Fix bug in initial condition for transform_real_to_unit_cell

[kronbichler]

Fixes #13246.

@blaisb could you please test this fix?

It turns out that our initial guess for the Newton iteration in the computation via the inverse quadratic approximation did not apply the normalization for the code path with bilinear/trilinear cells (when, in fact, the inverse approximation is only affine and not quadratic). I also cleaned up some internal functions.

[kronbichler]

/rebuild

[kronbichler]

This would fail with the previous version of the code, giving a point with unit coordinates around 12.

[blaisb]

Fixes #13246.

@blaisb could you please test this fix?

It turns out that our initial guess for the Newton iteration in the computation via the inverse quadratic approximation did not apply the normalization for the code path with bilinear/trilinear cells (when, in fact, the inverse approximation is only affine and not quadratic). I also cleaned up some internal functions.

This works with the test provided by #13269 and does not lose particles. Consequently once this is merge, I'll fix #13269 to just keep the test and remove the changes to the particle.

Thanks @kronbichler for taking a look at it. This is a much nicer solution.

[blaisb]

I'm not the best expert to review this, but it is a very clear and understandable PR. No comments on my side. Great work!

[tjhei]

👍