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<H2><A NAME="SECTION000131000000000000000">
The FrameSet Model</A>
</H2>
<P>
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.
<P>
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:
<P>
<OL>
<LI>Applying our first Mapping in reverse, so as to convert between
systems 2 and 1.
<P>
</LI>
<LI>Applying the second Mapping, as given, to convert between
systems 1 and 3.
</LI>
</OL>
<P>
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.
<P>
The FrameSetFrameSet (Figure <A HREF="node10.html#fig:frameset">7</A>) encapsulates these ideas. It
is a network composed of Frames and associated Mappings, in which
there is always exactly one path, <SPAN CLASS="textit">via</SPAN> 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.
<P>
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