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How to identify polygons with (approximate) right-angles?

HayleyGlover

Hi, I have a shapefile with thousands of polygons of all sorts of shapes, and am trying to extract only those which are roughly rectilinear (more or less straight edged, with angles that are close to 90 degrees, and have four sides) and eliminate all the round/irregular polygons. I've attached an image of some of the polygons I've been generating.

Is there a way to automatically identify polygons in ArcMap which have interior angles of (for example) 85-95 degrees? Most of what I have seen only looks at finding the angle (ie. compass bearing) of an overall polygon, which is not what I want.

Thank you so much in advance!

poly_eg.PNG

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DanPatterson_Retired

as a general function tool with a single line code change you can use

<SPAN class="comment token"># -*- coding: utf-8 -*-</SPAN>
<SPAN class="keyword token">import</SPAN> numpy <SPAN class="keyword token">as</SPAN> np

<SPAN class="keyword token">def</SPAN> <SPAN class="token function">angles_poly</SPAN><SPAN class="punctuation token">(</SPAN>a<SPAN class="punctuation token">,</SPAN> inside<SPAN class="operator token">=</SPAN><SPAN class="token boolean">True</SPAN><SPAN class="punctuation token">,</SPAN> in_deg<SPAN class="operator token">=</SPAN><SPAN class="token boolean">True</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="string token">"""Sequential angles from a poly* shape
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;NOTE: this line.... angle = np.sum(angles)
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; can be changed to `np.min`, `np.max`, np.ptp or others
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; depending on what needs to be returned
&nbsp;&nbsp;&nbsp; """</SPAN>
&nbsp;&nbsp;&nbsp; a <SPAN class="operator token">=</SPAN> a<SPAN class="punctuation token">.</SPAN>getPart<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; a <SPAN class="operator token">=</SPAN>np<SPAN class="punctuation token">.</SPAN>asarray<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN>i<SPAN class="punctuation token">.</SPAN>X<SPAN class="punctuation token">,</SPAN> i<SPAN class="punctuation token">.</SPAN>Y<SPAN class="punctuation token">]</SPAN> <SPAN class="keyword token">for</SPAN> j <SPAN class="keyword token">in</SPAN> a <SPAN class="keyword token">for</SPAN> i <SPAN class="keyword token">in</SPAN> j<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">if</SPAN> len<SPAN class="punctuation token">(</SPAN>a<SPAN class="punctuation token">)</SPAN> <SPAN class="operator token"><</SPAN> <SPAN class="number token">2</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">return</SPAN> None
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">elif</SPAN> len<SPAN class="punctuation token">(</SPAN>a<SPAN class="punctuation token">)</SPAN> <SPAN class="operator token">==</SPAN> <SPAN class="number token">2</SPAN><SPAN class="punctuation token">:</SPAN>&nbsp; <SPAN class="comment token"># **** check</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ba <SPAN class="operator token">=</SPAN> a<SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="operator token">-</SPAN> a<SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">return</SPAN> np<SPAN class="punctuation token">.</SPAN>arctan2<SPAN class="punctuation token">(</SPAN><SPAN class="operator token">*</SPAN>ba<SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">:</SPAN><SPAN class="punctuation token">:</SPAN><SPAN class="operator token">-</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">else</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; angles <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">]</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">if</SPAN> np<SPAN class="punctuation token">.</SPAN>allclose<SPAN class="punctuation token">(</SPAN>a<SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> a<SPAN class="punctuation token">[</SPAN><SPAN class="operator token">-</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>&nbsp; <SPAN class="comment token"># closed loop</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a <SPAN class="operator token">=</SPAN> a<SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">:</SPAN><SPAN class="operator token">-</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; r <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">(</SPAN><SPAN class="operator token">-</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="punctuation token">)</SPAN> <SPAN class="operator token">+</SPAN> tuple<SPAN class="punctuation token">(</SPAN>range<SPAN class="punctuation token">(</SPAN>len<SPAN class="punctuation token">(</SPAN>a<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN> <SPAN class="operator token">+</SPAN> <SPAN class="punctuation token">(</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">else</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; r <SPAN class="operator token">=</SPAN> tuple<SPAN class="punctuation token">(</SPAN>range<SPAN class="punctuation token">(</SPAN>len<SPAN class="punctuation token">(</SPAN>a<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">for</SPAN> i <SPAN class="keyword token">in</SPAN> range<SPAN class="punctuation token">(</SPAN>len<SPAN class="punctuation token">(</SPAN>r<SPAN class="punctuation token">)</SPAN><SPAN class="operator token">-</SPAN><SPAN class="number token">2</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; p0<SPAN class="punctuation token">,</SPAN> p1<SPAN class="punctuation token">,</SPAN> p2 <SPAN class="operator token">=</SPAN> a<SPAN class="punctuation token">[</SPAN>r<SPAN class="punctuation token">[</SPAN>i<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> a<SPAN class="punctuation token">[</SPAN>r<SPAN class="punctuation token">[</SPAN>i<SPAN class="operator token">+</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> a<SPAN class="punctuation token">[</SPAN>r<SPAN class="punctuation token">[</SPAN>i<SPAN class="operator token">+</SPAN><SPAN class="number token">2</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ba <SPAN class="operator token">=</SPAN> p1 <SPAN class="operator token">-</SPAN> p0
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; bc <SPAN class="operator token">=</SPAN> p1 <SPAN class="operator token">-</SPAN> p2
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; cr <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>cross<SPAN class="punctuation token">(</SPAN>ba<SPAN class="punctuation token">,</SPAN> bc<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; dt <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>dot<SPAN class="punctuation token">(</SPAN>ba<SPAN class="punctuation token">,</SPAN> bc<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ang <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>arctan2<SPAN class="punctuation token">(</SPAN>np<SPAN class="punctuation token">.</SPAN>linalg<SPAN class="punctuation token">.</SPAN>norm<SPAN class="punctuation token">(</SPAN>cr<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">,</SPAN> dt<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; angles<SPAN class="punctuation token">.</SPAN>append<SPAN class="punctuation token">(</SPAN>ang<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">if</SPAN> in_deg<SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; angles <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>degrees<SPAN class="punctuation token">(</SPAN>angles<SPAN class="punctuation token">)</SPAN>&nbsp; <SPAN class="comment token">#---- function to change ------</SPAN>
&nbsp;&nbsp;&nbsp; angle <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>sum<SPAN class="punctuation token">(</SPAN>angles<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">return</SPAN> angle
<SPAN class="comment token">#__esri_field_calculator_splitter__</SPAN>
<SPAN class="comment token">#angles_poly(!Shape!)</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>‍</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><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN></SPAN>

