[postgis-users] PostGIS layer spatial tolerance
Oxenstierna Andreas
Andreas.Oxenstierna at sweco.se
Mon Aug 31 04:53:31 PDT 2009
Yes, I am at least partly aware of floating-point positioning problems.
However, from my perspective absolute, calculated and interpolated positions are not so important.
Data accuracy in the selected CRS is in any case in the magnitude of 10 metres.
We need to preserve similarity for shared coordinates, so the client code can rebuild and use the polygon topology correctly.
I.e. what we save is what we get back for the next editing operation.
A non-redundant geometry model, like ArcInfo Coverage, Oracle topology models, S57 hydrographic standard or PostGIS Topology, should of course be better to use but not yet in place for our software platform.
Best Regards
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Andreas Oxenstierna
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Från: postgis-users-bounces at postgis.refractions.net [mailto:postgis-users-bounces at postgis.refractions.net] För Chris Hermansen
Skickat: den 28 augusti 2009 17:59
Till: PostGIS Users Discussion
Ämne: Re: [postgis-users] PostGIS layer spatial tolerance
Oxenstierna Andreas wrote:
> I come from the ESRI and Oracle world. Both ArcSDE and Oracle Spatial
> have user-defined spatial tolerance for each spatially enabled layer.
> This ensures that coordinates are exact, down to the last decimal (or
> integer for ArcSDE).
> I cannot find in the documentation or in the functionality that
> PostGIS has an awareness of spatial tolerance. What I can find is:
> "All floating point comparisons within the SQL-MM implementation are
> performed to a specified tolerance, currently 1E-8"
> but nothing about actual storage.
>
> For me, the easiest solution would be to use a spatial tolerance.
> Otherwise, we may need to round all coordinates in the application
> code to e.g. 14 valid digits.
Andreas, you state that the ArcSDE fixed point representation ensures that coordinates are exact. This is incorrect. What it ensures is that locations are represented to a fixed precision; that is all.
By way of example, if you draw a line between points A and B, and then try to represent the locations of points along that line, neither ArcSDE fixed point nor Shapefile floating point will get those positions exactly. In general, floating point will represent those locations more accurately though that depends on the coordinate system (more precisely, the X and Y offsets in the coordinate system) and on the number of digits in the floating point fraction.
The same is true with points along a curve.
The use of a binary floating point number to represent a real quantity generally involves some approximation. For example, you cannot represent 0.1,0.2,0.3 etc exactly in binary floating point. You can represent 0.25, 0.5, etc exactly. This is because the fractional part in binary floating point is, well, binary, and binary fractional numbers cannot generally represent decimal fractional numbers exactly.
Of course, rational numbers like 1/3 and irrational numbers like pi cannot be represented exactly either.
This representational error is proportionally small; it's the unit round off error of the representation.
So a GIS file format that uses floating point to represent location will inevitably be off by its unit round-off error on many locations. This is true of ESRI coverages, shape files, and I guess PostGIS.
However the absolute amount of error can be pretty large in a given coordinate system; UTM northings in 32 bit binary floating point have a round-off error on the order of a metre at my latitude.
Round-off error accumulates through arithmetic operations. One great way to lose a lot of representational accuracy is to subtract two nearly equal numbers using a fixed number of fractional digits, as does adding two very different sized numbers; and therefore as does accumulating inner products (calculating statistical variance, polygon areas, eigenvalues, etc). People tend to use 64 bit binary floating point these days to try to minimize these problems. Fixed-point number systems are generally worse at losing representational accuracy through computation.
Another thing to remember about fixed-point representations like ArcSDE:
numbers come from somewhere, go somewhere, and are compared to other numbers. So conversions between external (eg ASCII), internal floating point, and internal fixed point, are pretty common. For example, if you do a query "where northing <= 2345678.9" how do you think the constant is handled? Is it converted precisely into an ArcSDE back-end fixed point representation, or is the comparison done in floating point by converting the northing value from its back-end fixed point representation to floating point?
See http://en.wikipedia.org/wiki/IEEE_754-2008 for more info on floating point.
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Regards, (please note new mobile number below)
Chris Hermansen mailto:chris.hermansen at timberline.ca
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