Re: Abstract Core Ontology for SWSL Processes

PatH:
>>PatH:
>>[...]
>>>  BTW, the same abstraction works very well for space. Traditional
>>>  spatial models start with points (where you click the digitizing pen
>>>  on the map) then go to (oriented) line-segments (pair of points) then
>>>  to end-linked sequences (paths) then to closed paths (end=beginning
>>>  and no crossings) which define (oriented) 2-d regions. These all
>>>  build up very nicely as finite structures on points. You can even go
>>>  to 3-d and higher, using ideas from homology theory, by stitching
>>>  together 2-d cells into 2-d surfaces and defining closure by
>>>  cancellation of oriented edges. All of which suggests that this is
>>>  indeed a very robust (and certainly very simple) framework.
>>
>>That sounds great Pat - can you recommend any URI pointers ??
>>Thanks in advance :)
>
> Still no URI, but I found the relevant part of my paper copy of the
> 1997 USIGS Data Model. In sum, its basically this:
>
> Locations are described by Geometric-Spatial-Elements
> G-S-Es are Surfaces or Points or Lines or Volumes
> A Point in a Surface is a Surface-Point...
> <various subclassifications of surface types, eg fan-surface, etc.>
>
> Point is the locus of a Node
> Line is the locus of an Edge
> Surface may be covered by Faces
> .... <etc. relating actual topography items to topological idealizations>
>
> Now: Node, Edge, Ring, Face and Shell are all Topological-Elements,
> and they are related as follows:
> Node is identified by a Point (with coordinates)
> Edge has two Nodes (starting and ending) and may be a Ring-edge;
> Ring is composed of a Sequence of Ring-edges with a
> 'succeeding/preceding' relation on them;
> A Ring may be used as a Face-Ring, and may be Internal or External
> (only one external allowed);
> a Face is bounded by a Face-ring, and may itself be used as a
> Shell-face: and a Shell is composed of Shell-Faces.

Clear; google found
http://www.geovista.psu.edu/sites/geocomp99/Gc99/037/gc_037.htm
which is consistent with above and talks about the concepts of
Node, Edge, Face, Ring, Volume, Shell
and the relationships
node-edge, node-face, node-volume, edge-face, edge-volume, face-volume
It seems straightforward to OWL-ize those...

> USIGS didn't get into the 3-d homology stuff, but you can get that
> from a topology textbook. Basic idea: treat each edge piece as having
> an orientation and say that opposite orientations cancel. Then add up
> all the edges of all the rings of all the shell-faces. If the result
> is zero, the shell (surface) is closed; if not, then there are holes
> in the surface and the surplus edges are the edges of the hole(s).
> For an example, orient four triangles clockwise, join their edges
> into a tetrahedron so that matching edges cancel.  Now remove one of
> the four sides and do the edge arithmetic again. I bet there are
> algorithms based on this stuff built into the silicon hardware of an
> X-box these days.

Right and I believe it is possible to write down a set
of N3 implications which can be queried to get such kind
of evidence...

--
Jos De Roo, AGFA http://www.agfa.com/w3c/jdroo/

Received on Tuesday, 20 January 2004 16:50:34 UTC