How do I rotate a 3D matrix by 90 degrees counterclockwise?

Question

I'm trying to rotate a matrix counterclockwise by 90 degrees in Java. I found answers on how to do this with a 2D matrix, but my matrix is 3D.

Here's how I found out on how to do a 2D rotation:

static int[][] rotateCW(int[][] mat) {
    final int M = mat.length;
    final int N = mat[0].length;
    int[][] ret = new int[N][M];
    for (int r = 0; r < M; r++) {
        for (int c = 0; c < N; c++) {
            ret[c][M-1-r] = mat[r][c];
        }
    }
    return ret;
}

How would I go about rotating a 3D matrix then?

Presumably, you would leave one of the axes fixed in this rotation? Then the code should basically be exactly the same, except you have one extra `for` loop and you map that index unchanged. — Louis Wasserman, Jan 16 '13 at 20:38
In 3D the question is around which axis do you want to rotate? Its like in 2D if you want to rotate around one of the main axis (but it is complicated if you want to rotate around an other axis). — MrSmith42, Jan 16 '13 at 20:39
look at this http://stackoverflow.com/questions/8409197/generic-simple-3d-matrix-rotation-issue — Rachel Gallen, Jan 16 '13 at 20:43
Sorry for being unclear, I'd like to rotate the matrix around the x-axis. — NewGradDev, Jan 16 '13 at 20:45
also import javax.media.j3d then you can use the Transform3D — Rachel Gallen, Jan 16 '13 at 20:47
I'm not using Graphics here btw. I have a 3D matrix that is defined using arrays. How would I rotate that about the x-axis 90 degress counter-clockwise? Thanks! — NewGradDev, Jan 16 '13 at 20:49
also look at http://stackoverflow.com/questions/1330727/how-to-rotate-an-object-in-java-3d just saw your last comment don't know if it will be helpful — Rachel Gallen, Jan 16 '13 at 20:51

score 11 · Accepted Answer · edited May 05 '17 at 09:20

11

By multiplying your matrix with a rotation matrix

The basic matrix for the x-axis is:

        | 1     0      0    |
Rx(a) = | 0  cos(a) -sin(a) |
        | 0  sin(a)  cos(a) |

For 90 degrees simply set cos(90) = 0 and sin(90) = 1 which should lead to:

        | 1     0      0    |
Rx(a) = | 0     0     -1    |
        | 0     1      0    |

edited May 05 '17 at 09:20

P.J.Meisch

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answered Jan 16 '13 at 21:14

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http://stackoverflow.com/questions/14310347/gyroscope-issues-with-device-orientation/14311815#comment19887144_14311815 This was my original problem thread. The accepted answer on that page combined with your answer gave me the hints that i need to solve my issue. Thanks for all your help! :D – NewGradDev Jan 16 '13 at 21:54

How do I rotate a 3D matrix by 90 degrees counterclockwise?

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