Errors in geometry... the importance of Spatial Reference

DanPatterson_Retired

This thread Errors in arcpy's Polygon class originated a long time ago.

Recently threads have been appearing where the importance of having a spatial reference specified seems to have been forgotten.

The cause is known... the solution is easy, but the lesson isn't sticking.  Read and see for yourself ... as a refresher... or for those venturing into the world of coordinate geometry.

The fix... uncomment line 19  and fix the ending to line 26.  But at least give making a mistake a chance.

geometry_errors_demo.py

start <SPAN class="string token">""" Script: geometry_errors_demo.py Author: Dan.Patterson AT carleton.ca Modified: 2016-01-30 Purpose: Demonstrates calculating various properties for polygons Notes: Revised formatting from the original thread: geonet.esri.com/thread/10256 """</SPAN> <SPAN class="keyword token">import</SPAN> numpy <SPAN class="keyword token">as</SPAN> np <SPAN class="keyword token">import</SPAN> arcpy <SPAN class="keyword token">from</SPAN> textwrap <SPAN class="keyword token">import</SPAN> dedent triangle <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN> square <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN> rectangle <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">2</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">2</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN> polygons <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">[</SPAN>triangle<SPAN class="punctuation token">,</SPAN> square<SPAN class="punctuation token">,</SPAN> rectangle<SPAN class="punctuation token">]</SPAN> labels <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="string token">"Triangle"</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="string token">"Square"</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="string token">"Rectangle"</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="comment token">#SR = arcpy.SpatialReference(3395) # uncomment </SPAN> <SPAN class="comment token"># ---- arcpy section ------</SPAN> <SPAN class="keyword token">def</SPAN> <SPAN class="token function">arcpy_demo</SPAN><SPAN class="punctuation token">(</SPAN>polygons<SPAN class="punctuation token">,</SPAN> labels<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN> <SPAN class="string token">"""Demo of arcpy errors """</SPAN> polys <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">]</SPAN> c <SPAN class="operator token">=</SPAN> <SPAN class="number token">0</SPAN> <SPAN class="keyword token">for</SPAN> p <SPAN class="keyword token">in</SPAN> polygons<SPAN class="punctuation token">:</SPAN> poly <SPAN class="operator token">=</SPAN> arcpy<SPAN class="punctuation token">.</SPAN>Polygon<SPAN class="punctuation token">(</SPAN>arcpy<SPAN class="punctuation token">.</SPAN>Array<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">[</SPAN>arcpy<SPAN class="punctuation token">.</SPAN>Point<SPAN class="punctuation token">(</SPAN><SPAN class="operator token">*</SPAN>pair<SPAN class="punctuation token">)</SPAN> <SPAN class="keyword token">for</SPAN> pair <SPAN class="keyword token">in</SPAN> p<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN> <SPAN class="comment token">#... p]), SR)</SPAN> frmt <SPAN class="operator token">=</SPAN> <SPAN class="string token">""" {} Input coordinates: {} Polygon properties... Returned coordinates in WKT - {} area {:<20.16f} length {:<20.16f} centroid {:} true centroid {:} first point {:} last point {:} extent - (XMin, YMin, XMax, YMax, ZMin, ZMax, MMin, MMax) - values: {!s:} convex hull: (x,y), (x,y)...