Google Cartographer: Internal coordinate systems

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I am studying Google Cartographer SLAM. Working with submaps in the library API (which is not at all documented) I discovered the following entities representing coordinates:

• Trajectory (list of sensor poses with connected submaps)
• Global pose (submap pose)
• Local pose
• Slice pose
• Vector pose (the last one used to draw a submap on 2D surface using Cairo).

Could someone explain how these origin points and coordinate systems connected with each other and how to understand properly the transformations between them and submap points' 2D coordinates?

This is a repost of StackOverflow question https://stackoverflow.com/questions/7... made to increase the visibility of the topic in ROS community.