Delete/Extract some certain data from a list?

Question

These are some polygons for Voronoi mesh.

poly1={Polygon[{{442.997, 358.128}, {424., 329.},{436.438, 269.919}, {485.639, 320.816}}], 
Polygon[{{442.997, 358.128}, {445.321, 368.088}, {403.897, 370.269}, {415.662, 339.5}, {424., 329.}}], 
Polygon[{{445.321, 368.088}, {442.997, 358.128}, {485.639, 320.816}, {498.744, 331.34}, {464.802, 381.573}, {458.299, 382.565}}], 
Polygon[{{424., 329.}, {415.662, 339.5}, {351.171, 339.5}, {341.933, 321.272}, {417.449, 261.095}, {435.088, 266.485}, {436.438, 269.919}}],
Polygon[{{543.815, 331.653}, {565.059, 397.838}, {550.145, 438.549}, {510.5, 405.7}, {510.5, 333.086}}], 
Polygon[{{505.5, 348.5}, {508.086, 332.982}, {510.5, 333.086}, {510.5, 405.7}, {505.5, 402.7}}], 
Polygon[{{570.475, 297.83}, {609.854, 348.146}, {624., 375.429}, {625.503, 378.65}, {565.059, 397.838}, {543.815, 331.653}}], 
Polygon[{{549.527, 478.75}, {550.145, 438.549}, {565.059, 397.838}, {625.503, 378.65}, {776., 398.195}, {776., 478.75}}], 
Polygon[{{465.618, 478.75}, 479.103, 393.349}, {495.722, 397.392}, {505.5, 402.7}, {510.5, 405.7}, {550.145, 438.549}, {549.527, 478.75}}],
Polygon[{{505.5, 348.5}, {505.5, 402.7}, 495.722, 397.392}}],
Polygon[{{543.815, 331.653}, {565.059, 397.838}, {550.145, 438.549}, {510.5, 405.7}, {510.5, 333.086}}], 
Polygon[{{505.5, 348.5}, {508.086, 332.982}, {510.5, 333.086}, {510.5, 405.7}, {505.5, 402.7}}], 
Polygon[{{464.802, 381.573}, {498.744, 331.34}, {508.086, 332.982}, {505.5, 348.5}, {495.722, 397.392}, 479.103, 393.349}}], 
Polygon[{{465.618, 478.75}, {479.103, 393.349}, {495.722, 397.392}, {505.5, 402.7}, {510.5, 405.7}, {550.145, 438.549}, {549.527, 478.75}}],
Polygon[{{609.854, 348.146}, {624., 334.}, {624., 375.429}}],
Polygon[{{572.752, 292.812}, {705.658, 191.098}, {624., 
334.}, {609.854, 348.146}, {570.475, 297.83}}], 
Polygon[{{776., 398.195}, {625.503, 378.65}, {624., 375.429}, {624., 
334.}, {705.658, 191.098}, {776., 134.549}}],
Polygon[{{570.475, 297.83}, {609.854, 348.146}, {624., 
375.429}, {625.503, 378.65}, {565.059, 397.838}, {543.815, 
331.653}}], 
Polygon[{{776., 105.25}, {776., 134.549}, {705.658, 
191.098}, {572.752, 292.812}, {481.892, 231.621}, {493.478, 
206.559}, {568.92, 105.25}}], 
Polygon[{{505.5, 348.5}, {505.5, 402.7}, {495.722, 397.392}}], 
Polygon[{{505.5, 348.5}, {508.086, 332.982}, {510.5, 
333.086}, {510.5, 405.7}, {505.5, 402.7}}], 
Polygon[{{464.802, 381.573}, {498.744, 331.34}, {508.086, 
332.982}, {505.5, 348.5}, {495.722, 397.392}, {479.103, 
393.349}}], 
Polygon[{{445.321, 368.088}, {442.997, 358.128}, {485.639, 
320.816}, {498.744, 331.34}, {464.802, 381.573}, {458.299, 
382.565}}], 
Polygon[{{430.367, 478.75}, {443.24, 399.906}, {458.299, 
382.565}, {464.802, 381.573}, {479.103, 393.349}, {465.618, 
478.75}}], 
Polygon[{{465.618, 478.75}, {479.103, 393.349}, {495.722, 
397.392}, {505.5, 402.7}, {510.5, 405.7}, {550.145, 
438.549}, {549.527, 478.75}}], 
Polygon[{{442.997, 358.128}, {424., 329.}, {436.438, 
269.919}, {485.639, 320.816}}], 
Polygon[{{442.997, 358.128}, {445.321, 368.088}, {403.897, 
370.269}, {415.662, 339.5}, {424., 329.}}], 
Polygon[{{445.321, 368.088}, {458.299, 382.565}, {443.24, 
399.906}, {401.311, 381.457}, {399.794, 374.757}, {403.897, 
370.269}}], 
Polygon[{{464.802, 381.573}, {498.744, 331.34}, {508.086, 
