[Geojson] GeometryCollection not treated as a Geometry type

[John Herring]

Chris, 

	I usually avoid such discussions, but I am beginning to see a
divergence from what ISO 19107 actually says. So I'll make a couple of quick
observations  that need to be considered in any representation of geometry. 

	First, a geometry is a (probably infinite) set of spatial positions
(generically called points). This it that old "loci of points" stuff you get
in high school geometry class, but it is repeated in ISO 19107. There, a
GM_Object is subclassed from a thing called "Transfinite set of direct
positions" which is UMLese for a possibly infinite set of spatial location
defined by coordinates (or more precisely, definable by coordinates - as
long as the points are well-defined, how they are defined is of little or no
consequence).  

	The only non-infinite (finite) geometry is the point, or a finite
collection of points. Ergo, any line or surface is never equal to any
Multipoint (you can get into some nasty epistemological circles with this,
because any fixed direct position representation is by definition a finite
set, but the geometry represented by those direct positions can go far
beyond the original representation used. A line between two distinct integer
points contains an infinite number of real valued points, some of which
would require a representation never used in computers. The line from (0,0)
to (5,5) contains the points (SQRT(2), SQRT(2)), and (pi, pi). 

	Second, everything subtyped from GM_Object in ISO 19107 is a
geometry. This included all the collections. A collection is defined as a
geometry consisting of the set-union of its elements.

	Third, any two geometry representations are equal to one another if
and only if the resulting "transfinite set of positions" are equal as sets
of positions. 

	Fourth, the content of a geometry is defined by its "stored points"
in combination with its interpolation mechanisms. Different combinations can
be equal even it they share very few stored points in common. For example, a
two point line is equal to a line-string of a 1000 points if those points
are all collinear, lie between the same two endpoint as the first, and
contains those same endpoints. Orientation is an attribute of
representation, not of the underlying geometry, so a line from A to B is the
same geometry as a line from B to A. So a Collection containing these two
lines, is equal to either line by itself.

	There are probably other things that folks like to try to avoid
about geometry by placing artificial restrictions on representations, but
none of that works in the long run, and none of it is consistent with ISO
19107.  


Regards,
John

You do what you can when you can because you can.

The opinions expressed in this email are 
purely my own and do not necessarily 
represent the opinions of any organization
or otherwise sane person or persons.

John R. Herring
Architect, Spatial Products
Oracle Corporation
One Oracle Drive
Nashua, New Hampshire 03062
ph: 1 603 897 3216
fx: 1 603 897 3334

Annue cœptis - Novus Ordo Seclorum
  


-----Original Message-----
From: geojson-bounces at lists.geojson.org
[mailto:geojson-bounces at lists.geojson.org] On Behalf Of Christopher Schmidt
Sent: Friday, October 05, 2007 5:51 PM
To: geojson at lists.geojson.org
Subject: Re: [Geojson] GeometryCollection not treated as a Geometry type

On Fri, Oct 05, 2007 at 05:33:25PM -0400, Christopher Schmidt wrote:
> Currently, GeometryCollection is not treated as a geometry type. This 
> is essentially an oversight -- up until now, the people primarily 
> working on the spec didnt' really use GeometryCollection, to the best 
> of my knowledge.

After re-reading the spec, I realized that we kind of treated
GeometryCollection as a geometry. But not really. I had bumped the version
before that (thinking 'oh, people support draft4 now, people like OpenLayers
2.5'), but I'm just going to leave it at this point.

The change made to the spec is:

http://wiki.geojson.org/index.php?title=GeoJSON_draft_version_5&diff=157&old
id=155

Feedback welcome. Going to go through the rest of the doc now and see if
it's unclear anywhere else.

Regards,
--
Christopher Schmidt
MetaCarta
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