Write down the intentions and utilities of this library

[rafaelrojasmiliani]

Main motivation

Classic illustration of charts and change of coordinates

The principal motivation of this API is to overcome the "representation singularities" of the coordinate-representation of rotations (SO(3)) and the redundancy of its quaternion representation (Double covering, 4 coordinates).

In order to address this issue, this library intents to implement to formal description of manifolds using charts.
Read this to know more about charts in the rotations manifold.
Following this idea, this library should

• Allow the user to define a generic manifold element and find (fast) the charts that can map it to R^n.
• Allow the user to define a function between manifolds in a coordinate independent way and compose this function with charts.
• Allow to define function in coordinates, but allow the user to generate the covering partition of the manifold.
• Allow the user to find a chart that contains two points in a manifold (if exists)