change line 34 to

angles <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>ptp<SPAN class="punctuation token">(</SPAN>np<SPAN class="punctuation token">.</SPAN>abs<SPAN class="punctuation token">(</SPAN>angles<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN>‍<SPAN class="line-numbers-rows"><SPAN>‍</SPAN></SPAN>

now if you run this field calculation a square would have a deviation of 0 degrees, an equilateral triangle 0 etc.

So you might have to try a couple of other field calculations

angle <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>min<SPAN class="punctuation token">(</SPAN>angles<SPAN class="punctuation token">)</SPAN>
angle <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>max<SPAN class="punctuation token">(</SPAN>angles
etc
<SPAN class="line-numbers-rows"><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN></SPAN>

All comments

HayleyGlover

Thanks Darren - I'd been wondering if that function could be useful for me.

HayleyGlover

Thank you so much Dan, this is just what I was looking for.

HayleyGlover

Oh sorry - yes rectangular especially.

DarrenWiens2

Without specifically coding each requirement, you could look into running Minimum Bounding Geometry (RECTANGLE_BY_AREA) to create a rectangle for each feature, and select those meeting some threshold (e.g. 99% of area). The more rectangular the feature, the closer it will match the minimum rectangle.

bixb0012

trying to extract only those which are roughly rectilinear (more or less straight edged, with angles that are close to 90 degrees, and have four sides)

What is described in parentheses is rectangular, which is a special case of rectilinear. Are you interested in finding "roughly rectilinear" or "roughly rectangular?"

DanPatterson_Retired

as a general function tool with a single line code change you can use

<SPAN class="comment token"># -*- coding: utf-8 -*-</SPAN>
<SPAN class="keyword token">import</SPAN> numpy <SPAN class="keyword token">as</SPAN> np

