(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 381923, 11729]*) (*NotebookOutlinePosition[ 382799, 11759]*) (* CellTagsIndexPosition[ 382755, 11755]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ StyleBox["Mathematica", FontSize->18, FontWeight->"Plain", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" and cddmathlink\nUsing cddmathlink to compute complex convex \ hulls and drawing with ", FontSize->18, FontWeight->"Plain", FontColor->RGBColor[0, 0, 1]], StyleBox["Mathematica", FontSize->18, FontWeight->"Plain", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["\nby Komei Fukuda\nwith \na nice zonotope example\nof Russell \ Towle\n", FontSize->18, FontWeight->"Plain", FontColor->RGBColor[0, 0, 1]], StyleBox[" (Revised December 17, 2002)", FontSize->14, FontWeight->"Plain", FontColor->RGBColor[0, 0, 1]] }], "Title", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["Off[General::spell1];Off[General::spell]", "Input", InitializationCell->True, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ (* Russell Towle's codes to create projections (zonotopes) of hypercubes. *) cross[ {ax_, ay_, az_}, {bx_, by_, bz_} ] := (*cross product*) {ay bz - az by, az bx - ax bz, ax by - ay bx} mag[v_]:= Sqrt[Plus@@(v^2)] (*magnitude of a vector*) unit[v_]:= v/Sqrt[v.v] (*make unit vector*) tolerance=0.000001; collinear[ v1_, v2_ ] := (*test for collinearity*) Apply[And, Map[Abs[#]<tolerance&, cross[v1,v2]]] setStar[vlist_] := (*discard collinear vectors*) Module[{selected={}}, Scan[Function[v, If[v!={0,0,0} && Select[selected, collinear[v,#]&]=={}, AppendTo[selected,v]] ], 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L s .0035 w [ .01 .012 ] 0 setdash .52091 .74117 m .5 .79975 L s .0085 w [ ] 0 setdash .77234 .51051 m .75602 .56491 L s .75484 .4153 m .77234 .51051 L s .0035 w [ .01 .012 ] 0 setdash .44107 .73866 m .5 .79975 L s .0085 w [ ] 0 setdash .2479 .58379 m .30382 .64248 L s .22318 .48931 m .2479 .58379 L s .6046 .27394 m .66632 .32779 L s .58897 .7339 m .5 .79975 L s .69391 .65581 m .58897 .7339 L s .69391 .65581 m .60605 .72084 L s .75602 .56491 m .69391 .65581 L s .30562 .34381 m .28051 .39564 L s .41065 .26512 m .30562 .34381 L s .41065 .26512 m .38746 .31554 L s .39462 .72773 m .5 .79975 L s .30382 .64248 m .39462 .72773 L s .75484 .4153 m .73797 .46868 L s .66632 .32779 m .75484 .4153 L s .55971 .25816 m .66632 .32779 L s .55971 .25816 m .53919 .30868 L s .22318 .48931 m .27948 .5473 L s .28051 .39564 m .22318 .48931 L s .47871 .25444 m .53919 .30868 L s .47871 .25444 m .38746 .31554 L s .47841 .70687 m .5 .79975 L s .56055 .70953 m .5 .79975 L s .60605 .72084 m .5 .79975 L s .40941 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m .4469 .52558 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{282, 282}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, AnimationDisplayTime->0.383333, ImageCacheValid->False], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics3D %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0 