# Objective
`Dir3` and `Dir3A` can be rotated using `Quat`s. However, if enough
floating point error accumulates or (more commonly) the rotation itself
is degenerate (like not normalized), the resulting direction can also
become denormalized.
Currently, with debug assertions enabled, it panics in these cases with
the message `rotated.is_normalized()`. This error message is unclear,
doesn't give information about *how* it is denormalized (like is the
length too large, NaN, or something else), and is overall not very
helpful. Panicking for small-ish error might also be a bit too strict,
and has lead to unwanted crashes in crates like `bevy_xpbd` (although it
has also helped in finding actual bugs).
The error message should be clearer and give more context, and it
shouldn't cause unwanted crashes.
## Solution
Change the `debug_assert!` to a warning for small error with a (squared
length) threshold of 2e-4 and a panic for clear error with a threshold
of 2e-2. The warnings mention the direction type and the length of the
denormalized vector.
Here's what the error and warning look like:
```
Error: `Dir3` is denormalized after rotation. The length is 1.014242.
```
```
Warning: `Dir3A` is denormalized after rotation. The length is 1.0001414.
```
I gave the same treatment to `new_unchecked`:
```
Error: The vector given to `Dir3::new_unchecked` is not normalized. The length is 1.014242.
```
```
Warning: The vector given to `Dir3A::new_unchecked` is not normalized. The length is 1.0001414.
```
---
## Discussion
### Threshold values
The thresholds are somewhat arbitrary. 2e-4 is what Glam uses for the
squared length in `is_normalized` (after I corrected it in
bitshifter/glam-rs#480), and 2e-2 is just what I thought could be a
clear sign of something being critically wrong. I can definitely tune
them if there are better thresholds though.
### Logging
`bevy_math` doesn't have `bevy_log`, so we can't use `warn!` or
`error!`. This is why I made it use just `eprintln!` and `panic!` for
now. Let me know if there's a better way of logging errors in
`bevy_math`.
983da7677a