332.982}, {505.5, 348.5}, {495.722, 397.392}, {479.103, 
393.349}}], 
Polygon[{{445.321, 368.088}, {442.997, 358.128}, {485.639, 
320.816}, {498.744, 331.34}, {464.802, 381.573}, {458.299, 
382.565}}], 
Polygon[{{430.367, 478.75}, {443.24, 399.906}, {458.299, 
382.565}, {464.802, 381.573}, {479.103, 393.349}, {465.618, 
478.75}}], 
Polygon[{{609.854, 348.146}, {624., 334.}, {624., 375.429}}], 
Polygon[{{543.815, 331.653}, {565.059, 397.838}, {550.145, 
438.549}, {510.5, 405.7}, {510.5, 333.086}}], 
Polygon[{{572.752, 292.812}, {705.658, 191.098}, {624., 
334.}, {609.854, 348.146}, {570.475, 297.83}}], 
Polygon[{{776., 398.195}, {625.503, 378.65}, {624., 375.429}, {624., 
334.}, {705.658, 191.098}, {776., 134.549}}], 
Polygon[{{570.475, 297.83}, {609.854, 348.146}, {624., 
375.429}, {625.503, 378.65}, {565.059, 397.838}, {543.815, 
331.653}}], 
Polygon[{{549.527, 478.75}, {550.145, 438.549}, {565.059, 
397.838}, {625.503, 378.65}, {776., 398.195}, {776., 478.75}}], 
Polygon[{{568.92, 105.25}, {493.478, 206.559}, {450.574, 
182.043}, {416.444, 105.25}}], 
Polygon[{{401.402, 242.039}, {417.449, 261.095}, {341.933, 
321.272}, {332.108, 319.133}, {338.605, 267.158}}], 
Polygon[{{416.444, 105.25}, {450.574, 182.043}, {339.913, 
162.514}, {317.763, 138.438}, {315.55, 105.25}}], 
Polygon[{{288.602, 192.154}, {317.763, 138.438}, {339.913, 
162.514}, {401.402, 242.039}, {338.605, 267.158}}], 
Polygon[{{493.478, 206.559}, {481.892, 231.621}, {435.088, 
266.485}, {417.449, 261.095}, {401.402, 242.039}, {339.913, 
162.514}, {450.574, 182.043}}], 
Polygon[{{424., 329.}, {415.662, 339.5}, {351.171, 339.5}, {341.933, 
321.272}, {417.449, 261.095}, {435.088, 266.485}, {436.438, 
269.919}}], 
Polygon[{{776., 105.25}, {776., 134.549}, {705.658, 
191.098}, {572.752, 292.812}, {481.892, 231.621}, {493.478, 
206.559}, {568.92, 105.25}}], 
Polygon[{{442.997, 358.128}, {424., 329.}, {436.438, 
269.919}, {485.639, 320.816}}], 
Polygon[{{401.402, 242.039}, {417.449, 261.095}, {341.933, 
321.272}, {332.108, 319.133}, {338.605, 267.158}}], 
Polygon[{{415.662, 339.5}, {403.897, 370.269}, {399.794, 
374.757}, {356.729, 357.139}, {351.171, 339.5}}], 
Polygon[{{442.997, 358.128}, {445.321, 368.088}, {403.897, 
370.269}, {415.662, 339.5}, {424., 329.}}], 
Polygon[{{493.478, 206.559}, {481.892, 231.621}, {435.088, 
266.485}, {417.449, 261.095}, {401.402, 242.039}, {339.913, 
162.514}, {450.574, 182.043}}], 
Polygon[{{424., 329.}, {415.662, 339.5}, {351.171, 339.5}, {341.933, 
321.272}, {417.449, 261.095}, {435.088, 266.485}, {436.438, 
269.919}}], 
Polygon[{{290.399, 365.384}, {308.094, 315.836}, {332.108, 
319.133}, {341.933, 321.272}, {351.171, 339.5}, {356.729, 
357.139}, {345.49, 386.573}}], 
Polygon[{{568.92, 105.25}, {493.478, 206.559}, {450.574, 
182.043}, {416.444, 105.25}}], 
Polygon[{{572.752, 292.812}, {705.658, 191.098}, {624., 
334.}, {609.854, 348.146}, {570.475, 297.83}}], 
Polygon[{{776., 398.195}, {625.503, 378.65}, {624., 375.429}, {624., 
334.}, {705.658, 191.098}, {776., 134.549}}], 
Polygon[{{493.478, 206.559}, {481.892, 231.621}, {435.088, 
266.485}, {417.449, 261.095}, {401.402, 242.039}, {339.913, 
162.514}, {450.574, 182.043}}], 
Polygon[{{776., 105.25}, {776., 134.549}, {705.658, 
191.098}, {572.752, 292.812}, {481.892, 231.621}, {493.478, 
206.559}, {568.92, 105.25}}]}

