(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' 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). 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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[ 2151618, 88796]*) (*NotebookOutlinePosition[ 2158213, 88964]*) (* CellTagsIndexPosition[ 2156689, 88927]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["DGeometrica", "Title", PageWidth->PaperWidth], Cell[TextData[{ "A ", StyleBox["Mathematica", FontSlant->"Italic"], " package for differential geometry" }], "Subtitle", PageWidth->PaperWidth] }, Open ]], Cell[CellGroupData[{ Cell["Yoshihiko TAZAWA", "Author", PageWidth->PaperWidth], Cell[CellGroupData[{ Cell["\<\ School of Information Environment Tokyo Denki University 2-1200 Muzai-gakuendai Inzai, Chiba Pref. 270-1382 JAPAN tazawa@cck.dendai.ac.jp\ \>", "TextAboutAuthor", PageWidth->PaperWidth], Cell[CellGroupData[{ Cell["1. Abstract", "Section", PageWidth->PaperWidth], Cell[TextData[{ StyleBox[" This notebook is an introduction of the first half of ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["DGeometrica", PageWidth->PaperWidth, FontFamily->"Times New Roman", FontWeight->"Bold"], StyleBox[", a package for doing differential geometry of curves and \ surfaces by ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["Mathematica", PageWidth->PaperWidth, FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[".\n The geometry of curves and surfaces is a nice topic to deal \ with computer algebras. Alfred Gray's book [5] is a comprehensive \ introduction of how to utilize ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["Mathematica", PageWidth->PaperWidth, FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[" in differential geometry. He gave a tutorial talk [1] in the \ first IMS. His ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["Mathematica", PageWidth->PaperWidth, FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[" package is still downloadable from [4]. John Oprea published a \ book [9] based on Maple. Richard Palais and his group created a freeware \ 3D-XplorMath [5] which works on Macintosh OS and deals with many topics from \ differential geometry.\n In the third IMS the author gave a talk [2] and \ introduced several examples from the book [10] written in Japanese. The main \ part of ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["DGeometrica", PageWidth->PaperWidth, FontFamily->"Times New Roman", FontWeight->"Bold"], StyleBox[" is a set of ideas and ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["Mathematica", PageWidth->PaperWidth, FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[" commands contained in the [10]. The feature of ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["DGeometrica", PageWidth->PaperWidth, FontFamily->"Courier New", FontWeight->"Bold"], StyleBox[" compared to other packages is that the usage of numerical \ functions such as ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["NDSolve", PageWidth->PaperWidth, FontFamily->"Courier New", FontWeight->"Bold"], StyleBox[" or ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["NIntegrate", PageWidth->PaperWidth, FontFamily->"Courier New", FontWeight->"Bold"], StyleBox[" to do experimental approach and to extend the range of examples \ in differential geometry of curves and surfaces.\n This article consists of \ three materials: the present notebook, ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["DGeometrica", PageWidth->PaperWidth, FontFamily->"Times New Roman", FontWeight->"Bold"], StyleBox[" package files contained in a folder named DGeometrica, and a \ pair of ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["Mathematica", PageWidth->PaperWidth, FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[" notebooks ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["Plane- CurvesTest.nb", PageWidth->PaperWidth, FontFamily->"Courier New", FontWeight->"Bold"], StyleBox[" and ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["SpaceCurvesTest.nb", PageWidth->PaperWidth, FontFamily->"Courier New", FontWeight->"Bold"], StyleBox[". 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", StyleBox["dg-", PageWidth->PaperWidth, FontFamily->"Courier", FontWeight->"Bold"], StyleBox["commands without ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["Anim", PageWidth->PaperWidth, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" or ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["Fig", PageWidth->PaperWidth, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" like ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["dgCurvature", PageWidth->PaperWidth, FontFamily->"Courier", FontWeight->"Bold"], " are just for calculation. ", StyleBox["\n The present notebook is an outline of the package and \ introduces several commands in it", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox[". All Input cells in this notebook are set non-evaluatable in \ order to make the appearance stable. 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If the curve is of the form ", StyleBox["c", FontSlant->"Italic"], "(", StyleBox["x", FontSlant->"Italic"], ")=(", StyleBox["x", FontSlant->"Italic"], ", ", StyleBox["f", FontSlant->"Italic"], "(", StyleBox["x", FontSlant->"Italic"], ")), namely the graph of a function ", StyleBox["y ", FontSlant->"Italic"], "= ", StyleBox["f", FontSlant->"Italic"], "(", StyleBox["x", FontSlant->"Italic"], "), it is plotted by ", StyleBox["Plot", PageWidth->PaperWidth, FontFamily->"Courier", FontWeight->"Bold"], " of ", StyleBox["Mathematica", FontSlant->"Italic"], ", but it fails to show the discontinuity of functions. 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Segments with length greater than the 0.1 \ times width or the 0.1 times height of the box containing the curve are not \ shown. 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FontFamily->"Courier New", FontWeight->"Bold"], ". We can calculate the length of a fairly complicated curve by ", StyleBox["dgNumArcLength", PageWidth->PaperWidth, FontFamily->"Courier New", FontWeight->"Bold"], " numerically." }], "Text"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["c[t_]=\n {1.18445+0.215722*t-10.2437*t^2-13.3893*t^3+\n \ 25.9661*t^4+30.553*t^5-36.084*t^6,\n \ -0.6248+6.4332*t+0.151186*t^2-52.3013*t^3+\n \ 11.1881*t^4+139.806*t^5-105.033*t^6};\n", AspectRatioFixed->True, FontFamily->"Courier New"], "dg", StyleBox["NumArcLength", PageWidth->PaperWidth, FontFamily->"Courier New", FontWeight->"Bold"], "[0,1][c]" }], "Input", CellLabel->"In[31]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm\`7.180770467685628`\)], "Output", CellLabel->"Out[32]="] }, Open ]], Cell["\<\ The geometric meaning of the length of a curve is the limit of the \ length of the broken line jointing points on the curve, as the number of the \ points tends to infinity. 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StyleBox["Unlike the total curvature, the value of the total absolute \ curvature is not discrete. According to a well-known theorem, ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], "t", StyleBox["he total absolute curvature is greater than or equal to 2\[Pi], \ and it is equal to 2\[Pi] if and only if the curve is an ovaloid. ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], StyleBox["dgTotalAbsoluteCurvatureAnim", FontFamily->"Courier New", FontWeight->"Bold"], " shows the above using a homotopy. " }], "Text", PageWidth->PaperWidth], Cell[CellGroupData[{ Cell[TextData[StyleBox["?dgTotalAbsoluteCurvatureUnderHomotopyAnim", FontFamily->"Courier New", FontWeight->"Bold"]], "Input", CellLabel->"In[92]:="], Cell[BoxData[ \("dgTotalAbsoluteCurvatureUnderHomotopyAnim[cur11,cur22,t0,t1,n] returns \ the animation of the homotopy between the curves cur11(t) and cur22(t) , \ t0<=t<=t1, together with the change of Gauss map, total curvature, and total \ absolute curvature, with n scenes. All homotopy curves are not necessarili \ regular even if cur11(t) and cur22(t) are regular, so the values of the \ total curvature and total absolute curvature are not necessarily continuous \ in the homotopy parameter."