(x,y) - sequence: {:} """</SPAN> extent_str <SPAN class="operator token">=</SPAN> str<SPAN class="punctuation token">(</SPAN>poly<SPAN class="punctuation token">.</SPAN>extent<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">.</SPAN>replace<SPAN class="punctuation token">(</SPAN><SPAN class="string token">" "</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="string token">", "</SPAN><SPAN class="punctuation token">)</SPAN> args <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">[</SPAN>labels<SPAN class="punctuation token">[</SPAN>c<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> polygons<SPAN class="punctuation token">[</SPAN>c<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> poly<SPAN class="punctuation token">.</SPAN>WKT<SPAN class="punctuation token">,</SPAN> poly<SPAN class="punctuation token">.</SPAN>area<SPAN class="punctuation token">,</SPAN> poly<SPAN class="punctuation token">.</SPAN>length<SPAN class="punctuation token">,</SPAN> poly<SPAN class="punctuation token">.</SPAN>centroid<SPAN class="punctuation token">,</SPAN> poly<SPAN class="punctuation token">.</SPAN>trueCentroid<SPAN class="punctuation token">,</SPAN> poly<SPAN class="punctuation token">.</SPAN>firstPoint<SPAN class="punctuation token">,</SPAN> poly<SPAN class="punctuation token">.</SPAN>lastPoint<SPAN class="punctuation token">,</SPAN> extent_str<SPAN class="punctuation token">,</SPAN>poly<SPAN class="punctuation token">.</SPAN>hullRectangle<SPAN class="punctuation token">]</SPAN> <SPAN class="keyword token">print</SPAN><SPAN class="punctuation token">(</SPAN>dedent<SPAN class="punctuation token">(</SPAN>frmt<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">.</SPAN>format<SPAN class="punctuation token">(</SPAN><SPAN class="operator token">*</SPAN>args<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN> array<SPAN class="punctuation token">.</SPAN>removeAll<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">)</SPAN> polys<SPAN class="punctuation token">.</SPAN>append<SPAN class="punctuation token">(</SPAN>poly<SPAN class="punctuation token">)</SPAN> c <SPAN class="operator token">+=</SPAN> <SPAN class="number token">1</SPAN> <SPAN class="comment token"># ---- part B area determination ----</SPAN> <SPAN class="keyword token">def</SPAN> <SPAN class="token function">ring_area</SPAN><SPAN class="punctuation token">(</SPAN>x<SPAN class="punctuation token">,</SPAN> y<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN> <SPAN class="string token">"""x and y as separate lists or arrays from references above - assumes first and last points are the same so uses slices - exterior rings ordered clockwise - holes are ordered counter-clockwise """</SPAN> a0 <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>dot<SPAN class="punctuation token">(</SPAN>x<SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">:</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> y<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> a1 <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>dot<SPAN class="punctuation token">(</SPAN>x<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> y<SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">:</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN> area <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">(</SPAN>a0<SPAN class="operator token">-</SPAN>a1<SPAN class="punctuation token">)</SPAN> <SPAN class="operator token">*</SPAN> <SPAN class="number token">0.5</SPAN> <SPAN class="comment token"># np.abs(a0-a1) * 0.5 for unsigned area, ie no holes</SPAN> <SPAN class="keyword token">return</SPAN> area <SPAN class="keyword token">def</SPAN> <SPAN class="token function">poly_area</SPAN><SPAN class="punctuation token">(</SPAN>Xs<SPAN class="punctuation token">,</SPAN>Ys<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN> <SPAN class="string token">"""calculate areas for parts"""</SPAN> area <SPAN class="operator token">=</SPAN> <SPAN class="number token">0.0</SPAN> <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>Xs<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN> x <SPAN class="operator token">=</SPAN> Xs<SPAN class="punctuation token">[</SPAN>i<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">;</SPAN> y <SPAN class="operator token">=</SPAN> Ys<SPAN class="punctuation token">[</SPAN>i<SPAN class="punctuation token">]</SPAN> area <SPAN class="operator token">+=</SPAN> ring_area<SPAN class="punctuation token">(</SPAN>x<SPAN class="punctuation token">,</SPAN> y<SPAN class="punctuation token">)</SPAN> <SPAN class="keyword token">return</SPAN> area <SPAN class="keyword token">def</SPAN> <SPAN class="token function">area_demo</SPAN><SPAN class="punctuation token">(</SPAN>polygons<SPAN class="punctuation token">,</SPAN> labels<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN> <SPAN class="string token">"""Sample area calculations for simple geometry"""</SPAN> polygons <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">[</SPAN>np<SPAN class="punctuation token">.</SPAN>array<SPAN class="punctuation token">(</SPAN>i<SPAN class="punctuation token">)</SPAN> <SPAN class="keyword token">for</SPAN> i <SPAN class="keyword token">in</SPAN> polygons<SPAN class="punctuation token">]</SPAN> <SPAN class="comment token"># convert lists to arrays</SPAN> <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>polygons<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN> x <SPAN class="operator token">=</SPAN> polygons<SPAN class="punctuation token">[</SPAN>i<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">:</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">;</SPAN> y <SPAN class="operator token">=</SPAN> polygons<SPAN class="punctuation token">[</SPAN>i<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">:</SPAN><SPAN class="punctuation token">,</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN> area <SPAN class="operator token">=</SPAN> ring_area<SPAN class="punctuation token">(</SPAN>x<SPAN class="punctuation token">,</SPAN> y<SPAN class="punctuation token">)</SPAN> frmt <SPAN class="operator token">=</SPAN> <SPAN class="string token">"\nArea for {}\n{}\nArea... {}"</SPAN> <SPAN class="keyword token">print</SPAN><SPAN class="punctuation token">(</SPAN>frmt<SPAN class="punctuation token">.</SPAN>format<SPAN class="punctuation token">(</SPAN>labels<SPAN class="punctuation token">[</SPAN>i<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN>polygons<SPAN class="punctuation token">[</SPAN>i<SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> area<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN> <SPAN class="keyword token">if</SPAN> __name__<SPAN class="operator token">==</SPAN><SPAN class="string token">"__main__"</SPAN><SPAN class="punctuation token">:</SPAN> <SPAN class="string token">""" """</SPAN> arcpy_demo<SPAN class="punctuation token">(</SPAN>polygons<SPAN class="punctuation token">,</SPAN> labels<SPAN class="punctuation token">)</SPAN> area_demo<SPAN class="punctuation token">(</SPAN>polygons<SPAN class="punctuation token">,</SPAN> labels<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>‍</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><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>

