How to change the way representing polygons

Question

Polygon[{{{442.997, 358.128}, {424., 329.}, {436.438, 
269.919}, {485.639, 320.816}}, {{572.752, 
292.812}, {705.658, 191.098}, {624., 334.}, {609.854, 
348.146}, {570.475, 297.83}}, {{464.802, 381.573}, {498.744, 
331.34}, {508.086, 332.982}, {505.5, 348.5}, {495.722, 
397.392}, {479.103, 393.349}}, {{445.321, 368.088}, {442.997, 
358.128}, {485.639, 320.816}, {498.744, 331.34}, {464.802, 
381.573}, {458.299, 382.565}}, {{570.475, 297.83}, {609.854, 
348.146}, {624., 375.429}, {625.503, 378.65}, {565.059, 
397.838}, {543.815, 331.653}}, {{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}}}]

I want to change the representing way into the following

{Polygon[{{609.854, 348.146}, {624., 334.}, {624., 375.429}}], 
Polygon[{{181.75, 333.5}, {174.732, 335.659}, {169.333, 308.667}}], 
Polygon[{{505.5, 348.5}, {505.5, 402.7}, {495.722, 397.392}}], 
Polygon[{{442.997, 358.128}, {424., 329.}, {436.438, 
269.919}, {485.639, 320.816}}], 
Polygon[{{164.187, 285.679}, {151.82, 301.851}, {115.851, 
310.269}, {159.994, 247.949}}], 
Polygon[{{568.92, 105.25}, {493.478, 206.559}, {450.574, 
182.043}, {416.444, 105.25}}], 
Polygon[{{211.75, 105.25}, {192.852, 199.739}, {127.386, 
195.063}, {10.308, 105.25}}], 
Polygon[{{371.196, 478.75}, {401.311, 381.457}, {443.24, 
399.906}, {430.367, 478.75}}], 
Polygon[{{543.815, 331.653}, {565.059, 397.838}, {550.145, 
438.549}, {510.5, 405.7}, {510.5, 333.086}}], 
Polygon[{{173.74, 242.534}, {177.482, 278.082}, {164.187, 
285.679}, {159.994, 247.949}, {164.211, 239.253}}], 
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[{{415.662, 339.5}, {403.897, 370.269}, {399.794, 
374.757}, {356.729, 357.139}, {351.171, 339.5}}], 
Polygon[{{76.8045, 284.438}, {106.84, 315.197}, {108.887, 
328.131}, {92.7084, 370.825}, {32.397, 334.638}}], 
Polygon[{{209.734, 327.281}, {181.75, 333.5}, {169.333, 
308.667}, {168.212, 304.743}, {178.794, 304.413}}], 
Polygon[{{505.5, 348.5}, {508.086, 332.982}, {510.5, 
333.086}, {510.5, 405.7}, {505.5, 402.7}}]}

Is there anyone can answer the question?

Can you explain the connection between both "representations"? — Dr. belisarius, Mar 10 '16 at 16:59
Welcome to Mathematica.SE! I suggest the following: 0) Browse the common pitfalls question 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Read the [faq]! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! — Dr. belisarius, Mar 10 '16 at 16:59
@Dr.belisarius Hi if there is no connection, i just simply want to change the representing way? Like Polygon[{{{442.997, 358.128}, {424., 329.}, {436.438, 269.919}, {485.639, 320.816}}, {{572.752, 292.812}, {705.658, 191.098}, {624., 334.}, {609.854, 348.146}, {570.475, 297.83}}}] to Polygon[{{442.997, 358.128}, {424., 329.}, {436.438, 269.919}, {485.639, 320.816}}], Polygon[{{572.752, 292.812}, {705.658, 191.098}, {624., 334.}, {609.854, 348.146}, {570.475, 297.83}}] — JasonX, Mar 10 '16 at 17:10
@Xavier Thanks for your prompt reply, is that possible to paste the code for me?? — JasonX, Mar 10 '16 at 17:23

score 4 · Answer 1 · answered Mar 10 '16 at 17:39

Another way is with Thread:

Thread[Polygon[{{{442.997, 358.128}, {424., 329.}, {436.438, 
 269.919}, {485.639, 320.816}}, {{572.752, 292.812}, {705.658, 
 191.098}, {624., 334.}, {609.854, 348.146}, {570.475, 
 297.83}}, {{464.802, 381.573}, {498.744, 331.34}, {508.086, 
 332.982}, {505.5, 348.5}, {495.722, 397.392}, {479.103, 
 393.349}}, {{445.321, 368.088}, {442.997, 358.128}, {485.639, 
 320.816}, {498.744, 331.34}, {464.802, 381.573}, {458.299, 
 382.565}}, {{570.475, 297.83}, {609.854, 348.146}, {624., 
 375.429}, {625.503, 378.65}, {565.059, 397.838}, {543.815, 
 331.653}}, {{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[{{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[{{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}}]
}

score 2 · Accepted Answer · answered Mar 10 '16 at 17:28

poly = Polygon[{{{442.997, 358.128}, {424., 329.}, {436.438, 
      269.919}, {485.639, 320.816}}, {{572.752, 292.812}, {705.658, 
      191.098}, {624., 334.}, {609.854, 348.146}, {570.475, 
      297.83}}, {{464.802, 381.573}, {498.744, 331.34}, {508.086, 
      332.982}, {505.5, 348.5}, {495.722, 397.392}, {479.103, 
      393.349}}, {{445.321, 368.088}, {442.997, 358.128}, {485.639, 
      320.816}, {498.744, 331.34}, {464.802, 381.573}, {458.299, 
      382.565}}, {{570.475, 297.83}, {609.854, 348.146}, {624., 
      375.429}, {625.503, 378.65}, {565.059, 397.838}, {543.815, 
      331.653}}, {{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}}}];

You have not explained how, in general, to subdivide the original Polygon to get the shown representaion. Using instead the original list structure.

polys = Polygon /@ poly[[1]];

colors = ColorData[10] /@ Range[Length[polys]];

Graphics[Transpose[{colors, polys}]]

How to change the way representing polygons

2 Answers2