Austin Schuh | 405fa6c | 2015-09-06 18:13:55 -0700 | [diff] [blame] | 1 | (************** Content-type: application/mathematica ************** |
| 2 | |
| 3 | Mathematica-Compatible Notebook |
| 4 | |
| 5 | This notebook can be used with any Mathematica-compatible |
| 6 | application, such as Mathematica, MathReader or Publicon. The data |
| 7 | for the notebook starts with the line containing stars above. |
| 8 | |
| 9 | To get the notebook into a Mathematica-compatible application, do |
| 10 | one of the following: |
| 11 | |
| 12 | * Save the data starting with the line of stars above into a file |
| 13 | with a name ending in .nb, then open the file inside the |
| 14 | application; |
| 15 | |
| 16 | * Copy the data starting with the line of stars above to the |
| 17 | clipboard, then use the Paste menu command inside the application. |
| 18 | |
| 19 | Data for notebooks contains only printable 7-bit ASCII and can be |
| 20 | sent directly in email or through ftp in text mode. Newlines can be |
| 21 | CR, LF or CRLF (Unix, Macintosh or MS-DOS style). |
| 22 | |
| 23 | NOTE: If you modify the data for this notebook not in a Mathematica- |
| 24 | compatible application, you must delete the line below containing |
| 25 | the word CacheID, otherwise Mathematica-compatible applications may |
| 26 | try to use invalid cache data. |
| 27 | |
| 28 | For more information on notebooks and Mathematica-compatible |
| 29 | applications, contact Wolfram Research: |
| 30 | web: http://www.wolfram.com |
| 31 | email: info@wolfram.com |
| 32 | phone: +1-217-398-0700 (U.S.) |
| 33 | |
| 34 | Notebook reader applications are available free of charge from |
| 35 | Wolfram Research. |
| 36 | *******************************************************************) |
| 37 | |
| 38 | (*CacheID: 232*) |
| 39 | |
| 40 | |
| 41 | (*NotebookFileLineBreakTest |
| 42 | NotebookFileLineBreakTest*) |
| 43 | (*NotebookOptionsPosition[ 148963, 16022]*) |
| 44 | (*NotebookOutlinePosition[ 149846, 16054]*) |
| 45 | (* CellTagsIndexPosition[ 149802, 16050]*) |
| 46 | (*WindowFrame->Normal*) |
| 47 | |
| 48 | |
| 49 | |
| 50 | Notebook[{ |
| 51 | |
| 52 | |
| 53 | Cell[TextData[{ |
| 54 | StyleBox["Mathematica", |
| 55 | FontWeight->"Plain", |
| 56 | FontSlant->"Italic"], |
| 57 | StyleBox[" and cddmathlink\nUsing cddmathlink to compute complex convex \ |
| 58 | hulls and drawing with ", |
| 59 | FontWeight->"Plain"], |
| 60 | StyleBox["Mathematica", |
| 61 | FontWeight->"Plain", |
| 62 | FontSlant->"Italic"], |
| 63 | StyleBox["\nby Komei Fukuda\nwith \na nice zonotope example\nof Russell \ |
| 64 | Towle\n (April 17, 2001)", |
| 65 | FontWeight->"Plain"] |
| 66 | }], "Title", |
| 67 | ImageRegion->{{0, 1}, {0, 1}}], |
| 68 | |
| 69 | Cell[CellGroupData[{Cell["Off[General::spell1];Off[General::spell]", "Input", |
| 70 | InitializationCell->True, |
| 71 | ImageRegion->{{0, 1}, {0, 1}}], |
| 72 | |
| 73 | Cell["\<\ |
| 74 | |
| 75 | (* Russell Towle's codes to create projections (zonotopes) of |
| 76 | hypercubes. *) |
| 77 | |
| 78 | cross[ {ax_, ay_, az_}, {bx_, by_, bz_} ] := (*cross product*) |
| 79 | {ay bz - az by, az bx - ax bz, ax by - ay bx} |
| 80 | |
| 81 | mag[v_]:= Sqrt[Plus@@(v^2)] (*magnitude of a vector*) |
| 82 | |
| 83 | unit[v_]:= v/Sqrt[v.v] (*make unit vector*) |
| 84 | |
| 85 | tolerance=0.000001; |