Results

geometry_errors_demo<SPAN class="punctuation token">.</SPAN>py outputs Triangle Input coordinates<SPAN class="punctuation token">:</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">0.0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0.0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="number token">0.0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1.0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="number token">1.0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0.0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN> Polygon properties<SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN> Returned coordinates <SPAN class="keyword token">in</SPAN> WKT <SPAN class="operator token">-</SPAN> MULTIPOLYGON <SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">(</SPAN><SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1.0001220703125</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0</SPAN> <SPAN class="number token">1.0001220703125</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN> area <SPAN class="number token">0.5001220777630806</SPAN> length <SPAN class="number token">3.4146303364895956</SPAN> centroid <SPAN class="number token">0.3333740234375</SPAN> <SPAN class="number token">0.3333740234375</SPAN> NaN NaN true centroid <SPAN class="number token">0.3333740234375</SPAN> <SPAN class="number token">0.3333740234375</SPAN> NaN NaN first point <SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN> NaN NaN last point <SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN> NaN NaN extent <SPAN class="operator token">-</SPAN> <SPAN class="punctuation token">(</SPAN>XMin<SPAN class="punctuation token">,</SPAN> YMin<SPAN class="punctuation token">,</SPAN> XMax<SPAN class="punctuation token">,</SPAN> YMax<SPAN class="punctuation token">,</SPAN> ZMin<SPAN class="punctuation token">,</SPAN> ZMax<SPAN class="punctuation token">,</SPAN> MMin<SPAN class="punctuation token">,</SPAN> MMax<SPAN class="punctuation token">)</SPAN> <SPAN class="operator token">-</SPAN> values<SPAN class="punctuation token">:</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1.0001220703125</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1.0001220703125</SPAN><SPAN class="punctuation token">,</SPAN> NaN<SPAN class="punctuation token">,</SPAN> NaN<SPAN class="punctuation token">,</SPAN> NaN<SPAN class="punctuation token">,</SPAN> NaN convex hull<SPAN class="punctuation token">:</SPAN> <SPAN class="punctuation token">(</SPAN>x<SPAN class="punctuation token">,</SPAN>y<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">(</SPAN>x<SPAN class="punctuation token">,</SPAN>y<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">(</SPAN>x<SPAN class="punctuation token">,</SPAN>y<SPAN class="punctuation token">)</SPAN> <SPAN class="operator token">-</SPAN> sequence<SPAN class="punctuation token">:</SPAN> <SPAN class="number token">1.0001220703125</SPAN> <SPAN class="number token">2.22044604925031E-16</SPAN> <SPAN class="number token">0.50006103515625</SPAN> <SPAN class="operator token">-</SPAN><SPAN class="number token">0.50006103515625</SPAN> <SPAN class="operator token">-</SPAN><SPAN class="number token">0.50006103515625</SPAN> <SPAN class="number token">0.50006103515625</SPAN> <SPAN class="number token">0</SPAN> <SPAN class="number token">1.0001220703125</SPAN> Square Input coordinates<SPAN class="punctuation token">:</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">0.0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0.0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="number token">0.0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1.0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="number token">1.0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1.0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="number token">1.0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0.0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN> Polygon properties<SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN> Returned coordinates <SPAN class="keyword token">in</SPAN> WKT <SPAN class="operator token">-</SPAN> MULTIPOLYGON <SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">(</SPAN><SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1.0001220703125</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1.0001220703125</SPAN> <SPAN class="number token">1.0001220703125</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0</SPAN> <SPAN class="number token">1.0001220703125</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN> area <SPAN class="number token">1.0002441555261612</SPAN> length <SPAN class="number token">4.0004882812500000</SPAN> centroid <SPAN class="number token">0.50006103515625</SPAN> <SPAN class="number token">0.50006103515625</SPAN> NaN NaN true centroid <SPAN class="number token">0.50006103515625</SPAN> <SPAN class="number token">0.50006103515625</SPAN> NaN NaN first point <SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN> NaN NaN last point <SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN> NaN NaN extent <SPAN class="operator token">-</SPAN> <SPAN class="punctuation token">(</SPAN>XMin<SPAN class="punctuation token">,</SPAN> YMin<SPAN class="punctuation token">,</SPAN> XMax<SPAN class="punctuation token">,</SPAN> YMax<SPAN class="punctuation token">,</SPAN> ZMin<SPAN class="punctuation token">,</SPAN> ZMax<SPAN class="punctuation token">,</SPAN> MMin<SPAN class="punctuation token">,</SPAN> MMax<SPAN class="punctuation token">)</SPAN> <SPAN class="operator token">-</SPAN> values<SPAN class="punctuation token">:</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1.0001220703125</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1.0001220703125</SPAN><SPAN class="punctuation token">,</SPAN> NaN<SPAN class="punctuation token">,</SPAN> NaN<SPAN class="punctuation token">,</SPAN> NaN<SPAN class="punctuation