I don't really see the problem with expressing Equals in terms of the
DE-9IM. To my mind, this just adds some value to this predicate by
putting it under the same theoretical framework as the rest of the
"standard" predicates. If you don't like it, just ignore that definition.
I don't see the reason to be concerned about whether Contains and Equals
"have the same standing" or "will be adopted". The functionality is
there, is well-defined and clearly documented. Use it or don't use it -
your choice.
Your original question was concerning the behaviour of contains and
within on two topologically equal polygons. According to my analysis,
the observed behaviour is consistent with the definition of contains and
within in both GEOS/JTS and OGC-SFS. If you don't like this behaviour,
you'd better take it up with the OGC.
You wrote "How can 2 simple geometries be equal *and* contained *and*
within?". The reason is simple. Think of contains as >= and within as
<=. If A = B, then obviously A <= B and A >= B - there's no
contradiction here.
Martin
Todd Jellett wrote:
Hi Chris,
By "true predicate" I am just referring to the set of five mutually
exclusive, complete predicates that the SFS is based on and yes, there
is probably a better term that 'true'. Original?
Contains and Intersects are explicitly defined as "for user
convenience predicates" on page 2-19 of the SFS but Equals is just
listed as a method. Is changing Equals to be based on the DE-9IM and
promoting it to the same standing as the true/basic/core predicates
part of the SFS, or is this an extension to the SFS? Will it be
adopted? Equals is not built on true/basic/core predicates the way
Contains/Intersects is.
By "violating the mutual exclusivity of the predicates" I am just
saying that Contains and Equals are not members of the set of mutually
exclusive, complete predicates (so therefore, there is no problem with
mutual exclusivity) and I previously thought they were. In my original
question, I excluded Intersects but included Equals and Contains in
the group that I thought were mutually exclusive.
Todd
Chris Hodgson wrote:
Excellent research Todd, good to have it here to help others with any
similar confusion.
I'd just like to add that the only thing special about Disjoint,
Touches, Crosses, Within, and Overlaps is that they are both mutually
exclusive and complete as a set of predicates and thus good for using
as logical building blocks to more complicated operations. It doesn't
mean that contains/intersects/equals aren't also perfectly valid and
useful logical predicates. They are also based on the DE-9IM. Your
idea of "true" predicates might better be described as "basic" or
"core" ... "true" implies that other predicates are somehow "false"
when perhaps composite or complex would be a better term.
Talking about "violating the mutual exclusivity of the predicates"
doesn't make much sense when you're talking about predicates that
aren't part of the small set which is proved to be mutually exclusive.
Anyways, good to have all the references put together.
Chris
Todd Jellett wrote:
Martin Davis wrote:
I agree with Chris and Paul. The predicates are clearly not
intended to be mutually disjoint. They are probably intended to
capture the most common use cases in single functions (which allows
for some aggressive optimization - some day 8^).
Refractions: 3, Jellet: 1 - we win! 8^)
This is not quite the answer I was looking for.
What I expected was something more along the lines of:
Yes, the named spatial relationship predicates based on the DE-9IM
(Disjoint, Touches, Crosses, Within, and Overlaps) are indeed
mutually exclusive. For a complete proof that these predicates are
mutually exclusive see the reference:
Clementini Eliseo, Di Felice P., van Oostrom p., A Small Set of
Formal Topological Relationships Suitable for End-User Interaction,
in D. Abel and B. C. Ooi (Ed.), Advances in Spatial Databases, Third
International Symposium. SSD ’93. LNCS 692. Pp. 277-295.
Springer-Verlag. Singapore (1993).
Here is an quoted excerpt from section 4.3 of this paper
"In this section, we will prove that the five relationships are
mutually exclusive, that is, it cannot be the case that two
different relationships hold between two features; furthermore, we
will prove that they make a full covering of all possible
topological situations, that is, given two features, the
relationship between them must be one of the five."
You (Todd) are probably being confused by the fact that Contains and
Equals are not true predicates. If you look at page 2-15 of the SFS,
in the second paragraph, you will see the five unique predicates
listed. On page 2-19, the SFS defines for user convenience, the
predicates Contains and Intersects. Note that these two, are not
defined uniquely but instead are defined in terms of one of the five
unique and mutually exclusive predicates. ( a.Contains(b) <=>
b.Within(a) and a.Intersects(b) <=> !a.Disjoint(b) )
Equals is not even listed as a predicate in SFS. It is just listed
as a method. In ISO 19107, it can be seen that Equals comes from the
transfiniteSet class along with the other set theoretical operations
like intersection, union and difference. In 19107, the GM_Object
class is derived from transfiniteSet. The SFS chose to optimize away
the transfiniteSet class so the Equals method ended up in the
Geometry base class (corresponds to GM_Object in ISO 19107) with all
the other set theoretical methods.
So in conclusion, having Within, Contains, and Equals all come back
true for two given geometries does not violate the mutual
exclusivity of the predicates because Within is the only true
predicate.
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Martin Davis
Senior Technical Architect
Refractions Research, Inc.
(250) 383-3022
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