[postgis-users] bow-tie polygons and the like
Chris Hermansen
chris.hermansen at timberline.ca
Tue Apr 1 15:17:51 PDT 2008
Martin,
Thanks for the info. I ended up editing out the offending polygons with
OpenJump; there were only about 20. They were created by someone's
sloppy geoprocessing and we were the lucky beneficiaries.
I guess what is interesting is the self-intersecting and loop
self-intersecting polygons were built by ogr2ogr when converting from
ArcInfo coverages to PostGIS.
I need to think about this to decide whether I'm up to writing some code
to try to automate the kind of conversion you mention.
Again, thanks; and also to Nicolas who sent me in the right direction in
the first place.
Martin Davis wrote:
> Chris,
>
> This is a classic self-intersecting polygon, which self-touches at a
> single point. These are invalid according to the OGC model. They are
> valid in some other spatial models (notably ArcSDE), where they are
> referred to as "inverted polygons", and are used to represent polygons
> with a hole that touches an edge. In the OGC model, that situation
> must be represented as a polygon with a shell ring and a separate hole
> ring (which is in turn invalid in ArcSDE).
>
> You can inter-convert between the two models, but it does require some
> fussy bookkeeping.
>
> I'm a bit surprised by the area discrepancy - even if this shape is
> illegal, the area computation should be well-defined. At least,
> that's the way it would work in JTS/GEOS. The area code in PostGIS
> may be different, however.
>
>
>
> Chris Hermansen wrote:
>> Martin, all;
>>
>> Here is the wkt for the enclosing polygon:
>>
>> 53327 | SRID=1;POLYGON((1224673.7804 499721.97084,1224664.2479
>> 499721.56584,1224639.311 499709.63254,1224658.0919
>> 499675.28084,1224664.2479 499721.56584,1224673.1624
>> 499747.57644,1224676.7094 499739.52814,1224676.916
>> 499740.76654,1224692.459 499812.83074,1224668.6628
>> 499811.81964,1224658.0339 499811.36804,1224630.597
>> 499769.81704,1224627.078 499734.63704,1224622.024
>> 499724.36664,1224616.0171 499712.16004,1224595.8521
>> 499691.28704,1224573.8378 499685.40964,1224561.8108
>> 499682.19864,1224555.2798 499681.92114,1224553.7247
>> 499680.03974,1224549.0699 499678.79694,1224549.2472
>> 499674.62264,1224550.0095 499656.68104,1224534.9948
>> 499656.04304,1224527.759 499655.73564,1224525.1614
>> 499651.95204,1224525.556 499642.66424,1224526.0666
>> 499630.64754,1224527.1273 499605.67644,1224502.1236
>> 499604.61414,1224503.1844 499579.64304,1224478.1807
>> 499578.58064,1224479.2415 499553.60954,1224466.8676
>> 499553.08384,1224458.2316 499552.71694,1224454.6943
>> 499541.79814,1224454.9879 499534.88804,1224450.0691
>> 499527.35404,1224431.6821 499499.19104,1224417.7948
>> 499486.96474,1224416.8351 499484.88504,1224410.5131
>> 499470.72264,1224410.1876 499470.02924,1224409.5706
>> 499468.87504,1224408.8795 499467.76364,1224408.658
>> 499467.43914,1224405.783 499463.31414,1224405.2422
>> 499462.57484,1224404.4119 499461.56314,1224404.1681
>> 499461.29034,1224397.5431 499454.00904,1224397.4215
>> 499453.87654,1224386.8436 499442.45874,1224379.5284
>> 499434.45384,1224369.2823 499422.31714,1224369.0369
>> 499422.03184,1224368.1423 499421.07654,1224367.1869
>> 499420.18194,1224366.6558 499419.73214,1224355.8777
>> 499410.92434,1224341.2698 499396.04914,1224341.1422
>> 499395.92044,1224329.9105 499384.68884,1224324.2636
>> 499378.59734,1224302.9088 499332.37814,1224392.4667
>> 499355.14934,1224393.122 499355.91874,1224487.2901
>> 499450.78514,1224496.2156 499459.77684,1224493.9911
>> 499462.52154,1224506.465 499484.35254,1224564.6899
>> 499528.85044,1224605.2731 499587.61344,1224614.2741
>> 499599.88254,1224625.0241 499614.53564,1224653.1386
>> 499652.85784,1224658.315 499659.91354,1224667.3321
>> 499683.31754,1224673.7804 499721.97084))
>>
>> point 0 is the se corner of the bow tie. point 1 is the "knot" of the
>> bow-tie, and you will see it reappear as point 4. the triangle made up
>> of points 1, 2, 3, 4 is the one I mentioned previously that goes in the
>> wrong direction.
>>
>> I must confess to a slight simplification in my previous e-mails; the
>> bow tie is not quite perfectly formed; it's southeast corner has been
>> trimmed off so that the eastern "triangle" is actually a
>> quadrilateral. Sorry :D
>>
>> Martin Davis wrote:
>>
>>> Chris,
>>>
>>> Can you post the WKT for the problematic feature? (Ascii art is
>>> nifty, but not really a substitute for a 1600x1200 pixel display...
>>> 8^)
>>>
>>> Chris Hermansen wrote:
>>>
>>>> Hi Nicolas, all;
>>>>
>>>> Nicolas, I understand your comment. But after looking at the data
>>>> some
>>>> more in OpenJump, that appears to not be my problem.
>>>>
>>>> If I load the PostGIS theme into OpenJump and run the QA on it, I see
>>>> that it is the polygon that contains the bow-tie shaped figure that is
>>>> the problem.