| 86 | collinear[ v1_, v2_ ] := (*test for collinearity*) |
| 87 | Apply[And, Map[Abs[#]<tolerance&, cross[v1,v2]]] |
| 88 | |
| 89 | setStar[vlist_] := (*discard collinear vectors*) |
| 90 | Module[{selected={}}, |
| 91 | Scan[Function[v, If[v!={0,0,0} && |
| 92 | Select[selected, |
| 93 | collinear[v,#]&]=={}, |
| 94 | AppendTo[selected,v]] ], |
| 95 | vlist]; |
| 96 | |
| 97 | Print[Length[selected],\" zonal directions.\"]; |
| 98 | gStar=selected] (*gStar is global, list of non-collinear vectors*) |
| 99 | |
| 100 | \ |
| 101 | \>", "Input", |
| 102 | InitializationCell->True, |
| 103 | ImageRegion->{{0, 1}, {0, 1}}], |
| 104 | |
| 105 | Cell[CellGroupData[{Cell["\<\ |
| 106 | (* Here I set to a directory where I store |
| 107 | the packages I need *) |
| 108 | |
| 109 | SetDirectory[\"~/Math\"]\ |
| 110 | \>", "Input", |
| 111 | InitializationCell->True, |
| 112 | ImageRegion->{{0, 1}, {0, 1}}], |
| 113 | |
| 114 | Cell[OutputFormData["\<\ |
| 115 | \"/Users/fukuda/Math\"\ |
| 116 | \>", "\<\ |
| 117 | /Users/fukuda/Math\ |
| 118 | \ |
| 119 | \>"], "Output", |
| 120 | ImageRegion->{{0, 1}, {0, 1}}]}, Open]], |
| 121 | |
| 122 | Cell[CellGroupData[{Cell["cddml=Install[\"~/Math/cddmathlink\"]", "Input", |
| 123 | InitializationCell->True, |
| 124 | ImageRegion->{{0, 1}, {0, 1}}], |
| 125 | |
| 126 | Cell[OutputFormData["\<\ |
| 127 | LinkObject[\"~/Math/cddmathlink\", 6, 6]\ |
| 128 | \>", \ |
| 129 | "\<\ |
| 130 | LinkObject[~/Math/cddmathlink, 6, 6]\ |
| 131 | \>"], "Output", |
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| 133 | ImageRegion->{{0, 1}, {0, 1}}]}, Open]], |
| 134 | |
| 135 | Cell["Needs[\"ExtendGraphics`View3D`\"];", "Input", |
| 136 | InitializationCell->True, |
| 137 | ImageRegion->{{0, 1}, {0, 1}}], |
| 138 | |
| 139 | Cell["<<UnfoldPolytope.m", "Input", |
| 140 | InitializationCell->True, |
| 141 | ImageRegion->{{0, 1}, {0, 1}}], |
| 142 | |
| 143 | Cell["<<Combinatorica5.m", "Input", |
| 144 | InitializationCell->True, |
| 145 | ImageRegion->{{0, 1}, {0, 1}}], |
| 146 | |
| 147 | Cell["<<PolytopeSkeleton.m", "Input", |
| 148 | InitializationCell->True, |
| 149 | ImageRegion->{{0, 1}, {0, 1}}], |
| 150 | |
| 151 | Cell["<<IOPolyhedra.m", "Input", |
| 152 | InitializationCell->True, |
| 153 | ImageRegion->{{0, 1}, {0, 1}}], |
| 154 | |
| 155 | Cell["\<\ |
| 156 | (*the vectors which determine an n-merous polar zonohedron*) |
| 157 | (*3<=n, 0<=pitch<=90 degrees*) |
| 158 | |
| 159 | vectors[n_Integer,pitch_]:= |
| 160 | Table[N[{Cos[Degree pitch] Cos[2Pi i/n], |
| 161 | \tCos[Degree pitch] Sin[2Pi i/n], |
| 162 | \t-Sin[Degree pitch]},15], |
| 163 | \t{i,n}] (* modified by KF, precision 15 added *)\ |
| 164 | \>", "Input", |
| 165 | InitializationCell->True, |
| 166 | ImageRegion->{{0, 1}, {0, 1}}], |
| 167 | |
| 168 | Cell["\<\ |
| 169 | (*the pitch at which a polar zonohedron is |
| 170 | an isometric shadow of an n-cube*) |
| 171 | |
| 172 | N[1/Degree * ArcTan[(1/2)^(1/2)],15]; |
| 173 | \ |
| 174 | \>", "Input", |
| 175 | InitializationCell->True, |
| 176 | ImageRegion->{{0, 1}, {0, 1}}], |
| 177 | |
| 178 | Cell["\<\ |
| 179 | (*Here, we obtain the vectors for an isometric projection of |
| 180 | a d-cube into cyclic symmetry*) |
| 181 | |
| 182 | dim=8; |
| 183 | gen=Zonotope[vectors[dim, N[ 1/Degree * ArcTan[(1/2)^(1/2)],15 ] ] ]; |