These are the polygons I do not want from the above list

poly2={Polygon[{{442.997, 358.128}, {424., 329.}, {436.438, 
269.919}, {485.639, 320.816}}], 
Polygon[{{543.815, 331.653}, {565.059, 397.838}, {550.145, 
438.549}, {510.5, 405.7}, {510.5, 333.086}}], 
Polygon[{{505.5, 348.5}, {508.086, 332.982}, {510.5, 
333.086}, {510.5, 405.7}, {505.5, 402.7}}], 
Polygon[{{572.752, 292.812}, {705.658, 191.098}, {624., 
334.}, {609.854, 348.146}, {570.475, 297.83}}], 
Polygon[{{464.802, 381.573}, {498.744, 331.34}, {508.086, 
332.982}, {505.5, 348.5}, {495.722, 397.392}, {479.103, 
393.349}}], 
Polygon[{{445.321, 368.088}, {442.997, 358.128}, {485.639, 
320.816}, {498.744, 331.34}, {464.802, 381.573}, {458.299, 
382.565}}], 
Polygon[{{570.475, 297.83}, {609.854, 348.146}, {624., 
375.429}, {625.503, 378.65}, {565.059, 397.838}, {543.815, 
331.653}}], 
Polygon[{{493.478, 206.559}, {481.892, 231.621}, {435.088, 
266.485}, {417.449, 261.095}, {401.402, 242.039}, {339.913, 
162.514}, {450.574, 182.043}}], 
Polygon[{{424., 329.}, {415.662, 339.5}, {351.171, 339.5}, {341.933, 
321.272}, {417.449, 261.095}, {435.088, 266.485}, {436.438, 
269.919}}], 
Polygon[{{776., 105.25}, {776., 134.549}, {705.658, 
191.098}, {572.752, 292.812}, {481.892, 231.621}, {493.478, 
206.559}, {568.92, 105.25}}]}

Is there a way to delete the polygons I do not want from the list and save the rest of them?

Possible duplicate of Site - Cell Correspondence in Voronoi Diagram obtained via VoronoiMesh — RunnyKine, Mar 10 '16 at 18:09
@RunnyKine But I want to find the exact points and try to connect them? Is it possible? — JasonX, Mar 10 '16 at 18:14
Your question suggests you have the sites and want the cells that contain those points. What am I missing? What do you mean connect them? — RunnyKine, Mar 10 '16 at 18:24
@RunnyKine Actually I have the coordinate of the vertices of polygons (cells) and I wish to reversely find the sites, that is my question? Is that possible to be solved? — JasonX, Mar 10 '16 at 18:29
Ah, I see. But I don't have the free time to work on that now. — RunnyKine, Mar 10 '16 at 18:31
@RunnyKine May I ask you a question? {{{3.15429516, 1.68154241}, Polygon[{20, 11, 6, 15}]}, {{0.925806386, 3.57266721}, Polygon[{12, 3, 1, 13}]}, {{2.12535296, 3.88158116}, Polygon[{14, 5, 8, 18}]}, {{3.52419343, 0.689832144}, Polygon[{18, 8, 7, 17}]}} If the output was like this, how to extract only the points value — JasonX, Mar 11 '16 at 02:47
If you store that expression in a variable e.g. pts. Then just do pts[[All,1]] — RunnyKine, Mar 11 '16 at 02:55
Well, then just do pts = the output then do pts[[All,1]] — RunnyKine, Mar 11 '16 at 03:07

