Add methods to convert from geodetic and spherical coordinates to Cartesian coordinats

[MarkWieczorek]

In some cases, it is necessary to determine the Cartesian coordinates that correspond to a set of spherical or geodetic coordinates. The equations are trivial, and I propose adding the methods:

• spherical_to_cartesian
• geodetic_to_cartesian

These will be useful regarding my comments about the InSight lander....

[Phssilva]

In which class do you think these methods should be added?

[MarkWieczorek]

I see two possible ways to do this, and it might even make sense to do both.

First, we could just create some generic functions in the top level namespace to do the transformations, and then to use these internally (where needed) in the ellipsoid classes. Necessary low level functionality would include

• spherical_to_cartesian
• cartesian_spherical
• geodetic_to_cartesian
• cartesian_geodetic

Second, we could create a method like Ellipsoid.cartesian_coordinates(latitude, longitude, height=None, geodetic=true). I don't think it would make sense to input (x, y, z) coordinates to an ellipsoid, but we really should have an easy way to go from cartesian to spherical, and this could be done using the functions of the first approach.

[Phssilva]

Hello, I cloned the project and as usual, I always run the test before starting to edit the code. In this case, when the test is already failing due to redundancy, what do you recommend? I couldn't find any redundancy in the init.py file. Is there any related issue regarding this?

[leouieda]

@Phssilva see my comment on fatiando/ensaio#67

[leouieda]

@MarkWieczorek I think we could have:

1. Functions spherical_to_cartesian and cartesian_to_spherical. Neither of these require knowledge of the reference ellipsoid or reference sphere. They could be in a new boule/_transformations.py module.
2. Methods Ellipsoid.geodetic_to_cartesian and Ellipsoid.cartesian_to_geodetic. They do require knowledge of the ellipsoid so it makes sense to have them here.

Since they don't rely on each other, they could also be implemented in 2 separate pull requests.

[MarkWieczorek]

I'm going to close this, as the linked proposal supercedes this discussion.