gosper_island.data

1

486
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0.84693877551   0.194413866156
0.867346938776   0.194413866156
0.877551020408   0.212087853988
0.897959183673   0.212087853988
0.908163265306   0.22976184182
0.897959183673   0.247435829653
0.908163265306   0.265109817485
0.897959183673   0.282783805317
0.908163265306   0.30045779315
0.928571428571   0.30045779315
0.938775510204   0.318131780982
0.928571428571   0.335805768814
0.938775510204   0.353479756647
0.928571428571   0.371153744479
0.908163265306   0.371153744479
0.897959183673   0.388827732311
0.877551020408   0.388827732311
0.867346938776   0.406501720144
0.877551020408   0.424175707976
0.867346938776   0.441849695808
0.84693877551   0.441849695808
0.836734693878   0.459523683641
0.816326530612   0.459523683641
0.80612244898   0.477197671473
0.816326530612   0.494871659305
0.80612244898   0.512545647138
0.816326530612   0.53021963497
0.836734693878   0.53021963497
0.84693877551   0.547893622802
0.836734693878   0.565567610635
0.84693877551   0.583241598467
0.836734693878   0.600915586299
0.816326530612   0.600915586299
0.80612244898   0.618589574132
0.785714285714   0.618589574132
0.775510204082   0.636263561964
0.785714285714   0.653937549796
0.775510204082   0.671611537629
0.755102040816   0.671611537629
0.744897959184   0.689285525461

read_triangles.py

from __future__ import division
import numpy as np
import re

def triangle_area(points):
  p0, p1, p2 = points
  a = np.linalg.norm(p2 - p1)
  b = np.linalg.norm(p1 - p0)
  c = np.linalg.norm(p2 - p0)

  return 1/4*np.sqrt((a+b+c)*(b+c-a)*(c+a-b)*(a+b-c))

def triangle_com_inertia(points, area, com):
  p0, p1, p2 = points
  a = np.linalg.norm(p2 - p1)
  b = np.linalg.norm(p1 - p0)
  c = np.linalg.norm(p2 - p0)

  inertia = -1/48*np.sqrt(-(a-b-c)*(a+b-c)*(a-b+c)*(a+b+c))*(a**2-3*(b**2+c**2))

  return inertia - area*np.linalg.norm(com - p0)**2

with  open('triangles.data', 'r') as f:
  lines = f.readlines()

regex = re.compile('triangle #(\d+): (\d+) (\d+) (\d+)')

simplices = [None]*len(lines)
for line in lines:
  match = regex.match(line)
  groups = map(int, match.groups())
  simplices[groups[0]] = [groups[1]-1, groups[2]-1, groups[3]-1]

points = np.genfromtxt('gosper_island.data', skip_header=3)

area = 0
inertia = 0

for simplex in simplices:
  tri_points = [points[s, :] for s in simplex]
  com = np.sum(tri_points, axis=0)/3
  cur_area = triangle_area(tri_points)
  area += cur_area
  inertia += triangle_com_inertia(tri_points, cur_area, com) + cur_area*np.linalg.norm(com)**2

mass = 1.
radius = 1.

true = 3./4*mass*radius**2
print inertia/area
print true
print (inertia/area)/true