David G. Stork · Answer 1 · 2016-03-08T19:17:41.497

1

myR = DelaunayMesh[Flatten[plgs, 1]];

HighlightMesh[myR, Style[0, Black]]

To overlap:

Show[VoronoiMesh[Flatten[plgs, 1], 
  MeshCellStyle -> Directive[Opacity[0.2], Red]], 
 DelaunayMesh[Flatten[plgs, 1], PlotTheme -> "Lines"]]

edited Mar 08 '16 at 19:17

answered Mar 08 '16 at 18:38

David G. Stork

41,180
3
34
96

score 1 · Accepted Answer · answered Mar 13 '16 at 04:06

Apologies if I have misunderstood.

g1 = Graphics[{FaceForm[Yellow], EdgeForm[Black], poly1, Orange, 
    Intersection[poly1, poly2]}];
g2 = Graphics[{FaceForm[Orange], EdgeForm[Black], poly2}];
g3 = Graphics[{FaceForm[Yellow], EdgeForm[Black], 
    Complement[poly1, poly2]}];
Grid[{{"poly1 \[Union] poly2", "poly2=poly2 \[Intersection] poly1", 
   "poly1\\poly2"}, {g1, g2, g3}}]

Note: I had to "correct" some of the polygons. The "corrected" polygons follow. I may have made errors but the principles are clear.