| 184 | genc = Chop[gen,10^(-12)];\ |
| 185 | \>", "Input", |
| 186 | InitializationCell->True, |
| 187 | ImageRegion->{{0, 1}, {0, 1}}], |
| 188 | |
| 189 | Cell[CellGroupData[{Cell["\<\ |
| 190 | extlist=Map[Prepend[#,1]&,genc]; |
| 191 | {n,d}=Dimensions[extlist]\ |
| 192 | \>", "Input", |
| 193 | InitializationCell->True, |
| 194 | ImageRegion->{{0, 1}, {0, 1}}], |
| 195 | |
| 196 | Cell[OutputFormData["\<\ |
| 197 | {256, 4}\ |
| 198 | \>", "\<\ |
| 199 | {256, 4}\ |
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| 203 | |
| 204 | Cell[CellGroupData[{Cell["\<\ |
| 205 | {{inelist,equalities}, icd, iad,ecd,ead}= |
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| 209 | |
| 210 | Cell[CellGroupData[{Cell["{m,d}=Dimensions[inelist]", "Input", |
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| 212 | |
| 213 | Cell[OutputFormData["\<\ |
| 214 | {56, 4}\ |
| 215 | \>", "\<\ |
| 216 | {56, 4}\ |
| 217 | \>"], "Output", |
| 218 | ImageRegion->{{0, 1}, {0, 1}}]}, Open]], |
| 219 | |
| 220 | Cell[CellGroupData[{Cell["facets=Map[(Part[genc,#]) &, icd];", "Input", |
| 221 | ImageRegion->{{0, 1}, {0, 1}}], |
| 222 | |
| 223 | Cell[CellGroupData[{Cell["Length[facets]", "Input", |
| 224 | ImageRegion->{{0, 1}, {0, 1}}], |
| 225 | |
| 226 | Cell[OutputFormData["\<\ |
| 227 | 56\ |
| 228 | \>", "\<\ |
| 229 | 56\ |
| 230 | \>"], "Output", |
| 231 | ImageRegion->{{0, 1}, {0, 1}}]}, Open]], |
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| 233 | Cell["facets1=OrderFacets[facets];", "Input", |
| 234 | ImageRegion->{{0, 1}, {0, 1}}], |
| 235 | |
| 236 | Cell[CellGroupData[{Cell["viewpt={2, -2.4, 1}", "Input", |
| 237 | ImageRegion->{{0, 1}, {0, 1}}], |
| 238 | |
| 239 | Cell[OutputFormData["\<\ |
| 240 | {2, -2.4, 1}\ |
| 241 | \>", "\<\ |
| 242 | {2, -2.4, 1}\ |
| 243 | \>"], "Output", |
| 244 | ImageRegion->{{0, 1}, {0, 1}}]}, Open]], |
| 245 | |
| 246 | Cell[CellGroupData[{Cell["\<\ |
| 247 | Show[poly=Graphics3D[Polygon /@ facets1],Boxed->False, |
| 248 | ViewPoint->viewpt];\ |
| 249 | \>", "Input", |
| 250 | ImageRegion->{{0, 1}, {0, 1}}], |
| 251 | |
| 252 | Cell[GraphicsData["PostScript", "\<\ |
| 253 | %! |
| 254 | %%Creator: Mathematica |
| 255 | %%AspectRatio: 1.05969 |
| 256 | MathPictureStart |
| 257 | %% Graphics3D |
| 258 | /Courier findfont 10 scalefont setfont |
| 259 | % Scaling calculations |
| 260 | -0.05793 1.131557 0.028289 1.131557 [ |
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| 1341 | p |
| 1342 | .02 w |
| 1343 | .58474 .54131 Mdot |
| 1344 | P |
| 1345 | p |
| 1346 | .02 w |
| 1347 | .58474 .54131 Mdot |
| 1348 | P |
| 1349 | p |
| 1350 | .02 w |
| 1351 | .58474 .54131 Mdot |
| 1352 | P |
| 1353 | p |
| 1354 | .02 w |
| 1355 | .44733 .62922 Mdot |
| 1356 | P |
| 1357 | p |
| 1358 | .02 w |
| 1359 | .49244 .8078 Mdot |
| 1360 | P |
| 1361 | p |
| 1362 | .02 w |
| 1363 | .37681 .62736 Mdot |
| 1364 | P |
| 1365 | p |
| 1366 | .02 w |
| 1367 | .37681 .62736 Mdot |
| 1368 | P |
| 1369 | p |
| 1370 | .02 w |
| 1371 | .50785 .26916 Mdot |
| 1372 | P |
| 1373 | p |
| 1374 | .02 w |
| 1375 | .66686 .71666 Mdot |
| 1376 | P |
| 1377 | p |
| 1378 | .02 w |
| 1379 | .41502 .53628 Mdot |
| 1380 | P |
| 1381 | p |
| 1382 | .02 w |
| 1383 | .41502 .53628 Mdot |
| 1384 | P |
| 1385 | p |
| 1386 | .02 w |
| 1387 | .41502 .53628 Mdot |
| 1388 | P |
| 1389 | p |