<SPAN class="keyword token">def</SPAN> <SPAN class="token function">angles_poly</SPAN><SPAN class="punctuation token">(</SPAN>a<SPAN class="punctuation token">,</SPAN> inside<SPAN class="operator token">=</SPAN><SPAN class="token boolean">True</SPAN><SPAN class="punctuation token">,</SPAN> in_deg<SPAN class="operator token">=</SPAN><SPAN class="token boolean">True</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="string token">"""Sequential angles from a poly* shape
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;NOTE: this line.... angle = np.sum(angles)
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; can be changed to `np.min`, `np.max`, np.ptp or others
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; depending on what needs to be returned
&nbsp;&nbsp;&nbsp; """</SPAN>
&nbsp;&nbsp;&nbsp; a <SPAN class="operator token">=</SPAN> a<SPAN class="punctuation token">.</SPAN>getPart<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; a <SPAN class="operator token">=</SPAN>np<SPAN class="punctuation token">.</SPAN>asarray<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN>i<SPAN class="punctuation token">.</SPAN>X<SPAN class="punctuation token">,</SPAN> i<SPAN class="punctuation token">.</SPAN>Y<SPAN class="punctuation token">]</SPAN> <SPAN class="keyword token">for</SPAN> j <SPAN class="keyword token">in</SPAN> a <SPAN class="keyword token">for</SPAN> i <SPAN class="keyword token">in</SPAN> j<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">if</SPAN> len<SPAN class="punctuation token">(</SPAN>a<SPAN class="punctuation token">)</SPAN> <SPAN class="operator token"><</SPAN> <SPAN class="number token">2</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">return</SPAN> None
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">elif</SPAN> len<SPAN class="punctuation token">(</SPAN>a<SPAN class="punctuation token">)</SPAN> <SPAN class="operator token">==</SPAN> <SPAN class="number token">2</SPAN><SPAN class="punctuation token">:</SPAN>&nbsp; <SPAN class="comment token"># **** check</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ba <SPAN class="operator token">=</SPAN> a<SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="operator token">-</SPAN> a<SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">return</SPAN> np<SPAN class="punctuation token">.</SPAN>arctan2<SPAN class="punctuation token">(</SPAN><SPAN class="operator token">*</SPAN>ba<SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">:</SPAN><SPAN class="punctuation token">:</SPAN><SPAN class="operator token">-</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">else</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; angles <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">]</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">if</SPAN> np<SPAN class="punctuation token">.</SPAN>allclose<SPAN class="punctuation token">(</SPAN>a<SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> a<SPAN class="punctuation token">[</SPAN><SPAN class="operator token">-</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>&nbsp; <SPAN class="comment token"># closed loop</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a <SPAN class="operator token">=</SPAN> a<SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">:</SPAN><SPAN class="operator token">-</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; r <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">(</SPAN><SPAN class="operator token">-</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="punctuation token">)</SPAN> <SPAN class="operator token">+</SPAN> tuple<SPAN class="punctuation token">(</SPAN>range<SPAN class="punctuation token">(</SPAN>len<SPAN class="punctuation token">(</SPAN>a<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN> <SPAN class="operator token">+</SPAN> <SPAN class="punctuation token">(</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">else</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; r <SPAN class="operator token">=</SPAN> tuple<SPAN class="punctuation token">(</SPAN>range<SPAN class="punctuation token">(</SPAN>len<SPAN class="punctuation token">(</SPAN>a<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">for</SPAN> i <SPAN class="keyword token">in</SPAN> range<SPAN class="punctuation token">(</SPAN>len<SPAN class="punctuation token">(</SPAN>r<SPAN class="punctuation token">)</SPAN><SPAN class="operator token">-</SPAN><SPAN class="number token">2</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; p0<SPAN class="punctuation token">,</SPAN> p1<SPAN class="punctuation token">,</SPAN> p2 <SPAN class="operator token">=</SPAN> a<SPAN class="punctuation token">[</SPAN>r<SPAN class="punctuation token">[</SPAN>i<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> a<SPAN class="punctuation token">[</SPAN>r<SPAN class="punctuation token">[</SPAN>i<SPAN class="operator token">+</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> a<SPAN class="punctuation token">[</SPAN>r<SPAN class="punctuation token">[</SPAN>i<SPAN class="operator token">+</SPAN><SPAN class="number token">2</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ba <SPAN class="operator token">=</SPAN> p1 <SPAN class="operator token">-</SPAN> p0
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; bc <SPAN class="operator token">=</SPAN> p1 <SPAN class="operator token">-</SPAN> p2
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; cr <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>cross<SPAN class="punctuation token">(</SPAN>ba<SPAN class="punctuation token">,</SPAN> bc<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; dt <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>dot<SPAN class="punctuation token">(</SPAN>ba<SPAN class="punctuation token">,</SPAN> bc<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ang <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>arctan2<SPAN class="punctuation token">(</SPAN>np<SPAN class="punctuation token">.</SPAN>linalg<SPAN class="punctuation token">.</SPAN>norm<SPAN class="punctuation token">(</SPAN>cr<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">,</SPAN> dt<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; angles<SPAN class="punctuation token">.</SPAN>append<SPAN class="punctuation token">(</SPAN>ang<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">if</SPAN> in_deg<SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; angles <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>degrees<SPAN class="punctuation token">(</SPAN>angles<SPAN class="punctuation token">)</SPAN>&nbsp; <SPAN class="comment token">#---- function to change ------</SPAN>
&nbsp;&nbsp;&nbsp; angle <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>sum<SPAN class="punctuation token">(</SPAN>angles<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">return</SPAN> angle
<SPAN class="comment token">#__esri_field_calculator_splitter__</SPAN>
<SPAN class="comment token">#angles_poly(!Shape!)</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>‍</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><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN></SPAN>

change line 34 to

angles <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>ptp<SPAN class="punctuation token">(</SPAN>np<SPAN class="punctuation token">.</SPAN>abs<SPAN class="punctuation token">(</SPAN>angles<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN>‍<SPAN class="line-numbers-rows"><SPAN>‍</SPAN></SPAN>

now if you run this field calculation a square would have a deviation of 0 degrees, an equilateral triangle 0 etc.

So you might have to try a couple of other field calculations

angle <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>min<SPAN class="punctuation token">(</SPAN>angles<SPAN class="punctuation token">)</SPAN>
angle <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>max<SPAN class="punctuation token">(</SPAN>angles
etc
<SPAN class="line-numbers-rows"><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN></SPAN>

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