poly1 = {Polygon[{{442.997, 358.128}, {424., 329.}, {436.438, 
      269.919}, {485.639, 320.816}}], 
   Polygon[{{442.997, 358.128}, {445.321, 368.088}, {403.897, 
      370.269}, {415.662, 339.5}, {424., 329.}}], 
   Polygon[{{445.321, 368.088}, {442.997, 358.128}, {485.639, 
      320.816}, {498.744, 331.34}, {464.802, 381.573}, {458.299, 
      382.565}}], 
   Polygon[{{424., 329.}, {415.662, 339.5}, {351.171, 
      339.5}, {341.933, 321.272}, {417.449, 261.095}, {435.088, 
      266.485}, {436.438, 269.919}}], 
   Polygon[{{543.815, 331.653}, {565.059, 397.838}, {550.145, 
      438.549}, {510.5, 405.7}, {510.5, 333.086}}], 
   Polygon[{{505.5, 348.5}, {508.086, 332.982}, {510.5, 
      333.086}, {510.5, 405.7}, {505.5, 402.7}}], 
   Polygon[{{570.475, 297.83}, {609.854, 348.146}, {624., 
      375.429}, {625.503, 378.65}, {565.059, 397.838}, {543.815, 
      331.653}}], 
   Polygon[{{549.527, 478.75}, {550.145, 438.549}, {565.059, 
      397.838}, {625.503, 378.65}, {776., 398.195}, {776., 478.75}}], 
   Polygon[{{465.618, 478.75}, {479.103, 393.349}, {495.722, 
      397.392}, {505.5, 402.7}, {510.5, 405.7}, {550.145, 
      438.549}, {549.527, 478.75}}], 
   Polygon[{{505.5, 348.5}, {505.5, 402.7}, {495.722, 397.392}}], 
   Polygon[{{543.815, 331.653}, {565.059, 397.838}, {550.145, 
      438.549}, {510.5, 405.7}, {510.5, 333.086}}], 
   Polygon[{{505.5, 348.5}, {508.086, 332.982}, {510.5, 
      333.086}, {510.5, 405.7}, {505.5, 402.7}}], 
   Polygon[{{464.802, 381.573}, {498.744, 331.34}, {508.086, 
      332.982}, {505.5, 348.5}, {495.722, 397.392}, {479.103, 
      393.349}}], 
   Polygon[{{465.618, 478.75}, {479.103, 393.349}, {495.722, 
      397.392}, {505.5, 402.7}, {510.5, 405.7}, {550.145, 
      438.549}, {549.527, 478.75}}], 
   Polygon[{{609.854, 348.146}, {624., 334.}, {624., 375.429}}], 
   Polygon[{{572.752, 292.812}, {705.658, 191.098}, {624., 
      334.}, {609.854, 348.146}, {570.475, 297.83}}], 
   Polygon[{{776., 398.195}, {625.503, 378.65}, {624., 
      375.429}, {624., 334.}, {705.658, 191.098}, {776., 134.549}}], 
   Polygon[{{570.475, 297.83}, {609.854, 348.146}, {624., 
      375.429}, {625.503, 378.65}, {565.059, 397.838}, {543.815, 
      331.653}}], 
   Polygon[{{776., 105.25}, {776., 134.549}, {705.658, 
      191.098}, {572.752, 292.812}, {481.892, 231.621}, {493.478, 
      206.559}, {568.92, 105.25}}], 
   Polygon[{{505.5, 348.5}, {505.5, 402.7}, {495.722, 397.392}}], 
   Polygon[{{505.5, 348.5}, {508.086, 332.982}, {510.5, 
      333.086}, {510.5, 405.7}, {505.5, 402.7}}], 
   Polygon[{{464.802, 381.573}, {498.744, 331.34}, {508.086, 
      332.982}, {505.5, 348.5}, {495.722, 397.392}, {479.103, 
      393.349}}], 
   Polygon[{{445.321, 368.088}, {442.997, 358.128}, {485.639, 
      320.816}, {498.744, 331.34}, {464.802, 381.573}, {458.299, 
      382.565}}], 
   Polygon[{{430.367, 478.75}, {443.24, 399.906}, {458.299, 
      382.565}, {464.802, 381.573}, {479.103, 393.349}, {465.618, 
      478.75}}], 
   Polygon[{{465.618, 478.75}, {479.103, 393.349}, {495.722, 
      397.392}, {505.5, 402.7}, {510.5, 405.7}, {550.145, 
      438.549}, {549.527, 478.75}}], 
   Polygon[{{442.997, 358.128}, {424., 329.}, {436.438, 
      269.919}, {485.639, 320.816}}], 
   Polygon[{{442.997, 358.128}, {445.321, 368.088}, {403.897, 
      370.269}, {415.662, 339.5}, {424., 329.}}], 
   Polygon[{{445.321, 368.088}, {458.299, 382.565}, {443.24, 
      399.906}, {401.311, 381.457}, {399.794, 374.757}, {403.897, 
      370.269}}], 
   Polygon[{{464.802, 381.573}, {498.744, 331.34}, {508.086, 
      332.982}, {505.5, 348.5}, {495.722, 397.392}, {479.103, 
      393.349}}], 
   Polygon[{{445.321, 368.088}, {442.997, 358.128}, {485.639, 
      320.816}, {498.744, 331.34}, {464.802, 381.573}, {458.299, 
      382.565}}], 
   Polygon[{{430.367, 478.75}, {443.24, 399.906}, {458.299, 