| 1390 | .02 w |
| 1391 | .70561 .62571 Mdot |
| 1392 | P |
| 1393 | p |
| 1394 | .02 w |
| 1395 | .70561 .62571 Mdot |
| 1396 | P |
| 1397 | p |
| 1398 | .02 w |
| 1399 | .58996 .44401 Mdot |
| 1400 | P |
| 1401 | p |
| 1402 | .02 w |
| 1403 | .20513 .62282 Mdot |
| 1404 | P |
| 1405 | p |
| 1406 | .02 w |
| 1407 | .49686 .71267 Mdot |
| 1408 | P |
| 1409 | p |
| 1410 | .02 w |
| 1411 | .49686 .71267 Mdot |
| 1412 | P |
| 1413 | p |
| 1414 | .02 w |
| 1415 | .49686 .71267 Mdot |
| 1416 | P |
| 1417 | p |
| 1418 | .02 w |
| 1419 | .62873 .35218 Mdot |
| 1420 | P |
| 1421 | p |
| 1422 | .02 w |
| 1423 | .53553 .62116 Mdot |
| 1424 | P |
| 1425 | p |
| 1426 | .02 w |
| 1427 | .53553 .62116 Mdot |
| 1428 | P |
| 1429 | p |
| 1430 | .02 w |
| 1431 | .41878 .43835 Mdot |
| 1432 | P |
| 1433 | p |
| 1434 | .02 w |
| 1435 | .46448 .61925 Mdot |
| 1436 | P |
| 1437 | p |
| 1438 | .02 w |
| 1439 | .46448 .61925 Mdot |
| 1440 | P |
| 1441 | p |
| 1442 | .02 w |
| 1443 | .71193 .52854 Mdot |
| 1444 | P |
| 1445 | p |
| 1446 | .02 w |
| 1447 | .3248 .70862 Mdot |
| 1448 | P |
| 1449 | p |
| 1450 | .02 w |
| 1451 | .50327 .52717 Mdot |
| 1452 | P |
| 1453 | p |
| 1454 | .02 w |
| 1455 | .61845 .79907 Mdot |
| 1456 | P |
| 1457 | p |
| 1458 | .02 w |
| 1459 | .38592 .34334 Mdot |
| 1460 | P |
| 1461 | p |
| 1462 | .02 w |
| 1463 | .68034 .43389 Mdot |
| 1464 | P |
| 1465 | p |
| 1466 | .02 w |
| 1467 | .29147 .61462 Mdot |
| 1468 | P |
| 1469 | p |
| 1470 | .02 w |
| 1471 | .29147 .61462 Mdot |
| 1472 | P |
| 1473 | p |
| 1474 | .02 w |
| 1475 | .54038 .52335 Mdot |
| 1476 | P |
| 1477 | p |
| 1478 | .02 w |
| 1479 | .5864 .70544 Mdot |
| 1480 | P |
| 1481 | p |
| 1482 | .02 w |
| 1483 | .5864 .70544 Mdot |
| 1484 | P |
| 1485 | p |
| 1486 | .02 w |
| 1487 | .5864 .70544 Mdot |
| 1488 | P |
| 1489 | p |
| 1490 | .02 w |
| 1491 | .62566 .61292 Mdot |
| 1492 | P |
| 1493 | p |
| 1494 | .02 w |
| 1495 | .46871 .52118 Mdot |
| 1496 | P |
| 1497 | p |
| 1498 | .02 w |
| 1499 | .37398 .79405 Mdot |
| 1500 | P |
| 1501 | p |
| 1502 | .02 w |
| 1503 | .50785 .4281 Mdot |
| 1504 | P |
| 1505 | p |
| 1506 | .02 w |
| 1507 | .50785 .4281 Mdot |
| 1508 | P |
| 1509 | p |
| 1510 | .02 w |
| 1511 | .50785 .4281 Mdot |
| 1512 | P |
| 1513 | p |
| 1514 | .02 w |
| 1515 | .50785 .4281 Mdot |
| 1516 | P |
| 1517 | p |
| 1518 | .02 w |
| 1519 | .80422 .51927 Mdot |
| 1520 | P |
| 1521 | p |
| 1522 | .02 w |
| 1523 | .41301 .7013 Mdot |
| 1524 | P |
| 1525 | p |
| 1526 | .02 w |
| 1527 | .41301 .7013 Mdot |
| 1528 | P |
| 1529 | p |
| 1530 | .02 w |
| 1531 | .41301 .7013 Mdot |
| 1532 | P |
| 1533 | p |
| 1534 | .02 w |
| 1535 | .7099 .79274 Mdot |
| 1536 | P |
| 1537 | p |
| 1538 | .02 w |
| 1539 | .29418 .5159 Mdot |
| 1540 | P |
| 1541 | p |
| 1542 | .02 w |
| 1543 | .59174 .60749 Mdot |
| 1544 | P |
| 1545 | p |
| 1546 | .02 w |
| 1547 | .59174 .60749 Mdot |
| 1548 | P |
| 1549 | p |
| 1550 | .02 w |
| 1551 | .33323 .42224 Mdot |
| 1552 | P |
| 1553 | p |
| 1554 | .02 w |
| 1555 | .37971 .60624 Mdot |
| 1556 | P |
| 1557 | p |
| 1558 | .02 w |
| 1559 | .49662 .8823 Mdot |
| 1560 | P |
| 1561 | p |
| 1562 | .02 w |
| 1563 | .63137 .51396 Mdot |
| 1564 | P |
| 1565 | p |
| 1566 | .02 w |
| 1567 | .63137 .51396 Mdot |
| 1568 | P |
| 1569 | p |
| 1570 | .02 w |
| 1571 | .63137 .51396 Mdot |
| 1572 | P |
| 1573 | p |
