Using a circle in a union can change its Shape Area

[LarsUngerechts]

Hello there,

I have a problem with complex geometries and the Union command. 

Background: I have parcel Feature Classes and am calculating the coverage of construction polygons from several Feature Classes. I have to calculate those coverages and coverage combinations in a very precise way as the information will be used to elaborate lease agreements.

Method and problem. I use a parcel Feature Class and several construction Feature Classes. As I also need all possible combinations of constructions per parcel, I use the Union Geoprocessing tool (ArcGIS Pro 3.3) in order to combine all input layers. All Feature Classes are calculated into one result Feature Class which includes all intersecting geometries. Afterwards I use a Python script to quantify all coverages/coverage combinations and write those values in the parcel Feature Class. In general, the whole process does function pretty well. My problems start, when I use complex geometries (circles, ellipses in Geodatabases). When I have a circle and another feature without their borders intersecting, all is fine! The input and result Hape Areas of the circles are the same. If the circles boundary is intersected by the boundary of one of the other feature, it will be split (which is to expected). If I take the result areas, which belong to the circle from the union result, the combined Shape Area will not be the same as the input Shape Area (of course taking into account that all files have the same coordinate system, etc.).

ArcGIS Pro trys to use complex geometries (arcs) to reconstruct the geometry of the input circle but fails to match it completely. The only way I found to reduce this problem is to use higher precisions for the Resolution (0,00000001 meters) and Tolerance (0,00000003 meters) in the environmental settings. But still, I get roughly a 2 square centimeter error with a circle which has a radius of 40 meters.

Here some example values:

• Input circle: 1317.227075 m²
• Combined Union result areas of this circle (without modifying env-settings): 1317,197206 m²
• Combined Union result areas of this circle (with modifying env-settings): 1317,201008 m²

Is there a way to get more precise or even perfect results?

I have included an attchement with a set of demo data (parcels, construction 1 & construction 2).

I appreciate any help in this matter and thank you in advance for ideas and recommendations.

Beste regards

Lars

[DanPatterson]

What is the coordinate system of the inputs?  (to save downloading and loading the zip)

Is it area preserving? or just a conformal projected coordinate system?

Your approach at controlling the x,y tolerances is a good one

How Union works—ArcGIS Pro | Documentation

but the coordinate system may be the key

[LarsUngerechts]

Thank you for your input and question!

All files of the calculation have the same spatial reference (so there should be no reprojection error...). The system which all tests have been made in is ETRS 1989 (32 N - 6 digits): WKID 25832.  As far as I know it is area preserving. 

[DanPatterson]

ETRS89 / UTM zone 32N - EPSG:25832

seems to be a transverse mercator projection with a scale factor of 0,9996 which suggests to me that it is conformal not equal area.

I would contact Tech Support to see if they have any recommendations about a coordinate system that might be appropriate and/or whether 2.5 cm^2 is out of line with the areas calculated.  

I assume that arcs and true circles are being used and they aren't being represented by n-gons which would alter areas.