Check Geometry Fails in Shared-Origin Edge Case

JoshuaBixby

In the Hole lies outside shell and arcpy thread, the OP had geometries that were invalid but Esri tools were failing to detect them as such.  After some investigation, I discovered a shared-origin edge case where the Check Geometry will fail to detect an invalid geometry.

The following is a simplified example of the OP's geometries from the Hole lies outside shell and arcpy  thread.

In the example above, polygon a is valid while polygon b is invalid because of "hole" lies outside of the bounding geometry.  When run through Check Geometry, it will identify polygon b as invalid.  When the two parts are combined into a two-part multi-polygon, the Check Geometry tools fails to identify the polygon as invalid even though one of the two parts is invalid.

The following code creates a feature class containing three polygons (a, b, and ab), and then checks the geometry of all three:

<SPAN class="keyword token">import</SPAN> arcpy

SR <SPAN class="operator token">=</SPAN> arcpy<SPAN class="punctuation token">.</SPAN>SpatialReference<SPAN class="punctuation token">(</SPAN><SPAN class="number token">4326</SPAN><SPAN class="punctuation token">)</SPAN>
polys <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">{</SPAN>
    <SPAN class="string token">"a"</SPAN><SPAN class="punctuation token">:</SPAN><SPAN class="punctuation token">(</SPAN><SPAN class="string token">"MULTIPOLYGON(((10 5, 10 10, 0 10, 0 0, 10 0, 10 5)))"</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">,</SPAN>
    <SPAN class="string token">"b"</SPAN><SPAN class="punctuation token">:</SPAN><SPAN class="punctuation token">(</SPAN><SPAN class="string token">"MULTIPOLYGON(((10 5, 15 0, 20 5, 15 10, 10 5),(10 5, 7.5 2.5, 5 5, 7.5 7.5, 10 5)))"</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">,</SPAN>
    <SPAN class="string token">"ab"</SPAN><SPAN class="punctuation token">:</SPAN><SPAN class="punctuation token">(</SPAN><SPAN class="string token">"MULTIPOLYGON(((10 5, 10 10, 0 10, 0 0, 10 0, 10 5)),"</SPAN>
                        <SPAN class="string token">"((10 5, 15 0, 20 5, 15 10, 10 5),(10 5, 7.5 2.5, 5 5, 7.5 7.5, 10 5)))"</SPAN><SPAN class="punctuation token">)</SPAN>
<SPAN class="punctuation token">}</SPAN>

fc <SPAN class="operator token">=</SPAN> arcpy<SPAN class="punctuation token">.</SPAN>CopyFeatures_management<SPAN class="punctuation token">(</SPAN>
    <SPAN class="punctuation token">[</SPAN>arcpy<SPAN class="punctuation token">.</SPAN>FromWKT<SPAN class="punctuation token">(</SPAN>polys<SPAN class="punctuation token">[</SPAN>p<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> SR<SPAN class="punctuation token">)</SPAN> <SPAN class="keyword token">for</SPAN> p <SPAN class="keyword token">in</SPAN> polys<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN>
    arcpy<SPAN class="punctuation token">.</SPAN>CreateScratchName<SPAN class="punctuation token">(</SPAN>workspace<SPAN class="operator token">=</SPAN><SPAN class="string token">"memory"</SPAN><SPAN class="punctuation token">)</SPAN>
<SPAN class="punctuation token">)</SPAN>
chkGeom <SPAN class="operator token">=</SPAN> arcpy<SPAN class="punctuation token">.</SPAN>CheckGeometry_management<SPAN class="punctuation token">(</SPAN>fc<SPAN class="punctuation token">,</SPAN> arcpy<SPAN class="punctuation token">.</SPAN>CreateScratchName<SPAN class="punctuation token">(</SPAN>workspace<SPAN class="operator token">=</SPAN><SPAN class="string token">"memory"</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN>
<SPAN class="keyword token">print</SPAN><SPAN class="punctuation token">(</SPAN><SPAN class="operator token">*</SPAN>arcpy<SPAN class="punctuation token">.</SPAN>da<SPAN class="punctuation token">.</SPAN>SearchCursor<SPAN class="punctuation token">(</SPAN>chkGeom<SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="string token">"FEATURE_ID"</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="string token">"PROBLEM"</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">,</SPAN> sep<SPAN class="operator token">=</SPAN><SPAN class="string token">"\n"</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="line-numbers-rows"><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN></SPAN>

The result is that just one of the three polygons is identified as invalid:

<SPAN class="operator token">>></SPAN><SPAN class="operator token">></SPAN> <SPAN class="keyword token">print</SPAN><SPAN class="punctuation token">(</SPAN><SPAN class="operator token">*</SPAN>arcpy<SPAN class="punctuation token">.</SPAN>da<SPAN class="punctuation token">.</SPAN>SearchCursor<SPAN class="punctuation token">(</SPAN>chkGeom<SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="string token">"FEATURE_ID"</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="string token">"PROBLEM"</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">,</SPAN> sep<SPAN class="operator token">=</SPAN><SPAN class="string token">"\n"</SPAN><SPAN class="punctuation token">)</SPAN>
<SPAN class="punctuation token">(</SPAN><SPAN class="number token">2</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="string token">'incorrect ring ordering'</SPAN><SPAN class="punctuation token">)</SPAN>
<SPAN class="operator token">>></SPAN><SPAN class="operator token">></SPAN> <SPAN class="line-numbers-rows"><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN></SPAN>

Since the third polygon is a combined polygon, it should also be identified as invalid.

JoshuaBixby

Sergey Tolstov‌, thanks for the follow-up reply.

The additional information you provided is quite helpful to understanding the underlying Esri geometry model, but I am having a hard time finding where Esri's geometry model is documented.  I am aware of the Geometry objects—Common Data Types | ArcGIS for Developers documentation, but it seems incomplete, or at least abridged and more focused on the semantics of writing a geometry in JSON format than describing the underlying geometry model.  Ironically, the 20+ year old Shapefile Technical Description document (https://www.esri.com/library/whitepapers/pdfs/shapefile.pdf) contains more specifics about Esri geometries than the "current" geometry objects documentation online.  I also found some additional information in Java API Polygon on GitHub, but it seems odd to bury a geometry model in a Java API on GitHub.

Getting back to the specific example, I still don't understand why an invalid single-part polygon can be part of a valid multi-part polygon.  I understand that without the shared-vertex the new multi-part polygon creates a new violation that didn't exist before, i.e., without a shared vertex the two single-part polygons violate the "segments can touch other segments only at the end points" rule.  However, even with a shared vertex, one of the two polygons that makes up the new multi-part polygon is invalid.  Isn't an Esri polygon invalid if one of the parts is invalid by itself?