| 1574 | .02 w |
| 1575 | .53614 .78911 Mdot |
| 1576 | P |
| 1577 | p |
| 1578 | .02 w |
| 1579 | .55914 .51175 Mdot |
| 1580 | P |
| 1581 | p |
| 1582 | .02 w |
| 1583 | .41683 .60271 Mdot |
| 1584 | P |
| 1585 | p |
| 1586 | .02 w |
| 1587 | .41683 .60271 Mdot |
| 1588 | P |
| 1589 | p |
| 1590 | .02 w |
| 1591 | .46353 .7876 Mdot |
| 1592 | P |
| 1593 | p |
| 1594 | .02 w |
| 1595 | .59888 .41762 Mdot |
| 1596 | P |
| 1597 | p |
| 1598 | .02 w |
| 1599 | .71639 .69494 Mdot |
| 1600 | P |
| 1601 | p |
| 1602 | .02 w |
| 1603 | .45637 .5086 Mdot |
| 1604 | P |
| 1605 | p |
| 1606 | .02 w |
| 1607 | .50317 .69382 Mdot |
| 1608 | P |
| 1609 | p |
| 1610 | .02 w |
| 1611 | .38324 .50635 Mdot |
| 1612 | P |
| 1613 | p |
| 1614 | .02 w |
| 1615 | .38324 .50635 Mdot |
| 1616 | P |
| 1617 | p |
| 1618 | .02 w |
| 1619 | .38324 .50635 Mdot |
| 1620 | P |
| 1621 | p |
| 1622 | .02 w |
| 1623 | .68413 .59895 Mdot |
| 1624 | P |
| 1625 | p |
| 1626 | .02 w |
| 1627 | .68413 .59895 Mdot |
| 1628 | P |
| 1629 | p |
| 1630 | .02 w |
| 1631 | .28671 .78391 Mdot |
| 1632 | P |
| 1633 | p |
| 1634 | .02 w |
| 1635 | .4229 .41163 Mdot |
| 1636 | P |
| 1637 | p |
| 1638 | .02 w |
| 1639 | .5411 .69067 Mdot |
| 1640 | P |
| 1641 | p |
| 1642 | .02 w |
| 1643 | .58813 .87679 Mdot |
| 1644 | P |
| 1645 | p |
| 1646 | .02 w |
| 1647 | .72437 .50437 Mdot |
| 1648 | P |
| 1649 | p |
| 1650 | .02 w |
| 1651 | .46785 .68889 Mdot |
| 1652 | P |
| 1653 | p |
| 1654 | .02 w |
| 1655 | .60442 .31555 Mdot |
| 1656 | P |
| 1657 | p |
| 1658 | .02 w |
| 1659 | .20514 .50089 Mdot |
| 1660 | P |
| 1661 | p |
| 1662 | .02 w |
| 1663 | .50785 .59407 Mdot |
| 1664 | P |
| 1665 | p |
| 1666 | .02 w |
| 1667 | .50785 .59407 Mdot |
| 1668 | P |
| 1669 | p |
| 1670 | .02 w |
| 1671 | .50785 .59407 Mdot |
| 1672 | P |
| 1673 | p |
| 1674 | .02 w |
| 1675 | .50785 .59407 Mdot |
| 1676 | P |
| 1677 | p |
| 1678 | .02 w |
| 1679 | .50785 .59407 Mdot |
| 1680 | P |
| 1681 | p |
| 1682 | .02 w |
| 1683 | .50785 .59407 Mdot |
| 1684 | P |
| 1685 | p |
| 1686 | .02 w |
| 1687 | .81079 .68732 Mdot |
| 1688 | P |
| 1689 | p |
| 1690 | .02 w |
| 1691 | .41091 .87364 Mdot |
| 1692 | P |
| 1693 | p |
| 1694 | .02 w |
| 1695 | .548 .49888 Mdot |
| 1696 | P |
| 1697 | p |
| 1698 | .02 w |
| 1699 | .28943 .68455 Mdot |
| 1700 | P |
| 1701 | p |
| 1702 | .02 w |
| 1703 | .42686 .30886 Mdot |
| 1704 | P |
| 1705 | p |
| 1706 | .02 w |
| 1707 | .4743 .49659 Mdot |
| 1708 | P |
| 1709 | p |
| 1710 | .02 w |
| 1711 | .59361 .77824 Mdot |
| 1712 | P |
| 1713 | p |
| 1714 | .02 w |
| 1715 | .7311 .40241 Mdot |
| 1716 | P |
| 1717 | p |
| 1718 | .02 w |
| 1719 | .32934 .58912 Mdot |
| 1720 | P |
| 1721 | p |
| 1722 | .02 w |
| 1723 | .32934 .58912 Mdot |
| 1724 | P |
| 1725 | p |
| 1726 | .02 w |
| 1727 | .63412 .68295 Mdot |
| 1728 | P |
| 1729 | p |
| 1730 | .02 w |
| 1731 | .63412 .68295 Mdot |
| 1732 | P |
| 1733 | p |
| 1734 | .02 w |
| 1735 | .63412 .68295 Mdot |
| 1736 | P |
| 1737 | p |
| 1738 | .02 w |
| 1739 | .51262 .49248 Mdot |
| 1740 | P |
| 1741 | p |
| 1742 | .02 w |
| 1743 | .56029 .68113 Mdot |
| 1744 | P |
| 1745 | p |
| 1746 | .02 w |
| 1747 | .29477 .491 Mdot |
| 1748 | P |
| 1749 | p |
| 1750 | .02 w |
| 1751 | .41479 .77443 Mdot |
| 1752 | P |
| 1753 | p |
| 1754 | .02 w |
| 1755 | .55315 .39623 Mdot |
| 1756 | P |
| 1757 | p |