>>>>
>>>> I can represent this schematically as:
>>>>
>>>> +-----------------+
>>>> | |
>>>> | |><|
>>>> | |
>>>> +-----------------+
>>>>
>>>> (again, I hope this works out visually. I have done the figure in
>>>> fixed-width text).
>>>>
>>>> OpenJump's QA tool shows that there is an error in the enclosing
>>>> polygon
>>>> at the "bow-tie point", and that the enclosing polygon is a bad
>>>> feature.
>>>>
>>>> The triangle polygons themselves are not shown as bad features. There
>>>> are points shown at all corners of the triangles, ie there is no real
>>>> "bow-tie" type self intersection.
>>>>
>>>> The enclosing polygon contains all the edges shown in the above
>>>> figure,
>>>> including those of the triangles. Each triangle is a separate
>>>> polygon.
>>>>
>>>> I've traced the order of the edges of the enclosing polygon and it
>>>> appears that it is the ordering of these edges that is creating the
>>>> crossing / bow-tie in the enclosing polygon. That is, the enclosing
>>>> polygon's points define the edges as follows:
>>>>
>>>> pt 0: se corner of east triangle
>>>> pt 1: bow-tie point
>>>> pt 2: nw corner of west triangle
>>>> pt 3: sw corner of west triangle
>>>> pt 4: bow-tie point
>>>> pt 5: ne corner of east triangle
>>>> ... and off to the remainder of the enclosing polygon points
>>>>
>>>> So it appears to me that the edges of the western triangle are
>>>> actually
>>>> traversed in the wrong order in the enclosing polygon. As well,
>>>> clearly
>>>> there is a self-intersection in the enclosing polygon.
>>>>
>>>> I conclude from this that the order of traversal of the western
>>>> triangle
>>>> edges could be reversed and preserve the clockwise traversal of the
>>>> enclosing polygon's edges. However I think the fact that the bow-tie
>>>> point is traversed twice in the same polygon is a real problem that
>>>> must
>>>> be repaired (manually in this case, I guess).
>>>>
>>>> Does anyone have any comments on this? Thanks in advance!
>>>>
>>>> Nicolas Ribot wrote:
>>>>
>>>>
>>>>>> Good people;
>>>>>>
>>>>>> I have this odd problem that I hope others may clarify for me.
>>>>>>
>>>>>> I have a big ArcInfo polygon coverage produced by a sequence of
>>>>>> spatial
>>>>>> unions. One of the component polygon coverages was brutalized
>>>>>> somewhere
>>>>>> along the way and it has some polygons with triangular and bow-tie
>>>>>> inclusions.
>>>>>>
>>>>>> Nevertheless, the coverage is clean and sober as far as ArcInfo is
>>>>>> concerned.
>>>>>>
>>>>>> If you all can picture in your minds a bow-tie polygon |><|
>>>>>> where the
>>>>>> rightmost | of the bowtie is actually the edge of an enclosing
>>>>>> polygon, kind
>>>>>> of like:
>>>>>>
>>>>>> |
>>>>>> |><|
>>>>>> |
>>>>>>
>>>>>> (I sure hope that works out visually...)
>>>>>>
>>>>>> OK, when I use ogr2ogr to import this coverage into postgis 1.3.1 /
>>>>>> geos-3.0.0rc4, I see the following:
>>>>>>
>>>>>>
>>>>>>
>>>>>> the containing polygon fails at st_isValid()
>>>>>> the st_area() of the containing polygon appears to include the area
>>>>>> of the
>>>>>> bow-tie polygon, ie it is larger than the area copied over from the
>>>>>> ArcInfo
>>>>>> coverage by about the same amount as the area of the bow-tie
>>>>>> polygon When I
>>>>>> look at this little mess with OpenJump, sure enough the QA routines
>>>>>> find the
>>>>>> bow-tie and complain.
>>>>>>
>>>>>> The long and the short of this is that PostGIS returns slightly
>>>>>> more area
>>>>>> than ArcInfo does for the same big ugly polygon coverage, because
>>>>>> of the
>>>>>> apparent loss of these bow ties.
>>>>>>
>>>>>> What I'm not sure about is what exactly is wrong here. Is the
>>>>>> bow-tie
>>>>>> shape itself illegal? Or is it the fact that both sides of the
>>>>>> bow-tie
>>>>>> belong to the same polygon? Or something else I'm missing?
>>>>>>
>>>>>> Thanks for any light anyone can shed on this.
>>>>>>
>>>>>>
>>>>>>
>>>>> Hi,
>>>>> I will only give a partial answer:
>>>>> yes, a bowtie polygon is invalid for PostGIS (as stated in the OGC
>>>>> SFSQL documentation, polygon's boundary cannot cross itself).
>>>>> If you want to represent this with valid polygons, you will need 2
>>>>> triangles touching at one point.
>>>>>
>>>>> HTH
>>>>> nicolas
>>>>> _______________________________________________
>>>>> postgis-users mailing list
>>>>> postgis-users at postgis.refractions.net
>>>>> http://postgis.refractions.net/mailman/listinfo/postgis-users
>>>>>
>>>>
>>
>>
>>
>
--
Regards,
Chris Hermansen · mailto:clh at timberline.ca
tel:+1.604.714.2878 · fax:+1.604.733.0631
Timberline Natural Resource Group · http://www.timberline.ca
401 · 958 West 8th Avenue · Vancouver BC · Canada · V5Z 1E5
C'est ma façon de parler.
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