1 0 1 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath 0 g .0035 w [ .01 .012 ] 0 setdash .49468 .55264 m .59107 .61746 L s .49468 .55264 m .39971 .61679 L s .59067 .47397 m .49468 .55264 L s .40015 .47322 m .49468 .55264 L s .59067 .47397 m .68817 .5384 L s .63362 .38255 m .59067 .47397 L s .49621 .39395 m .59067 .47397 L s .40015 .47322 m .30399 .53695 L s .36086 .38139 m .40015 .47322 L s .49621 .39395 m .40015 .47322 L s .45798 .30081 m .49621 .39395 L s .53817 .30117 m .49621 .39395 L s .59107 .61746 m .63482 .67353 L s .59107 .61746 m .49617 .68267 L s .68817 .5384 m .59107 .61746 L s .39971 .61679 m .49617 .68267 L s .39971 .61679 m .3596 .67261 L s .30399 .53695 m .39971 .61679 L s .68817 .5384 m .73372 .59333 L s .73266 .44703 m .68817 .5384 L s .30399 .53695 m .26208 .59163 L s .26315 .44513 m .30399 .53695 L s .63362 .38255 m .73266 .44703 L s .59681 .28849 m .63362 .38255 L s .53817 .30117 m .63362 .38255 L s .49617 .68267 m .53869 .74034 L s .49617 .68267 m .4574 .74008 L s .36086 .38139 m .26315 .44513 L s .40153 .28761 m .36086 .38139 L s .45798 .30081 m .36086 .38139 L s .5 .20569 m .53817 .30117 L s .5 .20569 m .45798 .30081 L s .73266 .44703 m .77954 .50109 L s .69681 .35303 m .73266 .44703 L s .63482 .67353 m .59814 .73126 L s .63482 .67353 m .53869 .74034 L s .73372 .59333 m .63482 .67353 L s .26315 .44513 m .21999 .49891 L s .30295 .35132 m .26315 .44513 L s .3596 .67261 m .4574 .74008 L s .3596 .67261 m .40017 .73063 L s .26208 .59163 m .3596 .67261 L s .0085 w [ ] 0 setdash .73372 .59333 m .69862 .64987 L s .77954 .50109 m .73372 .59333 L s .0035 w [ .01 .012 ] 0 setdash .59681 .28849 m .69681 .35303 L s .5 .20569 m .59681 .28849 L s .40153 .28761 m .30295 .35132 L s .5 .20569 m .40153 .28761 L s .0085 w [ ] 0 setdash .26208 .59163 m .30114 .6485 L s .21999 .49891 m .26208 .59163 L s .5 .20569 m .59963 .26982 L s .5 .20569 m .54328 .25606 L s .5 .20569 m .46067 .25568 L s .5 .20569 m .40193 .26891 L s .0035 w [ .01 .012 ] 0 setdash .53869 .74034 m .5 .79975 L s .4574 .74008 m .5 .79975 L s .0085 w [ ] 0 setdash .69681 .35303 m .74368 .40616 L s .59963 .26982 m .69681 .35303 L s .30295 .35132 m .25995 .40414 L s .40193 .26891 m .30295 .35132 L s .59963 .26982 m .64501 .32173 L s .77954 .50109 m .74481 .55672 L s .74368 .40616 m .77954 .50109 L s .40193 .26891 m .36052 .32047 L s 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.61362 m .54389 .70803 L s .64637 .62477 m .54389 .70803 L s .50406 .61362 m .46011 .70776 L s .35921 .62376 m .46011 .70776 L s .60776 .5289 m .64637 .62477 L s .50403 .30783 m .60725 .37511 L s .50403 .30783 m .4025 .37424 L s .40203 .52812 m .35921 .62376 L s .70785 .46082 m .60776 .5289 L s .60725 .37511 m .70785 .46082 L s .29999 .45919 m .40203 .52812 L s .4025 .37424 m .29999 .45919 L s .60725 .37511 m .50579 .44271 L s .4025 .37424 m .50579 .44271 L s .60776 .5289 m .50406 .61362 L s .40203 .52812 m .50406 .61362 L s .50579 .44271 m .60776 .5289 L s .50579 .44271 m .40203 .52812 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{282, 282}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, AnimationDisplayTime->0.383333, ImageCacheValid->False], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch 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.39625 .27299 m .30627 .35877 L s .0085 w [ ] 0 setdash .5 .20569 m .59158 .26595 L s .5 .20569 m .52547 .25466 L s .5 .20569 m .44387 .25763 L s .5 .20569 m .39625 .27299 L s .0035 w [ .01 .012 ] 0 setdash .47498 .74103 m .5 .79975 L s .55535 .73903 m .5 .79975 L s .0085 w [ ] 0 setdash .74952 .58561 m .69732 .64385 L s .7783 .49149 m .74952 .58561 L s .2253 .5084 m .24583 .56302 L s .247 .41319 m .2253 .5084 L s .39625 .27299 m .33808 .32634 L s .4087 .73332 m .5 .79975 L s .3045 .65448 m .4087 .73332 L s .3045 .65448 m .39481 .72016 L s .24583 .56302 m .3045 .65448 L s .69551 .34551 m .72481 .39751 L s .59158 .26595 m .69551 .34551 L s .59158 .26595 m .61902 .31657 L s .60439 .7284 m .5 .79975 L s .69732 .64385 m .60439 .7284 L s .7783 .49149 m .72587 .54897 L s .72481 .39751 m .7783 .49149 L s .247 .41319 m .26822 .46681 L s .33808 .32634 m .247 .41319 L s .44387 .25763 m .46873 .30837 L s .44387 .25763 m .33808 .32634 L s .52547 .25466 m .61902 .31657 L s .52547 .25466 m .46873 .30837 L s .44309 .70915 m .5 .79975 L s .52583 .70702 m .5 .79975 L s .59286 .71511 m .5 .79975 L s .39481 .72016 m .5 .79975 L s .69732 .64385 m .59286 .71511 L s .72587 .54897 m .69732 .64385 L s .33656 .62847 m .39481 .72016 L s .24583 .56302 m .33656 .62847 L s .26822 .46681 m .24583 .56302 L s .33808 .32634 m .36113 .37868 L s .62014 .62063 m .59286 .71511 L s .72481 .39751 m .67086 .45411 L s .61902 .31657 m .72481 .39751 L s .61902 .31657 m .56321 .3719 L s .46843 .61405 m .44309 .70915 L s .33656 .62847 m .44309 .70915 L s .36047 .5321 m .33656 .62847 L s .46843 .61405 m .52583 .70702 L s .62014 .62063 m .52583 .70702 L s .72587 .54897 m .62014 .62063 L s .67086 .45411 m .72587 .54897 L s .26822 .46681 m .36047 .5321 L s .36113 .37868 m .26822 .46681 L s .46873 .30837 m .56321 .3719 L s .46873 .30837 m .36113 .37868 L s .56351 .52603 m .62014 .62063 L s .36113 .37868 m .455 .44341 L s .56351 .52603 m .46843 .61405 L s .36047 .5321 m .46843 .61405 L s .67086 .45411 m .56351 .52603 L s .56321 .3719 m .67086 .45411 L s .455 .44341 m .36047 .5321 L s .56321 .3719 m .455 .44341 L s .455 .44341 m .56351 .52603 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{282, 282}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, AnimationDisplayTime->0.383333, ImageCacheValid->False], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics3D %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0 1 0 1 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath 0 g .0035 w [ .01 .012 ] 0 setdash .48425 .47729 m .58699 .54993 L s .48425 .47729 m .38124 .54747 L s .41549 .3898 m .48425 .47729 L s .56194 .39178 m .48425 .47729 L s .58699 .54993 m .66635 .60935 L s .58699 .54993 m .48418 .62043 L s .66561 .46491 m .58699 .54993 L s .38124 .54747 m .48418 .62043 L s .38124 .54747 m .31043 .60528 L s .31127 .46037 m .38124 .54747 L s .48418 .62043 m .56249 .68093 L s .48418 .62043 m .41474 .67935 L s .56194 .39178 m .66561 .46491 L s .49336 .30275 m .56194 .39178 L s .56945 .29687 m .56194 .39178 L s .66561 .46491 m .74662 .52373 L s .67454 .37088 m .66561 .46491 L s .41549 .3898 m .31127 .46037 L s .42102 .29473 m .41549 .3898 L s .49336 .30275 m .41549 .3898 L s .31127 .46037 m .23877 .5175 L s .31539 .36595 m .31127 .46037 L s .66635 .60935 m .67612 .66419 L s .66635 .60935 m .56249 .68093 L s .74662 .52373 m .66635 .60935 L s .56249 .68093 m .5704 .73726 L s .56249 .68093 m .49327 .74147 L s .31043 .60528 m .41474 .67935 L s .31043 .60528 m .3137 .66023 L s .23877 .5175 m .31043 .60528 L s .5 .20569 m .49336 .30275 L s .41474 .67935 m .49327 .74147 L s .41474 .67935 m .41993 .73573 L s .56945 .29687 m .67454 .37088 L s .5 .20569 m .56945 .29687 L s .74662 .52373 m .75796 .57745 L s .75679 .4293 m .74662 .52373 L s .67454 .37088 m .75679 .4293 L s .60603 .28031 m .67454 .37088 L s .42102 .29473 m .31539 .36595 L s .5 .20569 m .42102 .29473 L s .31539 .36595 m .24194 .42252 L s .39375 .27721 m .31539 .36595 L s .0085 w [ ] 0 setdash .23877 .5175 m .24075 .57138 L s .24194 .42252 m .23877 .5175 L s .0035 w [ .01 .012 ] 0 setdash .49327 .74147 m .5 .79975 L s .5 .20569 m .60603 .28031 L s .0085 w [ ] 0 setdash .5 .20569 m .58068 .26246 L s .5 .20569 m .50686 .254 L s .5 .20569 m .42886 .26022 L s .5 .20569 m .39375 .27721 L s .0035 w [ .01 .012 ] 0 setdash .67612 .66419 m .5704 .73726 L s .0085 w [ ] 0 setdash .67612 .66419 m .6075 .7254 L s .75796 .57745 m .67612 .66419 L s .0035 w [ .01 .012 ] 0 setdash .60603 .28031 m .6882 .33813 L s .0085 w [ ] 0 setdash .39375 .27721 m .32082 .33297 L s .0035 w [ .01 .012 ] 0 setdash .5704 .73726 m .5 .79975 L s .3137 .66023 m .41993 .73573 L s .0085 w [ ] 0 setdash .3137 .66023 m .39228 .72318 L s .24075 .57138 m .3137 .66023 L s .75679 .4293 m .76847 .48201 L s .6882 .33813 m .75679 .4293 L s .0035 w [ .01 .012 ] 0 setdash .41993 .73573 m .5 .79975 L s .0085 w [ ] 0 setdash .75796 .57745 m .68995 .63792 L s .76847 .48201 m .75796 .57745 L s .24194 .42252 m .24401 .47537 L s .32082 .33297 m .24194 .42252 L s .58068 .26246 m .6882 .33813 L s .58068 .26246 m .58915 .31248 L s .24075 .57138 m .31915 .63378 L s .24401 .47537 m .24075 .57138 L s .6882 .33813 m .69871 .38965 L s .42886 .26022 m .43447 .31027 L s .42886 .26022 m .32082 .33297 L s .6075 .7254 m .5 .79975 L s .68995 .63792 m .6075 .7254 L s .39228 .72318 m .5 .79975 L s .31915 .63378 m .39228 .72318 L s .32082 .33297 m .3244 .38457 L s .42786 .71101 m .5 .79975 L s .50695 .70655 m .5 .79975 L s .58181 .71261 m .5 .79975 L s .50686 .254 m .58915 .31248 L s .50686 .254 m .43447 .31027 L s .76847 .48201 m .69965 .54192 L s .69871 .38965 m .76847 .48201 L s .68995 .63792 m .58181 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