| 1758 | .02 w |
| 1759 | .60092 .58523 Mdot |
| 1760 | P |
| 1761 | p |
| 1762 | .02 w |
| 1763 | .60092 .58523 Mdot |
| 1764 | P |
| 1765 | p |
| 1766 | .02 w |
| 1767 | .45521 .67854 Mdot |
| 1768 | P |
| 1769 | p |
| 1770 | .02 w |
| 1771 | .47878 .39364 Mdot |
| 1772 | P |
| 1773 | p |
| 1774 | .02 w |
| 1775 | .38044 .67669 Mdot |
| 1776 | P |
| 1777 | p |
| 1778 | .02 w |
| 1779 | .38044 .67669 Mdot |
| 1780 | P |
| 1781 | p |
| 1782 | .02 w |
| 1783 | .38044 .67669 Mdot |
| 1784 | P |
| 1785 | p |
| 1786 | .02 w |
| 1787 | .51943 .29676 Mdot |
| 1788 | P |
| 1789 | p |
| 1790 | .02 w |
| 1791 | .64009 .58151 Mdot |
| 1792 | P |
| 1793 | p |
| 1794 | .02 w |
| 1795 | .6881 .77144 Mdot |
| 1796 | P |
| 1797 | p |
| 1798 | .02 w |
| 1799 | .42098 .58017 Mdot |
| 1800 | P |
| 1801 | p |
| 1802 | .02 w |
| 1803 | .42098 .58017 Mdot |
| 1804 | P |
| 1805 | p |
| 1806 | .02 w |
| 1807 | .72925 .67506 Mdot |
| 1808 | P |
| 1809 | p |
| 1810 | .02 w |
| 1811 | .29761 .38735 Mdot |
| 1812 | P |
| 1813 | p |
| 1814 | .02 w |
| 1815 | .6066 .48241 Mdot |
| 1816 | P |
| 1817 | p |
| 1818 | .02 w |
| 1819 | .6066 .48241 Mdot |
| 1820 | P |
| 1821 | p |
| 1822 | .02 w |
| 1823 | .6066 .48241 Mdot |
| 1824 | P |
| 1825 | p |
| 1826 | .02 w |
| 1827 | .19829 .67219 Mdot |
| 1828 | P |
| 1829 | p |
| 1830 | .02 w |
| 1831 | .50785 .76755 Mdot |
| 1832 | P |
| 1833 | p |
| 1834 | .02 w |
| 1835 | .50785 .76755 Mdot |
| 1836 | P |
| 1837 | p |
| 1838 | .02 w |
| 1839 | .50785 .76755 Mdot |
| 1840 | P |
| 1841 | p |
| 1842 | .02 w |
| 1843 | .50785 .76755 Mdot |
| 1844 | P |
| 1845 | p |
| 1846 | .02 w |
| 1847 | .64778 .38504 Mdot |
| 1848 | P |
| 1849 | p |
| 1850 | .02 w |
| 1851 | .54891 .67054 Mdot |
| 1852 | P |
| 1853 | p |
| 1854 | .02 w |
| 1855 | .3841 .57426 Mdot |
| 1856 | P |
| 1857 | p |
| 1858 | .02 w |
| 1859 | .42502 .47664 Mdot |
| 1860 | P |
| 1861 | p |
| 1862 | .02 w |
| 1863 | .42502 .47664 Mdot |
| 1864 | P |
| 1865 | p |
| 1866 | .02 w |
| 1867 | .42502 .47664 Mdot |
| 1868 | P |
| 1869 | p |
| 1870 | .02 w |
| 1871 | .47354 .66866 Mdot |
| 1872 | P |
| 1873 | p |
| 1874 | .02 w |
| 1875 | .73617 .57238 Mdot |
| 1876 | P |
| 1877 | p |
| 1878 | .02 w |
| 1879 | .73617 .57238 Mdot |
| 1880 | P |
| 1881 | p |
| 1882 | .02 w |
| 1883 | .32528 .76361 Mdot |
| 1884 | P |
| 1885 | p |
| 1886 | .02 w |
| 1887 | .637 .85965 Mdot |
| 1888 | P |
| 1889 | p |
| 1890 | .02 w |
| 1891 | .39017 .37595 Mdot |
| 1892 | P |
| 1893 | p |
| 1894 | .02 w |
| 1895 | .51272 .66527 Mdot |
| 1896 | P |
| 1897 | p |
| 1898 | .02 w |
| 1899 | .70275 .4721 Mdot |
| 1900 | P |
| 1901 | p |
| 1902 | .02 w |
| 1903 | .2899 .66405 Mdot |
| 1904 | P |
| 1905 | p |
| 1906 | .02 w |
| 1907 | .55419 .56715 Mdot |
| 1908 | P |
| 1909 | p |
| 1910 | .02 w |
| 1911 | .55419 .56715 Mdot |
| 1912 | P |
| 1913 | p |
| 1914 | .02 w |
| 1915 | .60305 .7605 Mdot |
| 1916 | P |
| 1917 | p |
| 1918 | .02 w |
| 1919 | .47811 .56497 Mdot |
| 1920 | P |
| 1921 | p |
| 1922 | .02 w |
| 1923 | .47811 .56497 Mdot |
| 1924 | P |
| 1925 | p |
| 1926 | .02 w |
| 1927 | .37751 .85486 Mdot |
| 1928 | P |
| 1929 | p |
| 1930 | .02 w |
| 1931 | .5197 .4662 Mdot |
| 1932 | P |
| 1933 | p |
| 1934 | .02 w |
| 1935 | .5197 .4662 Mdot |
| 1936 | P |
| 1937 | p |
| 1938 | .02 w |
| 1939 | .5197 .4662 Mdot |
| 1940 | P |
| 1941 | p |
