Transform multiple frames

[romanarust]

Feature Request

Similar to transform_points and transform_vectors it would be great to have transform_frames.
Likewise, Frame should be extended with represent_(frames\points\vectors)_in_(local\global)_coordinate_system

[xarthurx]

the transform_frames can be simple made by transforming three basis and one point of the given frame?

[gonzalocasas]

As a side comment, I think we need to rename represent_(frames\points\vectors)_in_(local\global)_coordinate_system to a significantly more compact name?

I was checking how other libraries and tools do this, and I like the way matlab does it, so I would suggest the following:

1. Replace all represent_(frames\points\vectors)_in_(local\global)_coordinate_system methods with two static methods: local_to_global(obj, local) and global_to_local(obj, local).
2. Add local_to_global(self, local) and global_to_local(self, local) as instance methods to Point, Vector and potentially other classes as well.
3. The new static methods of Frame determine the kind of argument as follows: if it's a list of float, it's assumed to represent a point. Anything else needs to be passed as an instance (of Vector, Frame, etc).
4. If the argument is an instance, it needs to support the interface defined in item 2 (local_to_global(self, local) and global_to_local(self, local)), so the supported types is not hard-coded.
5. An additional, functional API could optionally be created as well, but I would question its value, because the static method proposed here basically serves the same function.

Once that is in place, the usage of this API would look like this:

# Defining some local coordinate system
rcs = Frame((100, 150, 0), (1, 0, 0), (0, 1, 0))

point = (10, 1, 10)
point_l = Frame.global_to_local(point, local=rcs)
point_g = Frame.local_to_global(pg, local=rcs)

[romanarust]

@gonzalocasas: Good suggestion!
I'll soon start a branch working on this, there are some other tasks related to this:
https://github.com/compas-dev/compas/projects/23#card-26510777