token">,</SPAN> NaN convex hull<SPAN class="punctuation token">:</SPAN> <SPAN class="punctuation token">(</SPAN>x<SPAN class="punctuation token">,</SPAN>y<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">(</SPAN>x<SPAN class="punctuation token">,</SPAN>y<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">(</SPAN>x<SPAN class="punctuation token">,</SPAN>y<SPAN class="punctuation token">)</SPAN> <SPAN class="operator token">-</SPAN> sequence<SPAN class="punctuation token">:</SPAN> <SPAN class="number token">6.12398146082414E-17</SPAN> <SPAN class="number token">1.0001220703125</SPAN> <SPAN class="number token">1.0001220703125</SPAN> <SPAN class="number token">1.0001220703125</SPAN> <SPAN class="number token">1.0001220703125</SPAN> <SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN> Rectangle Input coordinates<SPAN class="punctuation token">:</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">0.0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0.0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="number token">0.0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1.0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="number token">2.0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1.0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="number token">2.0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0.0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN> Polygon properties<SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN> Returned coordinates <SPAN class="keyword token">in</SPAN> WKT <SPAN class="operator token">-</SPAN> MULTIPOLYGON <SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">(</SPAN><SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">2.0001220703125</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">2.0001220703125</SPAN> <SPAN class="number token">1.0001220703125</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0</SPAN> <SPAN class="number token">1.0001220703125</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN> area <SPAN class="number token">2.0003662258386612</SPAN> length <SPAN class="number token">6.0004882812500000</SPAN> centroid <SPAN class="number token">1.00006103515625</SPAN> <SPAN class="number token">0.50006103515625</SPAN> NaN NaN true centroid <SPAN class="number token">1.00006103515625</SPAN> <SPAN class="number token">0.50006103515625</SPAN> NaN NaN first point <SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN> NaN NaN last point <SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN> NaN NaN extent <SPAN class="operator token">-</SPAN> <SPAN class="punctuation token">(</SPAN>XMin<SPAN class="punctuation token">,</SPAN> YMin<SPAN class="punctuation token">,</SPAN> XMax<SPAN class="punctuation token">,</SPAN> YMax<SPAN class="punctuation token">,</SPAN> ZMin<SPAN class="punctuation token">,</SPAN> ZMax<SPAN class="punctuation token">,</SPAN> MMin<SPAN class="punctuation token">,</SPAN> MMax<SPAN class="punctuation token">)</SPAN> <SPAN class="operator token">-</SPAN> values<SPAN class="punctuation token">:</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">2.0001220703125</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1.0001220703125</SPAN><SPAN class="punctuation token">,</SPAN> NaN<SPAN class="punctuation token">,</SPAN> NaN<SPAN class="punctuation token">,</SPAN> NaN<SPAN class="punctuation token">,</SPAN> NaN convex hull<SPAN class="punctuation token">:</SPAN> <SPAN class="punctuation token">(</SPAN>x<SPAN class="punctuation token">,</SPAN>y<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">(</SPAN>x<SPAN class="punctuation token">,</SPAN>y<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">(</SPAN>x<SPAN class="punctuation token">,</SPAN>y<SPAN class="punctuation token">)</SPAN> <SPAN class="operator token">-</SPAN> sequence<SPAN class="punctuation token">:</SPAN> <SPAN class="number token">6.12398146082414E-17</SPAN> <SPAN class="number token">1.0001220703125</SPAN> <SPAN class="number token">2.0001220703125</SPAN> <SPAN class="number token">1.0001220703125</SPAN> <SPAN class="number token">2.0001220703125</SPAN> <SPAN class="operator token">-</SPAN><SPAN class="number token">2.22044604925031E-16</SPAN> <SPAN class="number token">0</SPAN> <SPAN class="number token">0</SPAN> Area <SPAN class="keyword token">for</SPAN> Triangle <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="punctuation token">[</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="punctuation token">[</SPAN> <SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN> Area<SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">0.5</SPAN> Area <SPAN class="keyword token">for</SPAN> Square <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="punctuation token">[</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="punctuation token">[</SPAN> <SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="punctuation token">[</SPAN> <SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN> Area<SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">1.0</SPAN> Area <SPAN class="keyword token">for</SPAN> Rectangle <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="punctuation token">[</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="punctuation token">[</SPAN> <SPAN class="number token">2</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">1</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="punctuation token">[</SPAN> <SPAN class="number token">2</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN> Area<SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN><SPAN class="punctuation token">.</SPAN> <SPAN class="number token">2.0</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>‍</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><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN></SPAN>

Calculating the area old-school (67-83) proved that sometimes the old methods still have merit.