| 1942 | .02 w |
| 1943 | .83448 .56304 Mdot |
| 1944 | P |
| 1945 | p |
| 1946 | .02 w |
| 1947 | .41898 .75647 Mdot |
| 1948 | P |
| 1949 | p |
| 1950 | .02 w |
| 1951 | .29276 .55965 Mdot |
| 1952 | P |
| 1953 | p |
| 1954 | .02 w |
| 1955 | .29276 .55965 Mdot |
| 1956 | P |
| 1957 | p |
| 1958 | .02 w |
| 1959 | .60889 .65697 Mdot |
| 1960 | P |
| 1961 | p |
| 1962 | .02 w |
| 1963 | .60889 .65697 Mdot |
| 1964 | P |
| 1965 | p |
| 1966 | .02 w |
| 1967 | .60889 .65697 Mdot |
| 1968 | P |
| 1969 | p |
| 1970 | .02 w |
| 1971 | .33425 .46022 Mdot |
| 1972 | P |
| 1973 | p |
| 1974 | .02 w |
| 1975 | .50785 .94906 Mdot |
| 1976 | P |
| 1977 | p |
| 1978 | .02 w |
| 1979 | .65102 .55769 Mdot |
| 1980 | P |
| 1981 | p |
| 1982 | .02 w |
| 1983 | .65102 .55769 Mdot |
| 1984 | P |
| 1985 | p |
| 1986 | .02 w |
| 1987 | .52477 .35938 Mdot |
| 1988 | P |
| 1989 | p |
| 1990 | .02 w |
| 1991 | .57432 .55546 Mdot |
| 1992 | P |
| 1993 | p |
| 1994 | .02 w |
| 1995 | .4231 .65222 Mdot |
| 1996 | P |
| 1997 | p |
| 1998 | .02 w |
| 1999 | .4231 .65222 Mdot |
| 2000 | P |
| 2001 | p |
| 2002 | .02 w |
| 2003 | .4231 .65222 Mdot |
| 2004 | P |
| 2005 | p |
| 2006 | .02 w |
| 2007 | .74149 .75026 Mdot |
| 2008 | P |
| 2009 | p |
| 2010 | .02 w |
| 2011 | .46514 .55228 Mdot |
| 2012 | P |
| 2013 | p |
| 2014 | .02 w |
| 2015 | .38742 .55001 Mdot |
| 2016 | P |
| 2017 | p |
| 2018 | .02 w |
| 2019 | .38742 .55001 Mdot |
| 2020 | P |
| 2021 | p |
| 2022 | .02 w |
| 2023 | .65739 .45101 Mdot |
| 2024 | P |
| 2025 | p |
| 2026 | .02 w |
| 2027 | .70731 .64848 Mdot |
| 2028 | P |
| 2029 | p |
| 2030 | .02 w |
| 2031 | .55527 .74609 Mdot |
| 2032 | P |
| 2033 | p |
| 2034 | .02 w |
| 2035 | .47741 .74434 Mdot |
| 2036 | P |
| 2037 | p |
| 2038 | .02 w |
| 2039 | .62265 .34733 Mdot |
| 2040 | P |
| 2041 | p |
| 2042 | .02 w |
| 2043 | .19804 .54449 Mdot |
| 2044 | P |
| 2045 | p |
| 2046 | .02 w |
| 2047 | .51998 .64361 Mdot |
| 2048 | P |
| 2049 | p |
| 2050 | .02 w |
| 2051 | .51998 .64361 Mdot |
| 2052 | P |
| 2053 | p |
| 2054 | .02 w |
| 2055 | .51998 .64361 Mdot |
| 2056 | P |
| 2057 | p |
| 2058 | .02 w |
| 2059 | .39129 .44225 Mdot |
| 2060 | P |
| 2061 | p |
| 2062 | .02 w |
| 2063 | .28767 .7401 Mdot |
| 2064 | P |
| 2065 | p |
| 2066 | .02 w |
| 2067 | .43388 .34043 Mdot |
| 2068 | P |
| 2069 | p |
| 2070 | .02 w |
| 2071 | .61128 .83979 Mdot |
| 2072 | P |
| 2073 | p |
| 2074 | .02 w |
| 2075 | .75754 .43997 Mdot |
| 2076 | P |
| 2077 | p |
| 2078 | .02 w |
| 2079 | .33013 .63868 Mdot |
| 2080 | P |
| 2081 | p |
| 2082 | .02 w |
| 2083 | .65441 .73854 Mdot |
| 2084 | P |
| 2085 | p |
| 2086 | .02 w |
| 2087 | .52517 .53599 Mdot |
| 2088 | P |
| 2089 | p |
| 2090 | .02 w |
| 2091 | .52517 .53599 Mdot |
| 2092 | P |
| 2093 | p |
| 2094 | .02 w |
| 2095 | .42108 .83616 Mdot |
| 2096 | P |
| 2097 | p |
| 2098 | .02 w |
| 2099 | .56833 .43364 Mdot |
| 2100 | P |
| 2101 | p |
| 2102 | .02 w |
| 2103 | .48921 .43099 Mdot |
| 2104 | P |
| 2105 | p |
| 2106 | .02 w |
| 2107 | .38454 .7324 Mdot |
| 2108 | P |
| 2109 | p |
| 2110 | .02 w |
| 2111 | .66097 .63108 Mdot |
| 2112 | P |
| 2113 | p |
| 2114 | .02 w |
| 2115 | .29635 .42454 Mdot |
| 2116 | P |
| 2117 | p |
| 2118 | .02 w |
| 2119 | .62541 .52579 Mdot |
| 2120 | P |
| 2121 | p |
| 2122 | .02 w |
| 2123 | .62541 .52579 Mdot |
| 2124 | P |
