# [postgis-users] Semantics of difference() function

Martin Davis mbdavis at refractions.net
Mon Jun 9 12:18:24 PDT 2008

```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?
>>>
>>>> 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
>>>>>
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> postgis-users mailing list
>>>>> postgis-users at postgis.refractions.net
>>>>> <mailto:postgis-users at postgis.refractions.net>
>>>>> http://postgis.refractions.net/mailman/listinfo/postgis-users
>>>>>
>>>>
>>>> --
>>>> Martin Davis
>>>> Senior Technical Architect
>>>> Refractions Research, Inc.
>>>> (250) 383-3022
>>>>
>>>> _______________________________________________
>>>> postgis-users mailing list
>>>> postgis-users at postgis.refractions.net
>>>> <mailto:postgis-users at postgis.refractions.net>
>>>> http://postgis.refractions.net/mailman/listinfo/postgis-users
>>>
>>> ------------------------------------------------------------------------
>>>
>>>
>>> _______________________________________________
>>> postgis-users mailing list
>>> postgis-users at postgis.refractions.net
>>> http://postgis.refractions.net/mailman/listinfo/postgis-users
>>>
>>
>> --
>> Martin Davis
>> Senior Technical Architect
>> Refractions Research, Inc.
>> (250) 383-3022
>>
>> _______________________________________________
>> postgis-users mailing list
>> postgis-users at postgis.refractions.net
>> http://postgis.refractions.net/mailman/listinfo/postgis-users
>
> _______________________________________________
> postgis-users mailing list
> postgis-users at postgis.refractions.net
> http://postgis.refractions.net/mailman/listinfo/postgis-users
>

--
Martin Davis
Senior Technical Architect
Refractions Research, Inc.
(250) 383-3022

```