,1)<xmin || points(p,2)>ymax || points(p,2)<ymin || points(p,3)>zmax || points(p,3)<zmin )
        fprintf('Error: point %d is out of bounds.\n', p);
    else
        i = points(p,1) - xmin + 1;
        j = points(p,2) - ymin + 1;
        k = points(p,3) - zmin + 1;
        mat(i, j, k) = mat(i, j, k) + 1;
    end
end

The output matrix 'mat' contains non-zero entries when a 3D point exists, but you'll have to convert into indices. For example, if the first point in 'points' is [29 -76 -614], then

mat(29-xmin, -76-ymin, -614-zmin) ~= 0

[ting]

i have a question. so after finishing the loop, is mat a matrix of 272*272*272 with entries 1 or 0.

Also, if point data is (-133, -136, -771), all are min. Does it mean (-113, -136 -771) maps to martix(1, 1, 1) Thank you

[Bruno Pop-Stefanov]

If all your data points in your input vector are unique, then, yes, the matrix will only have 0's and 1's. Coordinate (i,j,k) in the output matrix is the number of points in the input vector that have corresponding coordinates (x,y,z). If you only want 0's and 1's, you can change line

mat(i, j, k) = mat(i, j, k) + 1;

to

mat(i, j, k) = 1;

Yes, (xmin, ymin, zmin) maps to (1, 1, 1).