| 2125 | p |
| 2126 | .02 w |
| 2127 | .52027 .82957 Mdot |
| 2128 | P |
| 2129 | p |
| 2130 | .02 w |
| 2131 | .38847 .62385 Mdot |
| 2132 | P |
| 2133 | p |
| 2134 | .02 w |
| 2135 | .43209 .51994 Mdot |
| 2136 | P |
| 2137 | p |
| 2138 | .02 w |
| 2139 | .43209 .51994 Mdot |
| 2140 | P |
| 2141 | p |
| 2142 | .02 w |
| 2143 | .76359 .62196 Mdot |
| 2144 | P |
| 2145 | p |
| 2146 | .02 w |
| 2147 | .52559 .7212 Mdot |
| 2148 | P |
| 2149 | p |
| 2150 | .02 w |
| 2151 | .56981 .61673 Mdot |
| 2152 | P |
| 2153 | p |
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| 2214 | % End of Graphics |
| 2215 | MathPictureEnd |
| 2216 | \ |
| 2217 | \>"], "Graphics", |
| 2218 | ImageSize->{266, 282}, |
| 2219 | ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, |
| 2220 | ImageRegion->{{0, 1}, {0, 1}}, |
| 2221 | ImageCacheValid->False]}, Open]]}, Open]], |
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| 2224 | amat=-Map[Drop[#,1]&, inelist]; |
| 2225 | bvec=Map[First[#]&, inelist]; |
| 2226 | \ |
| 2227 | \>", "Input", |
| 2228 | ImageRegion->{{0, 1}, {0, 1}}], |
| 2229 | |
| 2230 | Cell["\<\ |
| 2231 | skel3D[vp_]:= |
| 2232 | \tGraphics3D[ |
| 2233 | \t\tVisibleSkeleton[genc, ecd, ead, |
| 2234 | \t{amat, bvec}, vp] |
| 2235 | ]; |
| 2236 | \ |
| 2237 | \>", "Input", |
| 2238 | ImageRegion->{{0, 1}, {0, 1}}], |
| 2239 | |
| 2240 | Cell[CellGroupData[{Cell["\<\ |
| 2241 | uvp={20,20,20}; |
| 2242 | Show[skel3D[uvp], |
| 2243 | \t\tBoxed->False, |
| 2244 | \t\tViewPoint -> getMmaViewPoint[uvp,skel3D[uvp]], |
| 2245 | \t\tSphericalRegion->True |
| 2246 | \t]\ |
| 2247 | \>", "Input", |
| 2248 | ImageRegion->{{0, 1}, {0, 1}}], |
| 2249 | |
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| 2251 | %! |
| 2252 | %%Creator: Mathematica |
| 2253 | %%AspectRatio: 1 |
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| 2255 | %% Graphics3D |
| 2256 | /Courier findfont 10 scalefont setfont |
| 2257 | % Scaling calculations |
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| 3016 | % End of Graphics |
| 3017 | MathPictureEnd |
| 3018 | \ |
| 3019 | \>"], "Graphics", |
| 3020 | ImageSize->{282, 282}, |
| 3021 | ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, |
| 3022 | ImageRegion->{{0, 1}, {0, 1}}, |
| 3023 | ImageCacheValid->False], |
| 3024 | |
| 3025 | Cell[OutputFormData["\<\ |
| 3026 | Graphics3D[\"<<>>\"]\ |
| 3027 | \>", "\<\ |
| 3028 | -Graphics3D-\ |
| 3029 | \>"], \ |
| 3030 | "Output", |
| 3031 | ImageRegion->{{0, 1}, {0, 1}}]}, Open]], |
| 3032 | |
| 3033 | Cell[CellGroupData[{Cell["\<\ |
| 3034 | Do[ vp=circle[a,10,2]; |
| 3035 | \tShow[skel3D[getUserViewPoint[vp, skel3D[{0,0,0}]]], |
| 3036 | \t\tBoxed->False, |
| 3037 | \t\tViewPoint -> vp, SphericalRegion->True |
| 3038 | \t], |
| 3039 | \t{a,Pi/11,Pi,Pi/18} |
| 3040 | ] |
| 3041 | \ |
| 3042 | \>", "Input", |
| 3043 | ImageRegion->{{0, 1}, {0, 1}}, |
| 3044 | AnimationDisplayTime->8.28333, |
| 3045 | AnimationCycleOffset->1.0625, |
| 3046 | AnimationCycleRepetitions->Infinity], |
| 3047 | |
| 3048 | Cell[GraphicsData["PostScript", "\<\ |
| 3049 | %! |
| 3050 | %%Creator: Mathematica |
| 3051 | %%AspectRatio: 1 |
| 3052 | MathPictureStart |
| 3053 | %% Graphics3D |
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| 3055 | % Scaling calculations |
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