Trying to rotate a 3D matrix for full symmetry group (group theory)
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Hi all,
I currently have a 32x32x32 matrix and I'm trying to get all possible rotations of it (the full symmetry set) and store them all.
My code is shown below;
It takes a dataset as matrix and then rotates it in 7 different ways around the x axis, this gives me 8 out of the 24 rotations of the full set. Are there functions that do the same as what I did below for the other 2 axes (y and z)? I cannot find a function that does this, and am hesitant to remap everything manually since there's a dataset of 800.000 matrices that I have to do this with.
matrix = dataset(:,:,:,i);
matrix2=flip(matrix);
matrix3=flip(matrix,2);
matrix5=rot90(matrix);
matrix4=rot90(matrix,2);
matrix7=rot90(matrix,3);
matrix6=rot90(flip(matrix));
matrix8=rot90(flip(matrix),3);
7 Comments
Jan
on 7 Mar 2021
Note that rot3d90 handles multidimensional inputs directly. So you can omit the loop:
matrix2 = rot3d90(a,1,1);
matrix3 = rot3d90(a,1,2);
matrix4 = rot3d90(a,1,3);
matrix5 = rot3d90(a,2,2);
matrix6 = rot3d90(matrix5,1,1);
matrix7 = rot3d90(matrix5,1,2);
matrix8 = rot3d90(matrix5,1,3);
matrix9 = rot3d90(a,2,1);
matrix10 = rot3d90(a,2,3);
matrix11 = rot3d90(matrix9,3,1);
matrix12 = rot3d90(matrix9,3,2);
matrix13 = rot3d90(matrix9,3,3);
matrix14 = rot3d90(matrix10,3,1);
matrix15 = rot3d90(matrix10,3,2);
matrix16 = rot3d90(matrix10,3,3);
matrix17 = rot3d90(a,3,1);
matrix18 = rot3d90(a,3,3);
matrix19 = rot3d90(matrix17,2,1);
matrix20 = rot3d90(matrix17,2,2);
matrix21 = rot3d90(matrix17,2,3);
matrix22 = rot3d90(matrix18,2,1);
matrix23 = rot3d90(matrix18,2,2);
matrix24 = rot3d90(matrix18,2,3);
p = [4, 1, 2, 3];
fullset = cat(1, ...
permute(a, p), ...
permute(matrix2, p), ...
permute(matrix3, p), ...
permute(matrix4, p), ...
permute(matrix5, p), ...
permute(matrix6, p), ...
permute(matrix7, p), ...
permute(matrix8, p), ...
permute(matrix9, p), ...
permute(matrix10, p), ...
permute(matrix11, p), ...
permute(matrix12, p), ...
permute(matrix13, p), ...
permute(matrix14, p), ...
permute(matrix15, p), ...
permute(matrix16, p), ...
permute(matrix17, p), ...
permute(matrix18, p), ...
permute(matrix19, p), ...
permute(matrix20, p), ...
permute(matrix21, p), ...
permute(matrix22, p), ...
permute(matrix23, p), ...
permute(matrix24, p));
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