## The FrameSet Model

Consider a coordinate system (call it number 1) which is represented by a FrameFrame of some kind. Now consider a MappingMapping which, when applied to the coordinates in system 1 yields coordinates in another system, number 2. The Mapping therefore inter-relates coordinate systems 1 and 2.

Now consider a second Mapping which inter-relates system 1 and a further coordinate system, number 3. If we wanted to convert coordinates between systems 2 and 3, we could do so by:

1. Applying our first Mapping in reverse, so as to convert between systems 2 and 1.

2. Applying the second Mapping, as given, to convert between systems 1 and 3.

We are not limited to three coordinate systems, of course. In fact, we could continue to introduce any number of further coordinate systems, so long as we have a suitable Mapping for each one which relates it to one of the Frames already present. Continuing in this way, we can build up a network in which Frames are inter-related by Mappings in such a way that there is always a way of converting between any pair of coordinate systems.

The FrameSetFrameSet (Figure 7) encapsulates these ideas. It is a network composed of Frames and associated Mappings, in which there is always exactly one path, via Mappings, between any pair of Frames. Since we assemble FrameSets ourselves, they can be used to represent any coordinate systems we choose and to set up the particular relationships between them that we want.