triangles.data

triangle #0: 431 185 429
triangle #1: 430 431 429
triangle #2: 431 184 185
triangle #3: 186 429 185
triangle #4: 186 428 429
triangle #5: 188 428 186
triangle #6: 187 188 186
triangle #7: 188 427 428
triangle #8: 190 427 188
triangle #9: 189 190 188
triangle #10: 427 190 425
triangle #11: 426 427 425
triangle #12: 191 425 190
triangle #13: 425 191 423
triangle #14: 424 425 423
triangle #15: 192 423 191
triangle #16: 192 422 423
triangle #17: 193 422 192
triangle #18: 193 421 422
triangle #19: 194 421 193
triangle #20: 194 195 420
triangle #21: 421 194 420
triangle #22: 419 420 195
triangle #23: 196 419 195
triangle #24: 196 418 419
triangle #25: 197 418 196
triangle #26: 197 417 418
triangle #27: 198 417 197
triangle #28: 198 416 417
triangle #29: 199 416 198
triangle #30: 199 415 416
triangle #31: 200 415 199
triangle #32: 200 201 413
triangle #33: 415 200 413
triangle #34: 414 415 413
triangle #35: 202 413 201
triangle #36: 206 207 411
triangle #37: 203 206 411
triangle #38: 202 203 411
triangle #39: 413 202 411
triangle #40: 412 413 411
triangle #41: 203 205 206
triangle #42: 208 411 207
triangle #43: 208 410 411
triangle #44: 209 410 208
triangle #45: 209 409 410
triangle #46: 210 409 209
triangle #47: 409 210 407
triangle #48: 408 409 407
triangle #49: 211 407 210
triangle #50: 407 211 405
triangle #51: 406 407 405
triangle #52: 212 405 211
triangle #53: 212 213 404
triangle #54: 405 212 404
triangle #55: 214 404 213
triangle #56: 214 403 404
triangle #57: 215 403 214
triangle #58: 215 402 403
triangle #59: 401 402 215
triangle #60: 216 401 215
triangle #61: 216 400 401
triangle #62: 218 400 216
triangle #63: 217 218 216
triangle #64: 218 399 400
triangle #65: 220 399 218
triangle #66: 219 220 218
triangle #67: 220 398 399
triangle #68: 221 398 220
triangle #69: 221 397 398
triangle #70: 222 397 221
triangle #71: 222 396 397
triangle #72: 395 396 222
triangle #73: 392 395 222
triangle #74: 391 392 222
triangle #75: 224 391 222
triangle #76: 223 224 222
triangle #77: 392 394 395
triangle #78: 224 390 391
triangle #79: 389 390 224
triangle #80: 226 389 224
triangle #81: 225 226 224
triangle #82: 226 388 389
triangle #83: 227 388 226
triangle #84: 227 387 388
triangle #85: 228 387 227
triangle #86: 228 386 387
triangle #87: 229 386 228
triangle #88: 229 385 386
triangle #89: 230 385 229
triangle #90: 230 231 384
triangle #91: 385 230 384
triangle #92: 383 384 231
triangle #93: 232 383 231
triangle #94: 232 382 383
triangle #95: 233 382 232
triangle #96: 233 381 382
triangle #97: 362 381 233
triangle #98: 361 362 233
triangle #99: 234 361 233
triangle #100: 362 380 381
triangle #101: 234 360 361
triangle #102: 359 360 234
triangle #103: 356 359 234
triangle #104: 355 356 234
triangle #105: 236 355 234
triangle #106: 235 236 234
triangle #107: 356 358 359
triangle #108: 236 354 355
triangle #109: 353 354 236
triangle #110: 238 353 236
triangle #111: 237 238 236
triangle #112: 238 352 353
triangle #113: 254 352 238
triangle #114: 253 254 238
triangle #115: 239 253 238
triangle #116: 254 351 352
triangle #117: 239 252 253
triangle #118: 251 252 239
triangle #119: 248 251 239
triangle #120: 247 248 239
triangle #121: 240 247 239
triangle #122: 248 250 251
triangle #123: 240 246 247
triangle #124: 245 246 240
triangle #125: 242 245 240
triangle #126: 241 242 240
triangle #127: 242 244 245
triangle #128: 242 243 244
triangle #129: 248 249 250
triangle #130: 256 351 254
triangle #131: 255 256 254
triangle #132: 256 350 351
triangle #133: 272 350 256
triangle #134: 271 272 256
triangle #135: 257 271 256
triangle #136: 272 349 350
triangle #137: 257 270 271
triangle #138: 269 270 257
triangle #139: 266 269 257
triangle #140: 265 266 257
triangle #141: 258 265 257
triangle #142: 266 268 269
triangle #143: 258 264 265
triangle #144: 263 264 258
triangle #145: 260 263 258
triangle #146: 259 260 258
triangle #147: 260 262 263
triangle #148: 260 261 262
triangle #149: 266 267 268
triangle #150: 274 349 272
triangle #151: 273 274 272
triangle #152: 274 348 349
triangle #153: 347 348 274
triangle #154: 275 347 274
triangle #155: 275 346 347
triangle #156: 276 346 275
triangle #157: 276 345 346
triangle #158: 278 345 276
triangle #159: 277 278 276
