How do 3D coordinates map to a 3D matrix?
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ting
on 21 Nov 2013
Commented: Bruno Pop-Stefanov
on 22 Nov 2013
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?
3 Comments
Accepted Answer
Bruno Pop-Stefanov
on 21 Nov 2013
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
2 Comments
Bruno Pop-Stefanov
on 22 Nov 2013
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).
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