      382.565}, {464.802, 381.573}, {479.103, 393.349}, {465.618, 
      478.75}}], 
   Polygon[{{609.854, 348.146}, {624., 334.}, {624., 375.429}}], 
   Polygon[{{543.815, 331.653}, {565.059, 397.838}, {550.145, 
      438.549}, {510.5, 405.7}, {510.5, 333.086}}], 
   Polygon[{{572.752, 292.812}, {705.658, 191.098}, {624., 
      334.}, {609.854, 348.146}, {570.475, 297.83}}], 
   Polygon[{{776., 398.195}, {625.503, 378.65}, {624., 
      375.429}, {624., 334.}, {705.658, 191.098}, {776., 134.549}}], 
   Polygon[{{570.475, 297.83}, {609.854, 348.146}, {624., 
      375.429}, {625.503, 378.65}, {565.059, 397.838}, {543.815, 
      331.653}}], 
   Polygon[{{549.527, 478.75}, {550.145, 438.549}, {565.059, 
      397.838}, {625.503, 378.65}, {776., 398.195}, {776., 478.75}}], 
   Polygon[{{568.92, 105.25}, {493.478, 206.559}, {450.574, 
      182.043}, {416.444, 105.25}}], 
   Polygon[{{401.402, 242.039}, {417.449, 261.095}, {341.933, 
      321.272}, {332.108, 319.133}, {338.605, 267.158}}], 
   Polygon[{{416.444, 105.25}, {450.574, 182.043}, {339.913, 
      162.514}, {317.763, 138.438}, {315.55, 105.25}}], 
   Polygon[{{288.602, 192.154}, {317.763, 138.438}, {339.913, 
      162.514}, {401.402, 242.039}, {338.605, 267.158}}], 
   Polygon[{{493.478, 206.559}, {481.892, 231.621}, {435.088, 
      266.485}, {417.449, 261.095}, {401.402, 242.039}, {339.913, 
      162.514}, {450.574, 182.043}}], 
   Polygon[{{424., 329.}, {415.662, 339.5}, {351.171, 
      339.5}, {341.933, 321.272}, {417.449, 261.095}, {435.088, 
      266.485}, {436.438, 269.919}}], 
   Polygon[{{776., 105.25}, {776., 134.549}, {705.658, 
      191.098}, {572.752, 292.812}, {481.892, 231.621}, {493.478, 
      206.559}, {568.92, 105.25}}], 
   Polygon[{{442.997, 358.128}, {424., 329.}, {436.438, 
      269.919}, {485.639, 320.816}}], 
   Polygon[{{401.402, 242.039}, {417.449, 261.095}, {341.933, 
      321.272}, {332.108, 319.133}, {338.605, 267.158}}], 
   Polygon[{{415.662, 339.5}, {403.897, 370.269}, {399.794, 
      374.757}, {356.729, 357.139}, {351.171, 339.5}}], 
   Polygon[{{442.997, 358.128}, {445.321, 368.088}, {403.897, 
      370.269}, {415.662, 339.5}, {424., 329.}}], 
   Polygon[{{493.478, 206.559}, {481.892, 231.621}, {435.088, 
      266.485}, {417.449, 261.095}, {401.402, 242.039}, {339.913, 
      162.514}, {450.574, 182.043}}], 
   Polygon[{{424., 329.}, {415.662, 339.5}, {351.171, 
      339.5}, {341.933, 321.272}, {417.449, 261.095}, {435.088, 
      266.485}, {436.438, 269.919}}], 
   Polygon[{{290.399, 365.384}, {308.094, 315.836}, {332.108, 
      319.133}, {341.933, 321.272}, {351.171, 339.5}, {356.729, 
      357.139}, {345.49, 386.573}}], 
   Polygon[{{568.92, 105.25}, {493.478, 206.559}, {450.574, 
      182.043}, {416.444, 105.25}}], 
   Polygon[{{572.752, 292.812}, {705.658, 191.098}, {624., 
      334.}, {609.854, 348.146}, {570.475, 297.83}}], 
   Polygon[{{776., 398.195}, {625.503, 378.65}, {624., 
      375.429}, {624., 334.}, {705.658, 191.098}, {776., 134.549}}], 
   Polygon[{{493.478, 206.559}, {481.892, 231.621}, {435.088, 
      266.485}, {417.449, 261.095}, {401.402, 242.039}, {339.913, 
      162.514}, {450.574, 182.043}}], 
   Polygon[{{776., 105.25}, {776., 134.549}, {705.658, 
      191.098}, {572.752, 292.812}, {481.892, 231.621}, {493.478, 
      206.559}, {568.92, 105.25}}]};
poly2 = {Polygon[{{442.997, 358.128}, {424., 329.}, {436.438, 
      269.919}, {485.639, 320.816}}], 
   Polygon[{{543.815, 331.653}, {565.059, 397.838}, {550.145, 
      438.549}, {510.5, 405.7}, {510.5, 333.086}}], 
   Polygon[{{505.5, 348.5}, {508.086, 332.982}, {510.5, 
      333.086}, {510.5, 405.7}, {505.5, 402.7}}], 
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@JasonX thanks. I'm glad it was helpful :) – ubpdqn Mar 14 '16 at 00:01 — ubpdqn, Mar 14 '16 at 00:01

Delete/Extract some certain data from a list?

2 Answers2