# The Ray Tracer Challenge: Inversion of Rotation trouble

Title: Ray Trace Challenge: Inversion pg 49

I have gotten all my code (including my matrix multiplication and inversion routines) to pass the prescribed tests up through page 48, where we begin rotating on the X axis.

My code creates the desired result for the “half quarter” and “full quarter” rotations on the X axis.

However, on page 49 there is this last test proposed for the X rotations…

Next, add another test showing that the inverse of this rotation matrix simply
rotates in the opposite direction.

By an inversion, I do not get a rotation in the opposite direction. Instead, the point gets moved to 0,0,0

The matrix after the original PI/4 rotation operation looks like this…

``````Rotation PI/4.0 matrix values
Matrix values
| 1.0000        | 0.0000        | 0.0000        | 0.0000        |
| 0.0000        | 0.7071         | -0.7071        | 0.0000        |
| 0.0000        | 0.7071         | 0.7071          | 0.0000        |
| 0.0000        | 0.0000       | 0.0000        | 1.0000        |
``````

That matrix produces the desired result when multiplied by the tuple that represents the 0,1,0 starting point.

If I apply Inversion to that matrix, as the book directs, I get this matrix…

``````Rotation PI/4.0 matrix INVERTED values
Matrix values
| 1.0000         | 0.0000       | 0.0000        | 0.0000       |
| 0.0000        | 0.0000       | 0.0000        | 0.0000       |
| 0.0000        | 0.0000       | 0.0000        | 0.0000       |
| 0.0000        | 0.0000       | 0.0000        | 1.0000        |
``````

When multiplied by the 0,1,0 Tuple, this does not produce an opposite rotation, the Tuple is placed at 0,0,0.

Elsewhere on the internet I have read the correct way to reverse a rotation matrix is to transpose it.

Indeed, if I use my Transpose routine on the original rotation Matrix I get a matrix that produces a correct opposite rotation…

``````Rotation PI/4.0 matrix TRANSPOSED values
Matrix values
| 1.0000        | 0.0000      | 0.0000      | 0.0000       |
| 0.0000       | 0.7071       | 0.7071       | 0.0000       |
| 0.0000       | -0.7071      | 0.7071       | 0.0000       |
| 0.0000       | 0.0000       | 0.0000     | 1.0000        |

Rotation PI/4.0  TRANSPOSED point values
values:         x= 0.000        y= 0.707        z= -0.707       w= 1
``````

However, after searching this forum I have not seen any mention that the direction to invert rather than tranpose in this instance is a typo or other error.

What am I doing wrong?

Hold it… false alarm… I think.

Just by chance I caught a line of code where I was loading a double value into an int variable.

Fixing that has made the inverted rotation result come out correctly.

I wish I knew enough about matrix math to know why the wrong version was good enough for all the tests except that inverted rotation.

Excellent! I’m glad you figured it out. I was wondering if it wasn’t a rounding error, just given everything going to zero, but I hadn’t been able to think about it long enough to make my thoughts coherent.