My reasoning is as follows: the scaling transformation makes the sphere an ellipsoid, i.e. a sphere “flattened” on the y axis. Unlike a sphere, if you rotate an ellipsoid the normal change its orientation. So to me seems strange that with or without a rotation the normal stays the same.

For how the test is formulated, the normal lay on the y-z plane but my intuition says that it cannot be possible, the normal must have an x coordinate not equal to zero.

My thought is reinforced if you read the old errata page of the book:

Search for “normal_at” and you’ll find an errata on page 84 when a reader had a problem on the same test: with or without the rotation the test passed because the reader forgot to add the transpose operation.

The test was changed to add a scale and a rotation just to be sure to catch this error. In my opinion, this means that now the test must pass only with a rotation and not without it.

Just to be sure, I’ve added many more tests on my suite, with combinations of scaling, translations, and rotations.

What do you think about it? Please, let me know your thoughts!

Thank you