triangle #160: 278 344 345
triangle #161: 280 344 278
triangle #162: 279 280 278
triangle #163: 280 343 344
triangle #164: 281 343 280
triangle #165: 281 342 343
triangle #166: 341 342 281
triangle #167: 338 341 281
triangle #168: 337 338 281
triangle #169: 282 337 281
triangle #170: 338 340 341
triangle #171: 282 336 337
triangle #172: 335 336 282
triangle #173: 283 335 282
triangle #174: 283 334 335
triangle #175: 284 334 283
triangle #176: 284 285 333
triangle #177: 334 284 333
triangle #178: 286 333 285
triangle #179: 286 332 333
triangle #180: 287 332 286
triangle #181: 287 331 332
triangle #182: 288 331 287
triangle #183: 288 330 331
triangle #184: 329 330 288
triangle #185: 290 329 288
triangle #186: 289 290 288
triangle #187: 290 328 329
triangle #188: 292 328 290
triangle #189: 291 292 290
triangle #190: 292 327 328
triangle #191: 308 327 292
triangle #192: 307 308 292
triangle #193: 293 307 292
triangle #194: 308 326 327
triangle #195: 293 306 307
triangle #196: 305 306 293
triangle #197: 302 305 293
triangle #198: 301 302 293
triangle #199: 294 301 293
triangle #200: 302 304 305
triangle #201: 294 300 301
triangle #202: 299 300 294
triangle #203: 296 299 294
triangle #204: 295 296 294
triangle #205: 296 298 299
triangle #206: 296 297 298
triangle #207: 302 303 304
triangle #208: 310 326 308
triangle #209: 309 310 308
triangle #210: 310 325 326
triangle #211: 311 325 310
triangle #212: 311 324 325
triangle #213: 323 324 311
triangle #214: 320 323 311
triangle #215: 319 320 311
triangle #216: 312 319 311
triangle #217: 320 322 323
triangle #218: 312 318 319
triangle #219: 317 318 312
triangle #220: 314 317 312
triangle #221: 313 314 312
triangle #222: 314 316 317
triangle #223: 314 315 316
triangle #224: 320 321 322
triangle #225: 338 339 340
triangle #226: 356 357 358
triangle #227: 364 380 362
triangle #228: 363 364 362
triangle #229: 364 379 380
triangle #230: 365 379 364
triangle #231: 365 378 379
triangle #232: 377 378 365
triangle #233: 374 377 365
triangle #234: 373 374 365
triangle #235: 366 373 365
triangle #236: 374 376 377
triangle #237: 366 372 373
triangle #238: 371 372 366
triangle #239: 368 371 366
triangle #240: 367 368 366
triangle #241: 368 370 371
triangle #242: 368 369 370
triangle #243: 374 375 376
triangle #244: 392 393 394
triangle #245: 203 204 205
triangle #246: 433 184 431
triangle #247: 432 433 431
triangle #248: 184 433 182
triangle #249: 183 184 182
triangle #250: 434 182 433
triangle #251: 182 434 180
triangle #252: 181 182 180
triangle #253: 435 180 434
triangle #254: 435 179 180
triangle #255: 436 179 435
triangle #256: 436 178 179
triangle #257: 437 178 436
triangle #258: 437 438 177
triangle #259: 178 437 177
triangle #260: 176 177 438
triangle #261: 439 176 438
triangle #262: 439 175 176
triangle #263: 440 175 439
triangle #264: 440 174 175
triangle #265: 441 174 440
triangle #266: 441 173 174
triangle #267: 442 173 441
triangle #268: 442 172 173
triangle #269: 443 172 442
triangle #270: 443 444 170
triangle #271: 172 443 170
triangle #272: 171 172 170
triangle #273: 445 170 444
triangle #274: 449 450 168
triangle #275: 446 449 168
triangle #276: 445 446 168
triangle #277: 170 445 168
triangle #278: 169 170 168
triangle #279: 446 448 449
triangle #280: 451 168 450
triangle #281: 451 167 168
triangle #282: 452 167 451
triangle #283: 452 166 167
triangle #284: 453 166 452
triangle #285: 166 453 164
triangle #286: 165 166 164
triangle #287: 454 164 453
triangle #288: 164 454 162
triangle #289: 163 164 162
triangle #290: 455 162 454
triangle #291: 455 456 161
triangle #292: 162 455 161
triangle #293: 457 161 456
triangle #294: 457 160 161
triangle #295: 458 160 457
triangle #296: 458 159 160
triangle #297: 158 159 458
triangle #298: 459 158 458
triangle #299: 459 157 158
triangle #300: 461 157 459
triangle #301: 460 461 459
triangle #302: 461 156 157
triangle #303: 463 156 461
triangle #304: 462 463 461
triangle #305: 463 155 156
triangle #306: 464 155 463
triangle #307: 464 154 155
triangle #308: 465 154 464
triangle #309: 465 153 154
triangle #310: 152 153 465
triangle #311: 149 152 465
triangle #312: 148 149 465
triangle #313: 467 148 465
triangle #314: 466 467 465
triangle #315: 149 151 152
