Yes - but it doesn't provide the section LINESTRING(0 1, 2 1) inside the
polygon. I envision this also being provided by split(). (Otherwise
you have to run two operations, difference and intersection - with the
associated performance penalty, and also a risk that round-off will
cause results to be computed which don't precisely match)
Andy Anderson wrote:
Difference does seem to provide both sides of the subtractor:
select st_astext(st_difference(GEOMFROMTEXT('LINESTRING(-1 1, 3 1)'),
GEOMFROMTEXT('POLYGON((0 0, 2 0, 2 2, 0 2, 0 0))')))
returns
'MULTILINESTRING((-1 1,0 1),(2 1,3 1))'
-- Andy
On Jun 9, 2008, at 2:44 PM, Martin Davis wrote:
I see the difference (pun intended) between difference() and split()
being that split returns the geometries on both sides of the
splitting geometry, ordered so that the user can decide which one(s)
he wants. This is more powerful than difference, which only returns
a single geometry from one side of the split.
And I agree - I don't think polygons should be reduced to their
boundary first - the user can do this explicitly if they require it.
Andy Anderson wrote:
On Jun 5, 2008, at 11:43 AM, Martin Davis wrote:
I think the operation also is meaningful for the case (line,
polygon) => line (this is equivalent to a combination of
line.difference(polygon) and line.intersection(polygon) )
Ah, yes, split(line, polygon) should definitely be allowed. However,
I was originally imagining that split(line, polygon), as well as
split(polygon1, polygon2), should be the same as difference(*,
polygon), which is geometrically consistent with the simpler forms
split(*, line) and split(line, point):
####
----####---> becomes ---> --->
#### 1 2
But I see where it might be more useful for the polygon in the
second argument to be reduced to its boundary first:
#### +--+ ----####---> becomes
----|--|---> becomes ---> ---> --->
#### +--+ 1 2 3
But the latter is easily produced with the boundary function if
someone is so inclined:
split(polygon1, polygon2) == split(polygon1, boundary(polygon2))
split(line, polygon) == split(line, boundary(polygon))
This is more involved, but less confusing to those like me who learn
from consistency. What do other people think?
Having thought about this with an eye to implementation, I've take
the definition a bit further:
* The result of split(g1, g2) is a two-component
GeometryCollection, GC(c1, c2).
If you define split(line, polygon) as the combination of
difference(line, polygon) and intersection(line, polygon), then you
could have three components, right? This would also happen with
split(line1, line2) and line2 is a linear ring that crosses line1
twice.
* The first component c1 is the portion of g1 which lies to inside,
to the left of, or before, g2 (depending on whether g2 is a
polygon, line or point). The second component c2 is the portion of
g1 which lies outside, to the right of, or after g2. * The types of
c1 and c2 are the same as g1. c1 and c2 may be empty, in
degenerate cases (e.g,. where one or more components of g1 are not
intersected, or intersected only at their boundary).
It seems to me that "left" and "right" don't always work for lines,
as you could also have "below" or "above". Or are you referencing
the directionality of g2 here, as you traverse it? But if it's a
linear ring, the inner portion will be both to the left and right. I
wonder if it wouldn't make more sense to simply use the
directionality of g1 instead, describing its pieces as "first",
"second", etc., as I suggest in my drawings above?
As for polygons, there's no obvious spatial ordering for them,
unless you take their vertex order as significant. That seems
reasonable to me. For example,
split(POLYGON((0 0, 2 0, 2 2, 0 2, 0 0)), LINESTRING(1 -1, 1 3))
becomes GEOMETRYCOLLECTION(POLYGON((0 0, 1 0, 1 2, 0 2, 0 0)),
POLYGON((1 0, 2 0, 2 2, 1 2, 1 0)))
because the first polygon has the first vertex of the original and
the second polygon is built from later vertices. I'm not certain if
this could be consistently defined, though; it would require
comparisons of multiple vertices when one or more are shared by the
split polygons.
* Any components of g2 which have a position which is not
well-defined relative to g2 (e.g.which are not intersected, or
which are intersected only partially), are returned as components
of c1 (--- this rule is fairly arbitrary - a different strategy
might make equal sense)
So c1 is itself a Geometry Collection? This seems unnecessarily
complicated; I would prefer a flat object.
-- Andy
Andy Anderson wrote:
On Jun 4, 2008, at 11:49 AM, Martin Davis wrote:
To answer a question you posed on your blog, the reason that when
you subtract a line from a polygon you get basically the same
polygon, rather than say the polygon split into two halves, is
that if the latter was provided as a MultiPolygon it would be
invalid, because the halves would share line segments down the
middle. Also, if the line did not fully overlap the polygon
there's no choice - you have to return the original poly. The
behaviour is thus consistent between the two cases.
Unfortunately the SFS (and no other standard I'm aware of)
doesn't define the precise semantics of the overlay operations.
So I made 'em up! Hopefully they are consistent and reasonable.
There's no doubt alternative definitions which might be useful in
some cases - but you have to choose one definition for any given
function. (For the situation above, many people would like a
"cut polygon by line" operation - hopefully that will get
provided as a new function sometime soon).
I've seen "split" as a term that is commonly used for such
operations, e.g.
geometry = ST_Split(geometry1, geometry2)
This should be defined for geometry1 of dimensionality D ≥ 1 and
geometry2 of dimensionality D or D-1, i.e. (polygon, polygon),
(polygon, line), (line, line), and (line, point). The result
should be GeometryType(geometry) == 'GeometryCollection' where for
any n GeometryType(ST_GeometryN(geometry, n)) ==
GeometryType(geometry1).
-- Andy
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Martin Davis
Senior Technical Architect
Refractions Research, Inc.
(250) 383-3022
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_______________________________________________
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[email protected]
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--
Martin Davis
Senior Technical Architect
Refractions Research, Inc.
(250) 383-3022
_______________________________________________
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[email protected]
http://postgis.refractions.net/mailman/listinfo/postgis-users
_______________________________________________
postgis-users mailing list
[email protected]
http://postgis.refractions.net/mailman/listinfo/postgis-users
--
Martin Davis
Senior Technical Architect
Refractions Research, Inc.
(250) 383-3022
_______________________________________________
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