Providing it as spherical has a performance boost in edge cases, but is probably not worth the trouble.

The IAU Report contains the value W which is needed for that. However, it depends on time. Is time a member of the enum variant, or is it an argument to conversions?

Just like to_direction.

This is an optimisation. I want to achieve the following:

• An array of cartesian coords, spherical coords, or direction, only needs to store the reference frame once.
• Transforming an array of coords can be performed in parallel, maybe even using GPUs.

Beginning with Cartesian, Direction and Spherical.

The simple-si-units crate is very helpful for avoiding unit errors. However, since distance is measured in meters, the numbers get unnecessarily large for astronomical distances.
We could also think about defining an AstroDistance struct, which stores distance in Parsec and joins in with the simple-si-units crate.
In any case we can switch to f32 numbers to half the memory footprint.

$\cos \theta = \frac{a\cdot b}{|a| |b|}$
$\cos^2 \theta = \frac{(a\cdot b)^2}{|a|^2 |b|^2} = \frac{1}{2} + \frac{\cos 2 \theta}{2}$
This way we can avoid two squareroots.

For example, Cartesian to earth_equatorial needs to know the reference frame of the cartesian coordinates.

• trait ActiveRotation:
  • rotated
  • rotated_x
  • rotated_y
  • rotated_z
  • active_rotation_to_new_z_axis
• trait PassiveRotation:
  • passive_rotation_to_new_z_axis