triangle #316: 467 147 148
triangle #317: 146 147 467
triangle #318: 469 146 467
triangle #319: 468 469 467
triangle #320: 469 145 146
triangle #321: 470 145 469
triangle #322: 470 144 145
triangle #323: 471 144 470
triangle #324: 471 143 144
triangle #325: 472 143 471
triangle #326: 472 142 143
triangle #327: 473 142 472
triangle #328: 473 474 141
triangle #329: 142 473 141
triangle #330: 140 141 474
triangle #331: 475 140 474
triangle #332: 475 139 140
triangle #333: 476 139 475
triangle #334: 476 138 139
triangle #335: 119 138 476
triangle #336: 118 119 476
triangle #337: 477 118 476
triangle #338: 119 137 138
triangle #339: 477 117 118
triangle #340: 116 117 477
triangle #341: 113 116 477
triangle #342: 112 113 477
triangle #343: 479 112 477
triangle #344: 478 479 477
triangle #345: 113 115 116
triangle #346: 479 111 112
triangle #347: 110 111 479
triangle #348: 481 110 479
triangle #349: 480 481 479
triangle #350: 481 109 110
triangle #351: 11 109 481
triangle #352: 10 11 481
triangle #353: 482 10 481
triangle #354: 11 108 109
triangle #355: 482 9 10
triangle #356: 8 9 482
triangle #357: 5 8 482
triangle #358: 4 5 482
triangle #359: 483 4 482
triangle #360: 5 7 8
triangle #361: 483 3 4
triangle #362: 2 3 483
triangle #363: 485 2 483
triangle #364: 484 485 483
triangle #365: 485 1 2
triangle #366: 485 486 1
triangle #367: 5 6 7
triangle #368: 13 108 11
triangle #369: 12 13 11
triangle #370: 13 107 108
triangle #371: 29 107 13
triangle #372: 28 29 13
triangle #373: 14 28 13
triangle #374: 29 106 107
triangle #375: 14 27 28
triangle #376: 26 27 14
triangle #377: 23 26 14
triangle #378: 22 23 14
triangle #379: 15 22 14
triangle #380: 23 25 26
triangle #381: 15 21 22
triangle #382: 20 21 15
triangle #383: 17 20 15
triangle #384: 16 17 15
triangle #385: 17 19 20
triangle #386: 17 18 19
triangle #387: 23 24 25
triangle #388: 31 106 29
triangle #389: 30 31 29
triangle #390: 31 105 106
triangle #391: 104 105 31
triangle #392: 32 104 31
triangle #393: 32 103 104
triangle #394: 33 103 32
triangle #395: 33 102 103
triangle #396: 35 102 33
triangle #397: 34 35 33
triangle #398: 35 101 102
triangle #399: 37 101 35
triangle #400: 36 37 35
triangle #401: 37 100 101
triangle #402: 38 100 37
triangle #403: 38 99 100
triangle #404: 98 99 38
triangle #405: 95 98 38
triangle #406: 94 95 38
triangle #407: 39 94 38
triangle #408: 95 97 98
triangle #409: 39 93 94
triangle #410: 92 93 39
triangle #411: 40 92 39
triangle #412: 40 91 92
triangle #413: 41 91 40
triangle #414: 41 42 90
triangle #415: 91 41 90
triangle #416: 43 90 42
triangle #417: 43 89 90
triangle #418: 44 89 43
triangle #419: 44 88 89
triangle #420: 45 88 44
triangle #421: 45 87 88
triangle #422: 86 87 45
triangle #423: 47 86 45
triangle #424: 46 47 45
triangle #425: 47 85 86
triangle #426: 49 85 47
triangle #427: 48 49 47
triangle #428: 49 84 85
triangle #429: 65 84 49
triangle #430: 64 65 49
triangle #431: 50 64 49
triangle #432: 65 83 84
triangle #433: 50 63 64
triangle #434: 62 63 50
triangle #435: 59 62 50
triangle #436: 58 59 50
triangle #437: 51 58 50
triangle #438: 59 61 62
triangle #439: 51 57 58
triangle #440: 56 57 51
triangle #441: 53 56 51
triangle #442: 52 53 51
triangle #443: 53 55 56
triangle #444: 53 54 55
triangle #445: 59 60 61
triangle #446: 67 83 65
triangle #447: 66 67 65
triangle #448: 67 82 83
triangle #449: 68 82 67
triangle #450: 68 81 82
triangle #451: 80 81 68
triangle #452: 77 80 68
triangle #453: 76 77 68
triangle #454: 69 76 68
triangle #455: 77 79 80
triangle #456: 69 75 76
triangle #457: 74 75 69
triangle #458: 71 74 69
triangle #459: 70 71 69
triangle #460: 71 73 74
triangle #461: 71 72 73
triangle #462: 77 78 79
triangle #463: 95 96 97
triangle #464: 113 114 115
triangle #465: 121 137 119
triangle #466: 120 121 119
triangle #467: 121 136 137
triangle #468: 122 136 121
triangle #469: 122 135 136
triangle #470: 134 135 122
triangle #471: 131 134 122
triangle #472: 130 131 122
triangle #473: 123 130 122
triangle #474: 131 133 134
triangle #475: 123 129 130
triangle #476: 128 129 123
triangle #477: 125 128 123
triangle #478: 124 125 123
triangle #479: 125 127 128
triangle #480: 125 126 127
triangle #481: 131 132 133
triangle #482: 149 150 151
triangle #483: 446 447 448