\)], "Print", CellTags->"Info3352623551-6274727"] }, Open ]], Cell[CellGroupData[{ Cell["Example 1 (case: there is a singular cueve in the homotopy.)", \ "Subsubsection", FontColor->RGBColor[0, 0, 1], CellTags->{"TotalCurvatureHomotopyEg2", "TotalCurvatureHomotopyEg3"}], Cell[CellGroupData[{ Cell[TextData[{ "c11[t_]=N[{\n 0.51*Cos[2*Pi*t]-0.31*Cos[4*Pi*t]+\n \ 0.026*Cos[6*Pi*t]-\n 0.17*Sin[2*Pi*t]+0.34*Sin[4*Pi*t]+\n \ 0.12*Sin[6*Pi*t],\n0.001*Cos[2*Pi*t]+0.93*Cos[4*Pi*t]+\n \ 0.011*Cos[6*Pi*t]+\n 0.13*Sin[2*Pi*t]+0.12*Sin[4*Pi*t]+\n \ 0.042*Sin[6*Pi*t]}];\nc22[t_]={Cos[-2*Pi*t],Sin[-2*Pi*t]};\nTiming[", StyleBox["dgTotalAbsoluteCurvatureUnderHomotopyAnim", FontFamily->"Courier New", FontWeight->"Bold"], "[c11,c22,0,1,64];]" }], "Input", CellLabel->"In[93]:=", 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m .54896 1.07127 L s .40836 1.01152 m .39556 .99854 L s .58002 1.06968 m .56475 1.07115 L s .39556 .99854 m .38381 .98444 L s .38381 .98444 m .37323 .9693 L s .59463 1.06686 m .58002 1.06968 L s .60835 .47388 m .62087 .46719 L s .35634 .58252 m .36367 .58967 L s .37323 .9693 m .36391 .95317 L s 0 .6 1 r .02403 w .45051 1.25587 Mdot 0 0 0 r .01 w .60846 1.06273 m .59463 1.06686 L s 0 .6 1 r .02103 w .59463 1.06686 Mdot .01803 w .73875 .87785 Mdot .01503 w .88288 .68883 Mdot 0 .24 1 r .01203 w .04698 .49982 Mdot .00903 w .1911 .31081 Mdot .00603 w .33522 .1218 Mdot 1 0 0 r .007 w .66866 1.10259 m .6788 1.05997 L s .66866 1.10259 m .67978 1.06076 L s .66866 1.10259 m .68058 1.06164 L s .66866 1.10259 m .68118 1.06257 L s .66866 1.10259 m .68156 1.06354 L s .66866 1.10259 m .68172 1.06452 L s .66866 1.10259 m .68166 1.0655 L s .66866 1.10259 m .68137 1.06646 L s .66866 1.10259 m .68086 1.06736 L s .66866 1.10259 m .68015 1.0682 L s .66866 1.10259 m .67924 1.06895 L s .66866 1.10259 m .67817 1.06959 L s .66866 1.10259 m .67694 1.07012 L s .66866 1.10259 m .6756 1.07051 L s .66866 1.10259 m .67417 1.07076 L s .66866 1.10259 m .67268 1.07087 L s .66866 1.10259 m .67117 1.07083 L s .66866 1.10259 m .66966 1.07065 L s .66866 1.10259 m .66821 1.07032 L s .66866 1.10259 m .66682 1.06986 L s .66866 1.10259 m .66555 1.06927 L s .66866 1.10259 m .66441 1.06857 L s .66866 1.10259 m .66343 1.06777 L s .66866 1.10259 m .66263 1.0669 L s .66866 1.10259 m .66204 1.06596 L s .66866 1.10259 m .66166 1.06499 L s .66866 1.10259 m .6615 1.064 L s .66866 1.10259 m .66157 1.06302 L s .66866 1.10259 m .66186 1.06207 L s .66866 1.10259 m .66237 1.06117 L s .66866 1.10259 m .66308 1.06033 L s .66866 1.10259 m .66399 1.05959 L s .66866 1.10259 m .66507 1.05895 L s .66866 1.10259 m .66629 1.05842 L s .66866 1.10259 m .66763 1.05803 L s .66866 1.10259 m .66906 1.05778 L s .66866 1.10259 m .67054 1.05767 L s .66866 1.10259 m .67205 1.05771 L s .66866 1.10259 m .67355 1.0579 L s .66866 1.10259 m .67501 1.05822 L s .66866 1.10259 m .67639 1.05868 L s .66866 1.10259 m .67766 1.05927 L s 0 0 0 r .01 w .36391 .95317 m .35595 .93613 L s .62137 1.05731 m .60846 1.06273 L s .5948 .48162 m .60835 .47388 L s .35595 .93613 m .34944 .91827 L s .36367 .58967 m .37245 .59742 L s .63323 1.05064 m .62137 1.05731 L s .34944 .91827 m .34443 .89966 L s .58034 .49044 m .5948 .48162 L s 0 .72 1 r .02403 w .82643 1.24473 Mdot .02103 w .97109 1.055 Mdot 0 .36 1 r .01803 w .13203 .86528 Mdot .01503 w .2767 .67555 Mdot .01203 w .42136 .48582 Mdot .00903 w .56603 .29609 Mdot .00603 w .71069 .10637 Mdot 0 0 0 r .01 w .64393 1.04277 m .63323 1.05064 L s .34443 .89966 m .34099 .88039 L s 1 0 0 r .67861 .97347 m .67161 1.06426 L s 0 0 0 r .37245 .59742 m .38262 .60582 L s .65336 1.03375 m .64393 1.04277 L s .56512 .50035 m .58034 .49044 L s .34099 .88039 m .33915 .86057 L s .33915 .86057 m .33894 .84029 L s .66143 1.02362 m .65336 1.03375 L s .54929 .51134 m .56512 .50035 L s 0 .48 1 r .02403 w .21773 1.2335 Mdot .02103 w .36295 1.04305 Mdot .01803 w .50816 .85261 Mdot .01503 w .65338 .66216 Mdot .01203 w .79859 .47171 Mdot 0 0 0 r .01 w .38262 .60582 m .39406 .61488 L s .33894 .84029 m .34037 .81964 L s .66805 1.01247 m .66143 1.02362 L s 0 0 1 r .007 w .51891 .92996 m .56949 .93321 L s .51891 .92996 m .56976 .93356 L s .51891 .92996 m .56997 .93411 L s .51891 .92996 m .5701 .93485 L s .51891 .92996 m .57015 .93578 L s .51891 .92996 m .57012 .93687 L s .51891 .92996 m .57002 .93809 L s .51891 .92996 m .56984 .93943 L s .51891 .92996 m .56958 .94084 L s .51891 .92996 m .56926 .94229 L s .51891 .92996 m .56888 .94376 L s .51891 .92996 m .56845 .94522 L s .51891 .92996 m .56798 .94662 L s .51891 .92996 m .56748 .94794 L s .51891 .92996 m .56696 .94915 L s .51891 .92996 m .56643 .95023 L s .51891 .92996 m .56591 .95114 L s .51891 .92996 m .5654 .95187 L s .51891 .92996 m .56491 .95239 L s .51891 .92996 m .56447 .95271 L s .51891 .92996 m .56407 .95281 L s .51891 .92996 m .56373 .9527 L s .51891 .92996 m .56345 .95236 L s .51891 .92996 m .56325 .95181 L s .51891 .92996 m .56311 .95107 L s .51891 .92996 m .56306 .95014 L s .51891 .92996 m .56309 .94905 L s .51891 .92996 m .56319 .94783 L s .51891 .92996 m .56337 .94649 L s .51891 .92996 m .56363 .94508 L s .51891 .92996 m .56395 .94362 L s .51891 .92996 m .56433 .94214 L s .51891 .92996 m .56476 .94068 L s .51891 .92996 m .56523 .93928 L s .51891 .92996 m .56573 .93795 L s .51891 .92996 m .56626 .93674 L s .51891 .92996 m .56679 .93567 L s .51891 .92996 m .56731 .93476 L s .51891 .92996 m .56782 .93403 L s .51891 .92996 m .56831 .9335 L s .51891 .92996 m .56875 .93319 L s .51891 .92996 m .56915 .93309 L s 0 0 0 r .01 w .533 .52341 m .54929 .51134 L s .34037 .81964 m .34343 .79875 L s .67316 1.00034 m .66805 1.01247 L s .34343 .79875 m .34809 .7777 L s .39406 .61488 m .40669 .62463 L s .51643 .53653 m .533 .52341 L s 0 0 1 r .67861 .97347 m .56661 .94295 L s 0 0 0 r .34809 .7777 m .35432 .75661 L s 0 .6 1 r .02403 w .59562 1.22219 Mdot .02103 w .74139 1.03102 Mdot .01803 w .88716 .83984 Mdot 0 .24 1 r .01503 w .04171 .64867 Mdot .01203 w .18747 .4575 Mdot .00903 w .33324 .26633 Mdot .00603 w .47901 .07516 Mdot 0 0 0 r .01 w .49973 .55068 m .51643 .53653 L s .67669 .98731 m .67316 1.00034 L s .35432 .75661 m .36206 .73559 L s .48308 .56581 m .49973 .55068 L s .40669 .62463 m .42037 .63508 L s .36206 .73559 m .37124 .71473 L s .67861 .97347 m .67669 .98731 L s .46666 .58188 m .48308 .56581 L s .37124 .71473 m .38177 .69416 L s .45062 .59882 m .46666 .58188 L s .38177 .69416 m .39355 .67396 L s .43514 .61658 m .45062 .59882 L s .39355 .67396 m .40646 .65423 L s .42037 .63508 m .43514 .61658 L s .40646 .65423 m .42037 .63508 L s 0 .72 1 r .02403 w .9764 1.21079 Mdot 0 .36 1 r .02103 w .12772 1.01888 Mdot .01803 w .27404 .82698 Mdot 0 0 0 r .01 w .42037 .63508 m .43497 .64623 L s 0 .36 1 r .01503 w .42037 .63508 Mdot .01203 w .56669 .44318 Mdot .00903 w .71302 .25127 Mdot 0 1 0 r .01 w .67861 .97347 m .63842 1.04463 L s 0 0 0 r .67888 .95888 m .67861 .97347 L s .67749 .94364 m .67888 .95888 L s .43497 .64623 m .45036 .65809 L s .67446 .92784 m .67749 .94364 L s 0 .48 1 r .02403 w .36128 1.1993 Mdot .01803 w .65505 .81402 Mdot .02103 w .50816 1.00666 Mdot .01503 w .80193 .62138 Mdot 0 0 0 r .01 w .45036 .65809 m .46638 .67065 L s .66979 .91156 m .67446 .92784 L s .46638 .67065 m .48286 .68387 L s .66354 .8949 m .66979 .91156 L s .48286 .68387 m .49964 .69775 L s .65575 .87795 m .66354 .8949 L s 0 .6 1 r .02103 w .89154 .99434 Mdot .02403 w .74408 1.18772 Mdot 0 .24 1 r .01803 w .03632 .80096 Mdot .01503 w .18377 .60758 Mdot .00603 w .62612 .02744 Mdot .00903 w .47867 .22082 Mdot .01203 w .33122 .4142 Mdot 0 0 0 r .01 w .6465 .86081 m .65575 .87795 L s .49964 .69775 m .51654 .71224 L s .63588 .84356 m .6465 .86081 L s .51654 .71224 m .53339 .7273 L s .62398 .82631 m .63588 .84356 L s .53339 .7273 m .55002 .74288 L s .61094 .80913 m .62398 .82631 L s .55002 .74288 m .56625 .75892 L s 0 .36 1 r .02403 w .1233 1.17606 Mdot .01503 w .56737 .59367 Mdot .01803 w .41935 .7878 Mdot .02103 w .27133 .98193 Mdot .01203 w .71539 .39954 Mdot 0 0 0 r .01 w .59687 .79212 m .61094 .80913 L s .56625 .75892 m .58192 .77536 L s .58192 .77536 m .59687 .79212 L s 0 1 0 r .007 w .62087 1.07571 m .63351 1.05046 L s .62087 1.07571 m .63482 1.05128 L s .62087 1.07571 m .63231 1.04951 L s .62087 1.07571 m .63621 1.05196 L s .62087 1.07571 m .63124 1.04844 L s .62087 1.07571 m .63766 1.05247 L s .62087 1.07571 m .63033 1.0473 L s .62087 1.07571 m .63912 1.05281 L s .62087 1.07571 m .62961 1.04609 L s .62087 1.07571 m .64056 1.05296 L s .62087 1.07571 m .62908 1.04485 L s .62087 1.07571 m .64196 1.05293 L s .62087 1.07571 m .62876 1.0436 L s .62087 1.07571 m .64328 1.05271 L s .62087 1.07571 m .62865 1.04238 L s .62087 1.07571 m .64449 1.05231 L s .62087 1.07571 m .62877 1.04121 L s .62087 1.07571 m .64556 1.05174 L s .62087 1.07571 m .6291 1.04011 L s .62087 1.07571 m .64648 1.05101 L s .62087 1.07571 m .62963 1.03911 L s .62087 1.07571 m .64721 1.05014 L s .62087 1.07571 m .63037 1.03824 L s .62087 1.07571 m .64775 1.04915 L s .62087 1.07571 m .63128 1.03751 L s .62087 1.07571 m .64808 1.04805 L s .62087 1.07571 m .63236 1.03693 L s .62087 1.07571 m .6482 1.04688 L s .62087 1.07571 m .63357 1.03653 L s .62087 1.07571 m .6481 1.04565 L s .62087 1.07571 m .63488 1.03631 L s .62087 1.07571 m .64778 1.0444 L s .62087 1.07571 m .63628 1.03628 L s .62087 1.07571 m .64725 1.04316 L s .62087 1.07571 m .63773 1.03643 L s .62087 1.07571 m .64653 1.04195 L s .62087 1.07571 m .63919 1.03677 L s .62087 1.07571 m .64562 1.0408 L s .62087 1.07571 m .64064 1.03728 L s .62087 1.07571 m .64455 1.03974 L s .62087 1.07571 m .64203 1.03796 L s .62087 1.07571 m .64335 1.03878 L s 0 .48 1 r .02403 w .50816 1.1643 Mdot .02103 w .65676 .96942 Mdot .01803 w .80535 .77454 Mdot 0 .6 1 r .02403 w .89602 1.15245 Mdot 0 .24 1 r .02103 w .0308 .95681 Mdot .01803 w .17998 .76117 Mdot .00903 w .6275 .17424 Mdot .01203 w .47833 .36989 Mdot .01503 w .32915 .56553 Mdot 0 .36 1 r .71782 .55129 Mdot .01803 w .56807 .7477 Mdot .02103 w .41831 .94411 Mdot .02403 w .26855 1.14051 Mdot 0 .48 1 r .65851 1.12848 Mdot .02103 w .80886 .9313 Mdot 0 .24 1 r .02403 w .02515 1.11635 Mdot .01203 w .62891 .32452 Mdot .01503 w .47797 .52248 Mdot .01803 w .32703 .72044 Mdot .02103 w .17609 .91839 Mdot 0 .36 1 r .01803 w .72031 .70664 Mdot .02103 w .56878 .90538 Mdot .02403 w .41724 1.10412 Mdot 0 .48 1 r .81244 1.0918 Mdot 0 .24 1 r .01503 w .63036 .4784 Mdot .01803 w .47761 .67873 Mdot .02103 w .32486 .87905 Mdot .02403 w .17212 1.07938 Mdot 0 .36 1 r .56951 1.06686 Mdot .02103 w .72286 .86573 Mdot 0 .24 1 r .01803 w .63184 .63601 Mdot .02103 w .47724 .83876 Mdot .02403 w .32264 1.04152 Mdot 0 .36 1 r .72548 1.02869 Mdot 0 .24 1 r .02103 w .63336 .79748 Mdot .02403 w .47686 1.00272 Mdot .63491 .96297 Mdot 0 g .25 Mabswid .03479 .19498 m .63226 0 L s .63226 0 m .64186 .96901 L s .64186 .96901 m 0 1.13008 L s 0 1.13008 m .03479 .19498 L s .96734 .31522 m .63226 0 L s .63226 0 m .64186 .96901 L s .64186 .96901 m 1 1.22884 L s 1 1.22884 m .96734 .31522 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.522676 0.0154833 0.97619 0.634815 MathSubStart %% Graphics3D %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.0386954 1.0387 -0.017958 1.0387 [ [ 0 0 0 0 ] [ 1 1.00278 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.00278 L 0 1.00278 L closepath clip newpath 0 .72 1 r .02403 w .13996 .6194 Mdot .02103 w .06037 .42575 Mdot .02403 w .33848 .60074 Mdot 0 .6 1 r .04662 .74811 Mdot 0 .72 1 r .02103 w .2605 .40378 Mdot .02403 w .54323 .58149 Mdot 0 .6 1 r .24871 .73101 Mdot 0 .72 1 r .01803 w .18024 .20106 Mdot .02103 w .467 .38111 Mdot .02403 w .75451 .56163 Mdot 0 .6 1 r .02103 w .16739 .53089 Mdot .02403 w .45732 .71336 Mdot 0 .72 1 r .01803 w .38852 .17478 Mdot 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First, we joint small pieces of circles whose radii are determined by \ the curvature function and obtain a plane curve. Then, we twist the plane \ curve at each jointing point according to the torsion function and generates \ a space curve. The obtained space curve approximates the curve determined by \ the curvature and torsion, according to the Fundamental Theorem." }], "Text"], Cell[CellGroupData[{ Cell["?dgJointCircleSegments3DAnim", "Input", CellLabel->"In[2]:="], Cell[BoxData[ \("dgJointCircleSegments3D[curv,tors,{s,s0,s1},num] returns the animation \ of the approximation of a curve c[s], s0<=s<=s1, with the curvature function \ curv and the torsion function tors first by jointing num circle-segments \ whise radii are determined by the curvature function, and then by twisting it \ at each jointing point according to the torsion function. 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The following ", StyleBox["dgJointHelixSegments3DAnim", PageWidth->PaperWidth, FontFamily->"Courier New", FontWeight->"Bold"], " joints small pieces of helices whose curvature and torsion are constant \ values determined by the given curvature and torsion functions. At each \ jointing points, we joint them so that the moving frames of the two adjoining \ helices coincide. Comparing the output of this command to that of the \ previous one, we get better approximation and see that the helices are most \ basic curves among space curves." }], "Text"], Cell[CellGroupData[{ Cell["?dgJointHelixSegmentsAnim", "Input", CellLabel->"In[4]:="], Cell[BoxData[ \("dgJointHelixSegmentsAnim[kappa,tau,lgth,num,pltrng] returns an \ animation of piesewise smooth curves obtained by jointing pieces of helices \ that approximates the red curve with assined curvature kappa(s), torsion \ tau(s), and length lgth. The number of the segments varies from 2 to numand \ the PlotRange is pltrng. 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Mabswid .4424 .34016 m .44278 .33948 L s .42082 .41279 m .42084 .41205 L s .44278 .33948 m .44315 .3388 L s .42081 .41353 m .42082 .41279 L s .44315 .3388 m .44353 .33812 L s .50857 .57243 m .50849 .57198 L s .42079 .41427 m .42081 .41353 L s 1 0 0 r .0005 w .42405 .42058 m .42369 .41402 L s 0 0 1 r .5 Mabswid .55085 .4049 m .55096 .40476 L s .44353 .33812 m .44392 .33744 L s .42079 .415 m .42079 .41427 L s .44392 .33744 m .4443 .33677 L s 1 0 0 r .0005 w .44889 .33108 m .4526 .32512 L s 0 0 1 r .5 Mabswid .42079 .41573 m .42079 .415 L s .50865 .57287 m .50857 .57243 L s .4443 .33677 m .44469 .3361 L s .4208 .41646 m .42079 .41573 L s .55096 .40476 m .55106 .40463 L s .44469 .3361 m .44507 .33544 L s .42081 .41719 m .4208 .41646 L s .50874 .5733 m .50865 .57287 L s .44507 .33544 m .44546 .33477 L s .42083 .41791 m .42081 .41719 L s .55106 .40463 m .55116 .40451 L s .44546 .33477 m .44585 .33411 L s .42085 .41863 m .42083 .41791 L s .50882 .57374 m .50874 .5733 L s .44585 .33411 m .44625 .33345 L s .42088 .41934 m .42085 .41863 L s .44625 .33345 m .44664 .33279 L s .55116 .40451 m .55126 .4044 L s .42091 .42005 m .42088 .41934 L s .50891 .57417 m .50882 .57374 L s .44664 .33279 m .44704 .33214 L s .42096 .42076 m .42091 .42005 L s .44704 .33214 m .44743 .33149 L s 1 0 0 r .0005 w .55404 .40174 m .55456 .40123 L s 0 0 1 r .5 Mabswid .55126 .4044 m .55135 .40429 L s .421 .42147 m .42096 .42076 L s .509 .5746 m .50891 .57417 L s .44743 .33149 m .44783 .33084 L s 1 0 0 r .0005 w .42493 .42681 m .42405 .42058 L s 0 0 1 r .5 Mabswid .42106 .42217 m .421 .42147 L s 1 0 0 r .0005 w .4526 .32512 m .45645 .31944 L s 0 0 1 r .5 Mabswid .44783 .33084 m .44823 .3302 L s .50909 .57502 m .509 .5746 L s .42111 .42287 m .42106 .42217 L s .44823 .3302 m .44863 .32956 L s .55135 .40429 m .55143 .4042 L s .44863 .32956 m .44904 .32892 L s .42118 .42357 m .42111 .42287 L s .50918 .57544 m .50909 .57502 L s .44904 .32892 m .44944 .32828 L s .42125 .42426 m .42118 .42357 L s .55143 .4042 m .55151 .40411 L s .44944 .32828 m .44985 .32765 L s .42133 .42494 m .42125 .42426 L s .50927 .57586 m .50918 .57544 L s .44985 .32765 m .45026 .32702 L s .42141 .42563 m .42133 .42494 L s 1 0 0 r .0005 w .51214 .57742 m .51123 .5738 L s 0 0 1 r .5 Mabswid .55151 .40411 m .55158 .40403 L s .45026 .32702 m .45067 .32639 L s .4215 .42631 m .42141 .42563 L s .50936 .57627 m .50927 .57586 L s .45067 .32639 m .45108 .32577 L s .42159 .42698 m .4215 .42631 L s .55158 .40403 m .55165 .40396 L s .45108 .32577 m .45149 .32515 L s .50945 .57669 m .50936 .57627 L s .42169 .42766 m .42159 .42698 L s .45149 .32515 m .45191 .32453 L s .4218 .42832 m .42169 .42766 L s 1 0 0 r .0005 w .42633 .43266 m .42493 .42681 L s .45645 .31944 m .46042 .31405 L s 0 0 1 r .5 Mabswid .55165 .40396 m .55171 .4039 L s .45191 .32453 m .45232 .32392 L s .50955 .57709 m .50945 .57669 L s .42191 .42899 m .4218 .42832 L s .45232 .32392 m .45274 .32331 L s .42203 .42965 m .42191 .42899 L s .55171 .4039 m .55177 .40385 L s .45274 .32331 m .45316 .3227 L s .50964 .5775 m .50955 .57709 L s .42216 .4303 m .42203 .42965 L s .45316 .3227 m .45358 .3221 L s .50974 .5779 m .50964 .5775 L s .55177 .40385 m .55182 .4038 L s .45358 .3221 m .454 .3215 L s .42229 .43095 m .42216 .4303 L s .454 .3215 m .45442 .3209 L s .42243 .4316 m .42229 .43095 L s .50984 .5783 m .50974 .5779 L s .55182 .4038 m .55187 .40376 L s .45442 .3209 m .45485 .3203 L s .42257 .43224 m .42243 .4316 L s .45485 .3203 m .45527 .31971 L s .42272 .43287 m .42257 .43224 L s .50994 .57869 m .50984 .5783 L s .55187 .40376 m .55191 .40373 L s .45527 .31971 m .4557 .31913 L s 1 0 0 r .0005 w .55456 .40123 m .55456 .40144 L s 0 0 1 r .5 Mabswid .42287 .43351 m .42272 .43287 L s .4557 .31913 m .45613 .31854 L s .51004 .57908 m .50994 .57869 L s 1 0 0 r .0005 w .46042 .31405 m .46449 .30897 L s 0 0 1 r .5 Mabswid .42303 .43413 m .42287 .43351 L s .55191 .40373 m .55194 .40371 L s .45613 .31854 m .45656 .31796 L s 1 0 0 r .0005 w .42828 .43808 m .42633 .43266 L s 0 0 1 r .5 Mabswid .4232 .43476 m .42303 .43413 L s .51014 .57947 m .51004 .57908 L s .45656 .31796 m .45699 .31738 L s .42338 .43537 m .4232 .43476 L s .55194 .40371 m .55197 .4037 L s 1 0 0 r .0005 w .51312 .58075 m .51214 .57742 L s 0 0 1 r .5 Mabswid .45699 .31738 m .45742 .31681 L s .51024 .57986 m .51014 .57947 L s .42356 .43599 m .42338 .43537 L s .45742 .31681 m .45786 .31624 L s .55197 .4037 m .55199 .4037 L s .42374 .4366 m .42356 .43599 L s .45786 .31624 m .45829 .31567 L s .51034 .58024 m .51024 .57986 L s .45829 .31567 m .45873 .31511 L s .42393 .4372 m .42374 .4366 L s .55199 .4037 m .55201 .4037 L s .51044 .58062 m .51034 .58024 L s .45873 .31511 m .45917 .31455 L s .42413 .4378 m .42393 .4372 L s .45917 .31455 m .45961 .314 L s .42433 .43839 m .42413 .4378 L s .51055 .58099 m .51044 .58062 L s .55201 .4037 m .55202 .40371 L s .45961 .314 m .46005 .31345 L s .42455 .43898 m .42433 .43839 L s .51065 .58136 m .51055 .58099 L s .46005 .31345 m .46049 .3129 L s .55202 .40371 m .55202 .40373 L s 1 0 0 r .0005 w .46449 .30897 m .46865 .30421 L s 0 0 1 r .5 Mabswid .42476 .43956 m .42455 .43898 L s .46049 .3129 m .46093 .31235 L s .51076 .58173 m .51065 .58136 L s .42498 .44013 m .42476 .43956 L s 1 0 0 r .0005 w .43077 .44299 m .42828 .43808 L s 0 0 1 r .5 Mabswid .55202 .40373 m .55202 .40376 L s .46093 .31235 m .46137 .31181 L s .42521 .4407 m .42498 .44013 L s .51087 .5821 m .51076 .58173 L s .46137 .31181 m .46182 .31128 L s .55202 .40376 m .55201 .4038 L s .42545 .44127 m .42521 .4407 L s .46182 .31128 m .46227 .31075 L s .51097 .58246 m .51087 .5821 L s .42569 .44183 m .42545 .44127 L s .46227 .31075 m .46271 .31022 L s .55201 .4038 m .55199 .40384 L s 1 0 0 r .0005 w .55456 .40144 m .55402 .40235 L s 0 0 1 r .5 Mabswid .42593 .44238 m .42569 .44183 L s .46271 .31022 m .46316 .30969 L s .51108 .58282 m .51097 .58246 L s .42619 .44293 m .42593 .44238 L s .55199 .40384 m .55197 .4039 L s .46316 .30969 m .46361 .30917 L s .51119 .58317 m .51108 .58282 L s 1 0 0 r .0005 w .51417 .58382 m .51312 .58075 L s 0 0 1 r .5 Mabswid .42645 .44348 m .42619 .44293 L s .46361 .30917 m .46406 .30865 L s .55197 .4039 m .55195 .40396 L s .42671 .44401 m .42645 .44348 L s .46406 .30865 m .46451 .30814 L s .5113 .58352 m .51119 .58317 L s 1 0 0 r .0005 w .46865 .30421 m .4729 .29976 L s 0 0 1 r .5 Mabswid .46451 .30814 m .46497 .30763 L s .42698 .44455 m .42671 .44401 L s .55195 .40396 m .55191 .40403 L s .51141 .58387 m .5113 .58352 L s .46497 .30763 m .46542 .30713 L s .42726 .44507 m .42698 .44455 L s 1 0 0 r .0005 w .43382 .44733 m .43077 .44299 L s 0 0 1 r .5 Mabswid .55191 .40403 m .55187 .4041 L s .46542 .30713 m .46588 .30663 L s .51153 .58421 m .51141 .58387 L s .42754 .44559 m .42726 .44507 L s .46588 .30663 m .46633 .30613 L s .42783 .4461 m .42754 .44559 L s .55187 .4041 m .55183 .40419 L s .51164 .58455 m .51153 .58421 L s .46633 .30613 m .46679 .30564 L s .42813 .44661 m .42783 .4461 L s .51175 .58489 m .51164 .58455 L s .46679 .30564 m .46725 .30515 L s .55183 .40419 m .55178 .40428 L s .42843 .44711 m .42813 .44661 L s .46725 .30515 m .46771 .30467 L s .51187 .58522 m .51175 .58489 L s .01 w .42843 .44711 Mdot .5 Mabswid .42873 .44761 m .42843 .44711 L s .55178 .40428 m .55172 .40438 L s .46771 .30467 m .46817 .30419 L s .42905 .4481 m .42873 .44761 L s .51198 .58555 m .51187 .58522 L s .46817 .30419 m .46863 .30371 L s .55172 .40438 m .55165 .40449 L s .42937 .44858 m .42905 .4481 L s .46863 .30371 m .46909 .30324 L s 1 0 0 r .0005 w .4729 .29976 m .47721 .29565 L s 0 0 1 r .5 Mabswid .5121 .58588 m .51198 .58555 L s .4297 .44905 m .42937 .44858 L s .55165 .40449 m .55158 .40461 L s .46909 .30324 m .46955 .30277 L s 1 0 0 r .0005 w .55402 .40235 m .55289 .40392 L s 0 0 1 r .5 Mabswid .51221 .5862 m .5121 .58588 L s .43003 .44952 m .4297 .44905 L s .46955 .30277 m .47002 .30231 L s 1 0 0 r .0005 w .51527 .58661 m .51417 .58382 L s 0 0 1 r .5 Mabswid .55158 .40461 m .5515 .40473 L s 1 0 0 r .0005 w .43743 .45107 m .43382 .44733 L s 0 0 1 r .5 Mabswid .43037 .44997 m .43003 .44952 L s .47002 .30231 m .47048 .30185 L s .51233 .58652 m .51221 .5862 L s .5515 .40473 m .55142 .40486 L s .43072 .45043 m .43037 .44997 L s .47048 .30185 m .47095 .3014 L s .51245 .58683 m .51233 .58652 L s .43108 .45087 m .43072 .45043 L s .47095 .3014 m .47141 .30095 L s .55142 .40486 m .55133 .405 L s .51257 .58714 m .51245 .58683 L s .43144 .45131 m .43108 .45087 L s .47141 .30095 m .47188 .3005 L s .55133 .405 m .55123 .40515 L s .4318 .45173 m .43144 .45131 L s .47188 .3005 m .47235 .30006 L s .51268 .58745 m .51257 .58714 L s .43218 .45216 m .4318 .45173 L s .47235 .30006 m .47282 .29962 L s .55123 .40515 m .55112 .4053 L s .5128 .58775 m .51268 .58745 L s .47282 .29962 m .47329 .29919 L s .43256 .45257 m .43218 .45216 L s 1 0 0 r .0005 w .47721 .29565 m .48159 .29186 L s 0 0 1 r .5 Mabswid .55112 .4053 m .55101 .40547 L s .01 w .47329 .29919 Mdot .5 Mabswid .47329 .29919 m .47376 .29876 L s .51292 .58806 m .5128 .58775 L s .43295 .45298 m .43256 .45257 L s .55101 .40547 m .55089 .40564 L s .47376 .29876 m .47423 .29834 L s .43334 .45337 m .43295 .45298 L s .51304 .58835 m .51292 .58806 L s .47423 .29834 m .4747 .29791 L s .43374 .45376 m .43334 .45337 L s .55089 .40564 m .55077 .40581 L s 1 0 0 r .0005 w .44156 .45415 m .43743 .45107 L s 0 0 1 r .5 Mabswid .51317 .58865 m .51304 .58835 L s .4747 .29791 m .47518 .2975 L s .43415 .45415 m .43374 .45376 L s .55077 .40581 m .55064 .406 L s .47518 .2975 m .47565 .29708 L s .51329 .58893 m .51317 .58865 L s .43456 .45452 m .43415 .45415 L s 1 0 0 r .0005 w .55289 .40392 m .55116 .40613 L s .5164 .58914 m .51527 .58661 L s 0 0 1 r .5 Mabswid .47565 .29708 m .47612 .29667 L s .55064 .406 m .5505 .40619 L s .43498 .45489 m .43456 .45452 L s .51341 .58922 m .51329 .58893 L s .47612 .29667 m .4766 .29626 L s .43541 .45525 m .43498 .45489 L s .5505 .40619 m .55035 .40639 L s .51353 .5895 m .51341 .58922 L s .4766 .29626 m .47707 .29585 L s .43584 .4556 m .43541 .45525 L s .01 w .55035 .40639 Mdot .5 Mabswid .55035 .40639 m .5502 .4066 L s .47707 .29585 m .47755 .29545 L s .51366 .58978 m .51353 .5895 L s .01 w .51353 .5895 Mdot .5 Mabswid .43628 .45594 m .43584 .4556 L s 1 0 0 r .0005 w .48159 .29186 m .48603 .2884 L s 0 0 1 r .5 Mabswid .47755 .29545 m .47803 .29505 L s .5502 .4066 m .55004 .40681 L s .43672 .45628 m .43628 .45594 L s .51378 .59006 m .51366 .58978 L s .47803 .29505 m .4785 .29466 L s .43717 .4566 m .43672 .45628 L s .55004 .40681 m .54988 .40704 L s .5139 .59033 m .51378 .59006 L s .4785 .29466 m .47898 .29426 L s .43763 .45692 m .43717 .4566 L s .54988 .40704 m .5497 .40727 L s 1 0 0 r .0005 w .44622 .45653 m .44156 .45415 L s 0 0 1 r .5 Mabswid .47898 .29426 m .47946 .29388 L s .51403 .5906 m .5139 .59033 L s .4381 .45723 m .43763 .45692 L s .47946 .29388 m .47994 .29349 L s .5497 .40727 m .54952 .4075 L s .43856 .45753 m .4381 .45723 L s .51415 .59087 m .51403 .5906 L s .47994 .29349 m .48042 .29311 L s .43904 .45783 m .43856 .45753 L s .54952 .4075 m .54933 .40775 L s .51428 .59114 m .51415 .59087 L s .48042 .29311 m .4809 .29273 L s .43952 .45811 m .43904 .45783 L s .54933 .40775 m .54914 .408 L s .4809 .29273 m .48138 .29235 L s .51441 .5914 m .51428 .59114 L s .44001 .45839 m .43952 .45811 L s 1 0 0 r .0005 w .55116 .40613 m .5488 .40893 L s 0 0 1 r .5 Mabswid .54914 .408 m .54894 .40826 L s .48138 .29235 m .48186 .29198 L s 1 0 0 r .0005 w .51756 .59142 m .5164 .58914 L s 0 0 1 r .5 Mabswid .4405 .45866 m .44001 .45839 L s .51453 .59166 m .51441 .5914 L s .48186 .29198 m .48234 .29161 L s 1 0 0 r .0005 w .48603 .2884 m .49051 .28526 L s 0 0 1 r .5 Mabswid .54894 .40826 m .54873 .40852 L s .441 .45892 m .4405 .45866 L s .51466 .59192 m .51453 .59166 L s .48234 .29161 m .48283 .29125 L s .44151 .45917 m .441 .45892 L s .54873 .40852 m .54851 .4088 L s .48283 .29125 m .48331 .29089 L s .51478 .59217 m .51466 .59192 L s .44202 .45941 m .44151 .45917 L s .54851 .4088 m .54828 .40908 L s 1 0 0 r .0005 w .45135 .45818 m .44622 .45653 L s 0 0 1 r .5 Mabswid .48331 .29089 m .48379 .29053 L s .44254 .45965 m .44202 .45941 L s .51491 .59243 m .51478 .59217 L s .54828 .40908 m .54805 .40936 L s .48379 .29053 m .48428 .29018 L s .44306 .45987 m .44254 .45965 L s .51504 .59268 m .51491 .59243 L s .48428 .29018 m .48476 .28983 L s .54805 .40936 m .54781 .40966 L s .44359 .46009 m .44306 .45987 L s .48476 .28983 m .48525 .28948 L s .51516 .59292 m .51504 .59268 L s .44412 .4603 m .44359 .46009 L s .54781 .40966 m .54757 .40996 L s .48525 .28948 m .48574 .28913 L s .44466 .4605 m .44412 .4603 L s .51529 .59317 m .51516 .59292 L s .54757 .40996 m .54731 .41027 L s .48574 .28913 m .48622 .28879 L s .44521 .4607 m .44466 .4605 L s .54731 .41027 m .54705 .41058 L s .51542 .59341 m .51529 .59317 L s .48622 .28879 m .48671 .28846 L s .44576 .46088 m .44521 .4607 L s 1 0 0 r .0005 w .5488 .40893 m .54582 .41223 L s .49051 .28526 m .49505 .28245 L s 0 0 1 r .5 Mabswid .54705 .41058 m .54678 .4109 L s .51555 .59365 m .51542 .59341 L s .44631 .46105 m .44576 .46088 L s .48671 .28846 m .4872 .28812 L s .54678 .4109 m .5465 .41123 L s .44688 .46122 m .44631 .46105 L s .4872 .28812 m .48769 .28779 L s .51568 .59389 m .51555 .59365 L s 1 0 0 r .0005 w .51874 .59344 m .51756 .59142 L s .45693 .4591 m .45135 .45818 L s 0 0 1 r .5 Mabswid .44744 .46138 m .44688 .46122 L s .48769 .28779 m .48818 .28747 L s .5465 .41123 m .54622 .41156 L s .5158 .59412 m .51568 .59389 L s .44801 .46153 m .44744 .46138 L s .48818 .28747 m .48867 .28715 L s .54622 .41156 m .54593 .4119 L s .44859 .46167 m .44801 .46153 L s .51593 .59435 m .5158 .59412 L s .48867 .28715 m .48916 .28683 L s .54593 .4119 m .54563 .41224 L s .44917 .4618 m .44859 .46167 L s .48916 .28683 m .48965 .28651 L s .51606 .59458 m .51593 .59435 L s .54563 .41224 m .54533 .41259 L s .44976 .46193 m .44917 .4618 L s .48965 .28651 m .49014 .2862 L s .51619 .59481 m .51606 .59458 L s .45035 .46204 m .44976 .46193 L s .54533 .41259 m .54501 .41295 L s .49014 .2862 m .49063 .28589 L s .45095 .46215 m .45035 .46204 L s .54501 .41295 m .54469 .41331 L s .51632 .59503 m .51619 .59481 L s .49063 .28589 m .49113 .28559 L s .45155 .46225 m .45095 .46215 L s .54469 .41331 m .54436 .41368 L s 1 0 0 r .0005 w .49505 .28245 m .49963 .27996 L s 0 0 1 r .5 Mabswid .51645 .59525 m .51632 .59503 L s .49113 .28559 m .49162 .28529 L s .45216 .46234 m .45155 .46225 L s 1 0 0 r .0005 w .54582 .41223 m .54222 .41598 L s 0 0 1 r .5 Mabswid .54436 .41368 m .54403 .41405 L s 1 0 0 r .0005 w .46289 .45927 m .45693 .4591 L s 0 0 1 r .5 Mabswid .45277 .46242 m .45216 .46234 L s .49162 .28529 m .49212 .28499 L s .51657 .59547 m .51645 .59525 L s .54403 .41405 m .54369 .41443 L s .45338 .46249 m .45277 .46242 L s .49212 .28499 m .49261 .2847 L s .5167 .59568 m .51657 .59547 L s .54369 .41443 m .54334 .41482 L s .454 .46255 m .45338 .46249 L s .49261 .2847 m .49311 .28441 L s .45463 .46261 m .454 .46255 L s .54334 .41482 m .54298 .4152 L s .51683 .5959 m .5167 .59568 L s .49311 .28441 m .4936 .28413 L s 1 0 0 r .0005 w .51992 .59522 m .51874 .59344 L s 0 0 1 r .5 Mabswid .45526 .46265 m .45463 .46261 L s .54298 .4152 m .54262 .4156 L s .4936 .28413 m .4941 .28385 L s .51696 .59611 m .51683 .5959 L s .45589 .46269 m .45526 .46265 L s .54262 .4156 m .54225 .416 L s .4941 .28385 m .4946 .28357 L s .45653 .46272 m .45589 .46269 L s .51709 .59631 m .51696 .59611 L s .54225 .416 m .54187 .4164 L s .45717 .46274 m .45653 .46272 L s .4946 .28357 m .4951 .28329 L s .54187 .4164 m .54148 .41681 L s .51722 .59652 m .51709 .59631 L s .45782 .46276 m .45717 .46274 L s .4951 .28329 m .49559 .28302 L s 1 0 0 r .0005 w .46919 .45871 m .46289 .45927 L s 0 0 1 r .5 Mabswid .54148 .41681 m .54109 .41723 L s .45847 .46276 m .45782 .46276 L s .51735 .59672 m .51722 .59652 L s 1 0 0 r .0005 w .54222 .41598 m .53803 .42008 L s 0 0 1 r .5 Mabswid .49559 .28302 m .49609 .28276 L s 1 0 0 r .0005 w .49963 .27996 m .50425 .27779 L s 0 0 1 r .5 Mabswid .45912 .46275 m .45847 .46276 L s .54109 .41723 m .54069 .41764 L s .49609 .28276 m .49659 .2825 L s .45978 .46274 m .45912 .46275 L s .51748 .59692 m .51735 .59672 L s .54069 .41764 m .54029 .41807 L s .46044 .46272 m .45978 .46274 L s .49659 .2825 m .49709 .28224 L s .54029 .41807 m .53987 .41849 L s .51761 .59711 m .51748 .59692 L s .46111 .46269 m .46044 .46272 L s .49709 .28224 m .4976 .28198 L s .53987 .41849 m .53945 .41892 L s .46178 .46265 m .46111 .46269 L s .51773 .59731 m .51761 .59711 L s .53945 .41892 m .53903 .41936 L s .4976 .28198 m .4981 .28173 L s .46245 .46261 m .46178 .46265 L s .53903 .41936 m .53859 .4198 L s .51786 .5975 m .51773 .59731 L s .46312 .46255 m .46245 .46261 L s .4981 .28173 m .4986 .28148 L s .53859 .4198 m .53815 .42024 L s .4638 .46249 m .46312 .46255 L s .4986 .28148 m .4991 .28124 L s .51799 .59768 m .51786 .5975 L s 1 0 0 r .0005 w .47576 .45743 m .46919 .45871 L s 0 0 1 r .5 Mabswid .53815 .42024 m .5377 .42069 L s .46449 .46242 m .4638 .46249 L s .4991 .28124 m .49961 .281 L s 1 0 0 r .0005 w .52108 .59676 m .51992 .59522 L s 0 0 1 r .5 Mabswid .46517 .46234 m .46449 .46242 L s .5377 .42069 m .53725 .42114 L s .51812 .59787 m .51799 .59768 L s 1 0 0 r .0005 w .53803 .42008 m .53327 .42442 L s 0 0 1 r .5 Mabswid .46586 .46225 m .46517 .46234 L s .49961 .281 m .50011 .28077 L s .53725 .42114 m .53679 .42159 L s .46655 .46215 m .46586 .46225 L s .51825 .59805 m .51812 .59787 L s .53679 .42159 m .53632 .42205 L s .50011 .28077 m .50061 .28053 L s .46725 .46205 m .46655 .46215 L s .53632 .42205 m .53585 .42251 L s 1 0 0 r .0005 w .50425 .27779 m .50892 .27592 L s 0 0 1 r .5 Mabswid .51838 .59823 m .51825 .59805 L s .01 w .46725 .46205 Mdot .5 Mabswid .46795 .46194 m .46725 .46205 L s .50061 .28053 m .50112 .28031 L s .53585 .42251 m .53537 .42297 L s .46865 .46182 m .46795 .46194 L s .50112 .28031 m .50163 .28008 L s .53537 .42297 m .53488 .42344 L s .51851 .59841 m .51838 .59823 L s .46935 .46169 m .46865 .46182 L s .53488 .42344 m .53439 .42391 L s .47006 .46155 m .46935 .46169 L s .50163 .28008 m .50213 .27986 L s 1 0 0 r .0005 w .48251 .45548 m .47576 .45743 L s 0 0 1 r .5 Mabswid .51863 .59858 m .51851 .59841 L s .53439 .42391 m .53389 .42438 L s .47077 .4614 m .47006 .46155 L s .50213 .27986 m .50264 .27965 L s .53389 .42438 m .53338 .42485 L s .47148 .46125 m .47077 .4614 L s .51876 .59875 m .51863 .59858 L s 1 0 0 r .0005 w .53327 .42442 m .52801 .42892 L s 0 0 1 r .5 Mabswid .53338 .42485 m .53287 .42533 L s .4722 .46109 m .47148 .46125 L s .50264 .27965 m .50315 .27944 L s .47291 .46092 m .4722 .46109 L s .53287 .42533 m .53235 .42581 L s .51889 .59892 m .51876 .59875 L s .50315 .27944 m .50365 .27923 L s .47363 .46074 m .47291 .46092 L s .53235 .42581 m .53182 .42629 L s .47435 .46055 m .47363 .46074 L s .53182 .42629 m .53129 .42677 L s .50365 .27923 m .50416 .27902 L s .51902 .59909 m .51889 .59892 L s .47508 .46036 m .47435 .46055 L s .53129 .42677 m .53075 .42725 L s .4758 .46015 m .47508 .46036 L s .50416 .27902 m .50467 .27882 L s .53075 .42725 m .53021 .42774 L s 1 0 0 r .0005 w .48937 .45291 m .48251 .45548 L s 0 0 1 r .5 Mabswid .47653 .45994 m .4758 .46015 L s .51914 .59925 m .51902 .59909 L s .53021 .42774 m .52966 .42823 L s .47726 .45973 m .47653 .45994 L s .50467 .27882 m .50518 .27863 L s .52966 .42823 m .52911 .42872 L s .47799 .4595 m .47726 .45973 L s 1 0 0 r .0005 w .52223 .59807 m .52108 .59676 L s .52801 .42892 m .52228 .43345 L s 0 0 1 r .5 Mabswid .51927 .59941 m .51914 .59925 L s .52911 .42872 m .52855 .42921 L s 1 0 0 r .0005 w .50892 .27592 m .51363 .27435 L s 0 0 1 r .5 Mabswid .50518 .27863 m .50569 .27844 L s .47872 .45927 m .47799 .4595 L s .52855 .42921 m .52798 .4297 L s .47946 .45903 m .47872 .45927 L s .52798 .4297 m .52741 .43019 L s .5194 .59957 m .51927 .59941 L s .50569 .27844 m .5062 .27825 L s .48019 .45878 m .47946 .45903 L s .52741 .43019 m .52683 .43068 L s .48093 .45852 m .48019 .45878 L s .52683 .43068 m .52625 .43118 L s .5062 .27825 m .50671 .27806 L s .48166 .45826 m .48093 .45852 L s 1 0 0 r .0005 w .49625 .44978 m .48937 .45291 L s 0 0 1 r .5 Mabswid .51952 .59972 m .5194 .59957 L s .52625 .43118 m .52566 .43167 L s .4824 .45799 m .48166 .45826 L s .52566 .43167 m .52507 .43217 L s .48314 .45771 m .4824 .45799 L s .50671 .27806 m .50723 .27788 L s 1 0 0 r .0005 w .52228 .43345 m .51617 .43791 L s 0 0 1 r .5 Mabswid .48388 .45743 m .48314 .45771 L s .52507 .43217 m .52447 .43266 L s .51965 .59987 m .51952 .59972 L s .48462 .45713 m .48388 .45743 L s .52447 .43266 m .52386 .43316 L s .50723 .27788 m .50774 .27771 L s .48536 .45684 m .48462 .45713 L s .52386 .43316 m .52325 .43366 L s .48611 .45653 m .48536 .45684 L s .52325 .43366 m .52264 .43415 L s .51978 .60002 m .51965 .59987 L s 1 0 0 r .0005 w .50307 .44618 m .49625 .44978 L s 0 0 1 r .5 Mabswid .48685 .45622 m .48611 .45653 L s .50774 .27771 m .50825 .27754 L s .52264 .43415 m .52202 .43465 L s .48759 .4559 m .48685 .45622 L s .52202 .43465 m .5214 .43514 L s 1 0 0 r .0005 w .51617 .43791 m .50974 .44219 L s 0 0 1 r .5 Mabswid .48833 .45558 m .48759 .4559 L s .5214 .43514 m .52077 .43564 L s .5199 .60017 m .51978 .60002 L s .50825 .27754 m .50876 .27737 L s .48908 .45525 m .48833 .45558 L s .52077 .43564 m .52013 .43613 L s .48982 .45491 m .48908 .45525 L s 1 0 0 r .0005 w .50974 .44219 m .50307 .44618 L s 0 0 1 r .01 w .52013 .43613 Mdot .5 Mabswid .52013 .43613 m .51949 .43663 L s .49056 .45457 m .48982 .45491 L s .51949 .43663 m .51885 .43712 L s .50876 .27737 m .50928 .2772 L s .4913 .45422 m .49056 .45457 L s .51885 .43712 m .51821 .43761 L s .52003 .60031 m .5199 .60017 L s .49204 .45386 m .4913 .45422 L s .51821 .43761 m .51755 .4381 L s .49278 .4535 m .49204 .45386 L s .51755 .4381 m .5169 .43859 L s .49352 .45313 m .49278 .4535 L s .5169 .43859 m .51624 .43908 L s .50928 .2772 m .50979 .27704 L s .49426 .45276 m .49352 .45313 L s .51624 .43908 m .51557 .43957 L s .495 .45238 m .49426 .45276 L s .51557 .43957 m .51491 .44005 L s .52015 .60045 m .52003 .60031 L s .49574 .452 m .495 .45238 L s .51491 .44005 m .51423 .44053 L s .49648 .45161 m .49574 .452 L s .51423 .44053 m .51356 .44101 L s .49721 .45122 m .49648 .45161 L s .01 w .50979 .27704 Mdot .5 Mabswid .50979 .27704 m .51031 .27689 L s .51356 .44101 m .51288 .44149 L s .49795 .45082 m .49721 .45122 L s .51288 .44149 m .5122 .44197 L s 1 0 0 r .0005 w .51363 .27435 m .51838 .27307 L s 0 0 1 r .5 Mabswid .49868 .45041 m .49795 .45082 L s .5122 .44197 m .51151 .44244 L s .49941 .45001 m .49868 .45041 L s .51151 .44244 m .51082 .44291 L s .50014 .44959 m .49941 .45001 L s .51082 .44291 m .51013 .44338 L s .50087 .44917 m .50014 .44959 L s .52028 .60059 m .52015 .60045 L s .51013 .44338 m .50943 .44385 L s .5016 .44875 m .50087 .44917 L s .50943 .44385 m .50873 .44431 L s .50232 .44833 m .5016 .44875 L s .50873 .44431 m .50803 .44477 L s .50304 .4479 m .50232 .44833 L s .50803 .44477 m .50733 .44523 L s .51031 .27689 m .51082 .27673 L s .50376 .44746 m .50304 .4479 L s .50733 .44523 m .50662 .44568 L s .50448 .44702 m .50376 .44746 L s .50662 .44568 m .50591 .44613 L s .5052 .44658 m .50448 .44702 L s .50591 .44613 m .5052 .44658 L s .5204 .60072 m .52028 .60059 L s .51082 .27673 m .51134 .27658 L s 1 0 0 r .0005 w .52335 .59917 m .52223 .59807 L s 0 0 1 r .5 Mabswid .51134 .27658 m .51186 .27644 L s .52053 .60085 m .5204 .60072 L s .51186 .27644 m .51237 .27629 L s .52065 .60098 m .52053 .60085 L s .51237 .27629 m .51289 .27615 L s .52077 .60111 m .52065 .60098 L s .51289 .27615 m .51341 .27601 L s .5209 .60123 m .52077 .60111 L s .51341 .27601 m .51393 .27587 L s .51393 .27587 m .51445 .27574 L s .52102 .60135 m .5209 .60123 L s .51445 .27574 m .51497 .27561 L s .52114 .60147 m .52102 .60135 L s 1 0 0 r .0005 w .51838 .27307 m .52318 .27208 L s 0 0 1 r .5 Mabswid .51497 .27561 m .51549 .27548 L s .52126 .60159 m .52114 .60147 L s .51549 .27548 m .51601 .27536 L s .52138 .6017 m .52126 .60159 L s .51601 .27536 m .51653 .27524 L s .51653 .27524 m .51705 .27512 L s .5215 .60181 m .52138 .6017 L s 1 0 0 r .0005 w .52443 .60004 m .52335 .59917 L s 0 0 1 r .5 Mabswid .51705 .27512 m .51757 .275 L s .52162 .60192 m .5215 .60181 L s .51757 .275 m .51809 .27489 L s .52174 .60202 m .52162 .60192 L s .51809 .27489 m .51862 .27478 L s .52186 .60212 m .52174 .60202 L s .51862 .27478 m .51914 .27467 L s .51914 .27467 m .51966 .27457 L s .52198 .60222 m .52186 .60212 L s 1 0 0 r .0005 w .52318 .27208 m .52802 .27136 L s 0 0 1 r .5 Mabswid .51966 .27457 m .52019 .27447 L s .5221 .60231 m .52198 .60222 L s .52019 .27447 m .52071 .27437 L s .52221 .60241 m .5221 .60231 L s .52071 .27437 m .52124 .27427 L s .52124 .27427 m .52177 .27418 L s .52233 .60249 m .52221 .60241 L s .52177 .27418 m .52229 .27409 L s .52245 .60258 m .52233 .60249 L s .52229 .27409 m .52282 .27401 L s .52256 .60267 m .52245 .60258 L s .52282 .27401 m .52335 .27392 L s 1 0 0 r .0005 w .52545 .60071 m .52443 .60004 L s 0 0 1 r .5 Mabswid .52268 .60275 m .52256 .60267 L s .52335 .27392 m .52388 .27384 L s .52388 .27384 m .52441 .27377 L s .52279 .60282 m .52268 .60275 L s .52441 .27377 m .52494 .27369 L s 1 0 0 r .0005 w .52802 .27136 m .53291 .2709 L s 0 0 1 r .5 Mabswid .5229 .6029 m .52279 .60282 L s .01 w .52279 .60282 Mdot .5 Mabswid .52494 .27369 m .52547 .27362 L s .52302 .60297 m .5229 .6029 L s .52547 .27362 m .526 .27355 L s .52313 .60305 m .52302 .60297 L s .526 .27355 m .52653 .27349 L s .52653 .27349 m .52706 .27342 L s .52324 .60311 m .52313 .60305 L s .52706 .27342 m .52759 .27336 L s .52335 .60318 m .52324 .60311 L s .52759 .27336 m .52813 .27331 L s .52346 .60325 m .52335 .60318 L s .52813 .27331 m .52866 .27325 L s .52357 .60331 m .52346 .60325 L s .52866 .27325 m .52919 .2732 L s .52919 .2732 m .52973 .27315 L s 1 0 0 r .0005 w .52643 .60117 m .52545 .60071 L s 0 0 1 r .5 Mabswid .52368 .60337 m .52357 .60331 L s 1 0 0 r .0005 w .53291 .2709 m .53785 .27071 L s 0 0 1 r .5 Mabswid .52973 .27315 m .53026 .27311 L s .52379 .60343 m .52368 .60337 L s .53026 .27311 m .5308 .27307 L s .5239 .60348 m .52379 .60343 L s .5308 .27307 m .53134 .27303 L s .52401 .60354 m .5239 .60348 L s .53134 .27303 m .53188 .27299 L s .53188 .27299 m .53241 .27296 L s .52411 .60359 m .52401 .60354 L s .53241 .27296 m .53295 .27293 L s .52422 .60364 m .52411 .60359 L s .53295 .27293 m .53349 .2729 L s .52433 .60368 m .52422 .60364 L s .53349 .2729 m .53403 .27288 L s .53403 .27288 m .53457 .27286 L s .52443 .60373 m .52433 .60368 L s 1 0 0 r .0005 w .53785 .27071 m .54284 .27076 L s 0 0 1 r .5 Mabswid .53457 .27286 m .53511 .27284 L s .52453 .60377 m .52443 .60373 L s .53511 .27284 m .53566 .27283 L s .52464 .60381 m .52453 .60377 L s 1 0 0 r .0005 w .52733 .60145 m .52643 .60117 L s 0 0 1 r .5 Mabswid .53566 .27283 m .5362 .27282 L s .52474 .60385 m .52464 .60381 L s .5362 .27282 m .53674 .27281 L s .53674 .27281 m .53729 .2728 L s .52484 .60389 m .52474 .60385 L s .53729 .2728 m .53783 .2728 L s .52494 .60392 m .52484 .60389 L s .53783 .2728 m .53838 .2728 L s .52504 .60395 m .52494 .60392 L s .53838 .2728 m .53892 .2728 L s .53892 .2728 m .53947 .27281 L s .52514 .60398 m .52504 .60395 L s .53947 .27281 m .54002 .27282 L s 1 0 0 r .0005 w .54284 .27076 m .54788 .27104 L s 0 0 1 r .5 Mabswid .52524 .60401 m .52514 .60398 L s .54002 .27282 m .54056 .27283 L s .52534 .60404 m .52524 .60401 L s .54056 .27283 m .54111 .27284 L s .52544 .60406 m .52534 .60404 L s .54111 .27284 m .54166 .27286 L s .54166 .27286 m .54221 .27288 L s .52554 .60408 m .52544 .60406 L s 1 0 0 r .0005 w .52816 .60153 m .52733 .60145 L s 0 0 1 r .5 Mabswid .54221 .27288 m .54276 .27291 L s .52563 .6041 m .52554 .60408 L s .54276 .27291 m .54331 .27294 L s .52573 .60412 m .52563 .6041 L s .54331 .27294 m .54387 .27297 L s .54387 .27297 m .54442 .273 L s .52582 .60413 m .52573 .60412 L s .54442 .273 m .54497 .27304 L s 1 0 0 r .0005 w .54788 .27104 m .55298 .27156 L s 0 0 1 r .5 Mabswid .52591 .60414 m .52582 .60413 L s .54497 .27304 m .54553 .27307 L s .52601 .60416 m .52591 .60414 L s .54553 .27307 m .54608 .27312 L s .54608 .27312 m .54664 .27316 L s .5261 .60416 m .52601 .60416 L s .54664 .27316 m .54719 .27321 L s .52619 .60417 m .5261 .60416 L s .54719 .27321 m .54775 .27326 L s .52628 .60417 m .52619 .60417 L s .54775 .27326 m .54831 .27332 L s .54831 .27332 m .54887 .27337 L s .52637 .60418 m .52628 .60417 L s .54887 .27337 m .54943 .27343 L s 1 0 0 r .0005 w .5289 .60143 m .52816 .60153 L s 0 0 1 r .5 Mabswid .52645 .60418 m .52637 .60418 L s .01 w .54943 .27343 Mdot .5 Mabswid .54943 .27343 m .54999 .2735 L s 1 0 0 r .0005 w .55298 .27156 m .55813 .2723 L s 0 0 1 r .5 Mabswid .52654 .60417 m .52645 .60418 L s .54999 .2735 m .55055 .27356 L s .55055 .27356 m .55111 .27363 L s .52663 .60417 m .52654 .60417 L s .55111 .27363 m .55167 .2737 L s .52671 .60416 m .52663 .60417 L s .55167 .2737 m .55223 .27377 L s .52679 .60415 m .52671 .60416 L s .55223 .27377 m .5528 .27384 L s .5528 .27384 m .55336 .27392 L s .52688 .60414 m .52679 .60415 L s .55336 .27392 m .55392 .274 L s .52696 .60413 m .52688 .60414 L s .55392 .274 m .55449 .27408 L s .52704 .60411 m .52696 .60413 L s .55449 .27408 m .55505 .27417 L s 1 0 0 r .0005 w .55813 .2723 m .56335 .27325 L s 0 0 1 r .5 Mabswid .55505 .27417 m .55562 .27425 L s .52712 .6041 m .52704 .60411 L s .55562 .27425 m .55619 .27434 L s 1 0 0 r .0005 w .52956 .60116 m .5289 .60143 L s 0 0 1 r .5 Mabswid .5272 .60408 m .52712 .6041 L s .55619 .27434 m .55676 .27443 L s .52727 .60406 m .5272 .60408 L s .55676 .27443 m .55733 .27452 L s .55733 .27452 m .55789 .27462 L s .52735 .60403 m .52727 .60406 L s .55789 .27462 m .55846 .27471 L s .52742 .60401 m .52735 .60403 L s .55846 .27471 m .55904 .27481 L s .5275 .60398 m .52742 .60401 L s .55904 .27481 m .55961 .27492 L s .55961 .27492 m .56018 .27502 L s .52757 .60395 m .5275 .60398 L s .56018 .27502 m .56075 .27513 L s 1 0 0 r .0005 w .56335 .27325 m .56863 .2744 L s 0 0 1 r .5 Mabswid .52764 .60392 m .52757 .60395 L s .56075 .27513 m .56133 .27524 L s .52771 .60388 m .52764 .60392 L s .56133 .27524 m .5619 .27535 L s .5619 .27535 m .56248 .27546 L s .52778 .60385 m .52771 .60388 L s .56248 .27546 m .56305 .27558 L s .52785 .60381 m .52778 .60385 L s 1 0 0 r .0005 w .53011 .60072 m .52956 .60116 L s 0 0 1 r .5 Mabswid .56305 .27558 m .56363 .27569 L s .52792 .60377 m .52785 .60381 L s .56363 .27569 m .5642 .27581 L s .5642 .27581 m .56478 .27594 L s .52798 .60373 m .52792 .60377 L s .56478 .27594 m .56536 .27606 L s .52805 .60368 m .52798 .60373 L s .56536 .27606 m .56594 .27619 L s 1 0 0 r .0005 w .56863 .2744 m .57397 .27575 L s 0 0 1 r .5 Mabswid .56594 .27619 m .56652 .27632 L s .52811 .60364 m .52805 .60368 L s .56652 .27632 m .5671 .27645 L s .52817 .60359 m .52811 .60364 L s .5671 .27645 m .56768 .27658 L s .52824 .60354 m .52817 .60359 L s .56768 .27658 m .56827 .27672 L s .56827 .27672 m .56885 .27685 L s .5283 .60349 m .52824 .60354 L s .56885 .27685 m .56944 .27699 L s .52835 .60343 m .5283 .60349 L s .56944 .27699 m .57002 .27714 L s .57002 .27714 m .57061 .27728 L s .52841 .60338 m .52835 .60343 L s 1 0 0 r .0005 w .53056 .60011 m .53011 .60072 L s 0 0 1 r .5 Mabswid .57061 .27728 m .57119 .27743 L s .52847 .60332 m .52841 .60338 L s 1 0 0 r .0005 w .57397 .27575 m .57938 .27728 L s 0 0 1 r .5 Mabswid .57119 .27743 m .57178 .27758 L s .52852 .60326 m .52847 .60332 L s .57178 .27758 m .57237 .27773 L s .57237 .27773 m .57296 .27788 L s .52857 .6032 m .52852 .60326 L s .57296 .27788 m .57355 .27804 L s .52863 .60313 m .52857 .6032 L s .57355 .27804 m .57414 .27819 L s .57414 .27819 m .57473 .27835 L s .52868 .60307 m .52863 .60313 L s .57473 .27835 m .57532 .27852 L s .52873 .603 m .52868 .60307 L s .57532 .27852 m .57591 .27868 L s .52877 .60293 m .52873 .603 L s .57591 .27868 m .57651 .27885 L s .57651 .27885 m .5771 .27901 L s 1 0 0 r .0005 w .57938 .27728 m .58487 .27899 L s 0 0 1 r .5 Mabswid .52882 .60285 m .52877 .60293 L s .5771 .27901 m .5777 .27918 L s .52886 .60278 m .52882 .60285 L s .5777 .27918 m .5783 .27936 L s 1 0 0 r .0005 w .53089 .59934 m .53056 .60011 L s 0 0 1 r .5 Mabswid .5783 .27936 m .57889 .27953 L s .52891 .6027 m .52886 .60278 L s .57889 .27953 m .57949 .27971 L s .52895 .60263 m .52891 .6027 L s .57949 .27971 m .58009 .27989 L s .58009 .27989 m .58069 .28007 L s .52899 .60255 m .52895 .60263 L s .01 w .52895 .60263 Mdot .5 Mabswid .58069 .28007 m .58129 .28025 L s .52903 .60246 m .52899 .60255 L s .58129 .28025 m .58189 .28044 L s .52907 .60238 m .52903 .60246 L s .58189 .28044 m .5825 .28062 L s 1 0 0 r .0005 w .58487 .27899 m .59042 .28088 L s 0 0 1 r .5 Mabswid .5825 .28062 m .5831 .28081 L s .5291 .60229 m .52907 .60238 L s .5831 .28081 m .5837 .281 L s .52914 .60221 m .5291 .60229 L s .5837 .281 m .58431 .2812 L s .58431 .2812 m .58491 .28139 L s .52917 .60212 m .52914 .60221 L s .58491 .28139 m .58552 .28159 L s .5292 .60202 m .52917 .60212 L s .58552 .28159 m .58613 .28179 L s .58613 .28179 m .58674 .28199 L s 1 0 0 r .0005 w .53109 .59841 m .53089 .59934 L s 0 0 1 r .5 Mabswid .52923 .60193 m .5292 .60202 L s .58674 .28199 m .58735 .2822 L s .52926 .60184 m .52923 .60193 L s .58735 .2822 m .58796 .2824 L s 1 0 0 r .0005 w .59042 .28088 m .59605 .28294 L s 0 0 1 r .5 Mabswid .58796 .2824 m .58857 .28261 L s .52929 .60174 m .52926 .60184 L s .58857 .28261 m .58918 .28282 L s .52932 .60164 m .52929 .60174 L s .58918 .28282 m .5898 .28303 L s .5898 .28303 m .59041 .28324 L s .52934 .60154 m .52932 .60164 L s .59041 .28324 m .59102 .28346 L s .52936 .60143 m .52934 .60154 L s .59102 .28346 m .59164 .28368 L s .59164 .28368 m .59226 .2839 L s .52938 .60133 m .52936 .60143 L s .59226 .2839 m .59288 .28412 L s .5294 .60122 m .52938 .60133 L s .01 w .59288 .28412 Mdot .5 Mabswid .59288 .28412 m .59349 .28434 L s .59349 .28434 m .59411 .28457 L s 1 0 0 r .0005 w .59605 .28294 m .60176 .28515 L s 0 0 1 r .5 Mabswid .52942 .60111 m .5294 .60122 L s .59411 .28457 m .59473 .28479 L s .52944 .601 m .52942 .60111 L s .59473 .28479 m .59536 .28502 L s 1 0 0 r .0005 w .53115 .59734 m .53109 .59841 L s 0 0 1 r .5 Mabswid .59536 .28502 m .59598 .28525 L s .52945 .60089 m .52944 .601 L s .59598 .28525 m .5966 .28549 L s .52946 .60078 m .52945 .60089 L s .5966 .28549 m .59723 .28572 L s .59723 .28572 m .59785 .28596 L s .52948 .60066 m .52946 .60078 L s .59785 .28596 m .59848 .2862 L s .59848 .2862 m .59911 .28644 L s .52949 .60054 m .52948 .60066 L s .59911 .28644 m .59973 .28668 L s 1 0 0 r .0005 w .60176 .28515 m .60754 .28752 L s 0 0 1 r .5 Mabswid .52949 .60043 m .52949 .60054 L s .59973 .28668 m .60036 .28693 L s .60036 .28693 m .60099 .28717 L s .5295 .6003 m .52949 .60043 L s .60099 .28717 m .60162 .28742 L s .5295 .60018 m .5295 .6003 L s .60162 .28742 m .60226 .28767 L s .60226 .28767 m .60289 .28792 L s .52951 .60006 m .5295 .60018 L s .60289 .28792 m .60352 .28817 L s .52951 .59993 m .52951 .60006 L s .60352 .28817 m .60416 .28843 L s 1 0 0 r .0005 w .53107 .59611 m .53115 .59734 L s 0 0 1 r .5 Mabswid .60416 .28843 m .60479 .28869 L s .52951 .5998 m .52951 .59993 L s .60479 .28869 m .60543 .28895 L s 1 0 0 r .0005 w .60754 .28752 m .61342 .29003 L s 0 0 1 r .5 Mabswid .60543 .28895 m .60607 .28921 L s .52951 .59967 m .52951 .5998 L s .60607 .28921 m .60671 .28947 L s .5295 .59954 m .52951 .59967 L s .60671 .28947 m .60735 .28973 L s .60735 .28973 m .60799 .29 L s .5295 .59941 m .5295 .59954 L s .60799 .29 m .60863 .29027 L s .52949 .59927 m .5295 .59941 L s .60863 .29027 m .60927 .29053 L s .60927 .29053 m .60992 .29081 L s .52948 .59913 m .52949 .59927 L s .60992 .29081 m .61056 .29108 L s .61056 .29108 m .61121 .29135 L s .52947 .59899 m .52948 .59913 L s .61121 .29135 m .61185 .29163 L s 1 0 0 r .0005 w .61342 .29003 m .61937 .29269 L s 0 0 1 r .5 Mabswid .52946 .59885 m .52947 .59899 L s .61185 .29163 m .6125 .29191 L s .6125 .29191 m .61315 .29218 L s .52944 .59871 m .52946 .59885 L s .61315 .29218 m .6138 .29247 L s 1 0 0 r .0005 w .53083 .59475 m .53107 .59611 L s 0 0 1 r .5 Mabswid .6138 .29247 m .61445 .29275 L s .52942 .59857 m .52944 .59871 L s .61445 .29275 m .6151 .29303 L s .52941 .59842 m .52942 .59857 L s .6151 .29303 m .61576 .29332 L s .61576 .29332 m .61641 .2936 L s .52939 .59827 m .52941 .59842 L s .61641 .2936 m .61707 .29389 L s .61707 .29389 m .61772 .29418 L s .52936 .59813 m .52939 .59827 L s 1 0 0 r .0005 w .61937 .29269 m .62542 .29548 L s 0 0 1 r .5 Mabswid .61772 .29418 m .61838 .29448 L s .61838 .29448 m .61904 .29477 L s .52934 .59798 m .52936 .59813 L s .61904 .29477 m .6197 .29506 L s .52931 .59782 m .52934 .59798 L s .6197 .29506 m .62036 .29536 L s .62036 .29536 m .62102 .29566 L s .52929 .59767 m .52931 .59782 L s .62102 .29566 m .62168 .29596 L s .62168 .29596 m .62234 .29626 L s .52926 .59751 m .52929 .59767 L s .62234 .29626 m .62301 .29656 L s .62301 .29656 m .62367 .29687 L s .52923 .59736 m .52926 .59751 L s 1 0 0 r .0005 w .62542 .29548 m .63155 .2984 L s 0 0 1 r .5 Mabswid .62367 .29687 m .62434 .29717 L s .52919 .5972 m .52923 .59736 L s 1 0 0 r .0005 w .53042 .59324 m .53083 .59475 L s 0 0 1 r .5 Mabswid .62434 .29717 m .625 .29748 L s .625 .29748 m .62567 .29779 L s .52916 .59704 m .52919 .5972 L s .62567 .29779 m .62634 .2981 L s .62634 .2981 m .62701 .29841 L s .52912 .59688 m .52916 .59704 L s .62701 .29841 m .62768 .29872 L s .62768 .29872 m .62836 .29904 L s .52908 .59671 m .52912 .59688 L s .62836 .29904 m .62903 .29935 L s .52904 .59655 m .52908 .59671 L s .62903 .29935 m .6297 .29967 L s .6297 .29967 m .63038 .29999 L s 1 0 0 r .0005 w .63155 .2984 m .63778 .30143 L s 0 0 1 r .5 Mabswid .529 .59638 m .52904 .59655 L s .63038 .29999 m .63106 .30031 L s .63106 .30031 m .63173 .30063 L s .52895 .59621 m .529 .59638 L s .63173 .30063 m .63241 .30095 L s .63241 .30095 m .63309 .30127 L s .52891 .59604 m .52895 .59621 L s .63309 .30127 m .63377 .3016 L s .63377 .3016 m .63445 .30192 L s .52886 .59587 m .52891 .59604 L s .63445 .30192 m .63514 .30225 L s .63514 .30225 m .63582 .30258 L s .52881 .5957 m .52886 .59587 L s 1 0 0 r .0005 w .52983 .59161 m .53042 .59324 L s 0 0 1 r .5 Mabswid .63582 .30258 m .63651 .30291 L s 1 0 0 r .0005 w .63778 .30143 m .64411 .30458 L s 0 0 1 r .5 Mabswid .63651 .30291 m .63719 .30324 L s .52875 .59552 m .52881 .5957 L s .63719 .30324 m .63788 .30357 L s .63788 .30357 m .63857 .3039 L s .5287 .59535 m .52875 .59552 L s .63857 .3039 m .63926 .30424 L s .63926 .30424 m .63995 .30457 L s .52864 .59517 m .5287 .59535 L s .63995 .30457 m .64064 .30491 L s .64064 .30491 m .64133 .30525 L s .52858 .59499 m .52864 .59517 L s .01 w .64133 .30525 Mdot .5 Mabswid .64133 .30525 m .64202 .30559 L s .52852 .59481 m .52858 .59499 L s .64202 .30559 m .64272 .30593 L s 1 0 0 r .0005 w .64411 .30458 m .65053 .30784 L s 0 0 1 r .5 Mabswid .64272 .30593 m .64341 .30627 L s .52846 .59463 m .52852 .59481 L s .64341 .30627 m .64411 .30662 L s .64411 .30662 m .64481 .30696 L s .64481 .30696 m .64551 .30731 L s .52839 .59445 m .52846 .59463 L s .64551 .30731 m .64621 .30765 L s .64621 .30765 m .64691 .308 L s .52833 .59426 m .52839 .59445 L s .64691 .308 m .64762 .30835 L s .64762 .30835 m .64832 .3087 L s .52826 .59408 m .52833 .59426 L s .64832 .3087 m .64903 .30906 L s 1 0 0 r .0005 w .52905 .58984 m .52983 .59161 L s 0 0 1 r .5 Mabswid .64903 .30906 m .64974 .30941 L s .52819 .59389 m .52826 .59408 L s 1 0 0 r .0005 w .65053 .30784 m .65705 .31119 L s 0 0 1 r .5 Mabswid .64974 .30941 m .65044 .30976 L s .65044 .30976 m .65115 .31012 L s .52811 .5937 m .52819 .59389 L s .65115 .31012 m .65186 .31048 L s .65186 .31048 m .65258 .31084 L s .52804 .59351 m .52811 .5937 L s .65258 .31084 m .65329 .3112 L s .65329 .3112 m .65401 .31156 L s .52796 .59332 m .52804 .59351 L s .65401 .31156 m .65472 .31192 L s .65472 .31192 m .65544 .31228 L s .52788 .59313 m .52796 .59332 L s .65544 .31228 m .65616 .31265 L s 1 0 0 r .0005 w .65705 .31119 m .66368 .31463 L s 0 0 1 r .5 Mabswid .65616 .31265 m .65688 .31301 L s .01 w .8131 .37859 Mdot .5 Mabswid .8124 .37847 m .8131 .37859 L s .65688 .31301 m .6576 .31338 L s .5278 .59293 m .52788 .59313 L s .6576 .31338 m .65832 .31375 L s .81169 .37835 m .8124 .37847 L s .65832 .31375 m .65904 .31411 L s .81099 .37822 m .81169 .37835 L s .52771 .59274 m .5278 .59293 L s .65904 .31411 m .65977 .31448 L s .81028 .37808 m .81099 .37822 L s .65977 .31448 m .66049 .31485 L s .80956 .37795 m .81028 .37808 L s .52763 .59254 m .52771 .59274 L s .66049 .31485 m .66122 .31522 L s .80885 .37781 m .80956 .37795 L s .66122 .31522 m .66195 .3156 L s .66195 .3156 m .66268 .31597 L s .80813 .37766 m .80885 .37781 L s .52754 .59234 m .52763 .59254 L s .66268 .31597 m .66341 .31634 L s 1 0 0 r .0005 w .66368 .31463 m .67041 .31814 L s 0 0 1 r .5 Mabswid .80741 .37752 m .80813 .37766 L s .66341 .31634 m .66414 .31672 L s 1 0 0 r .0005 w .52806 .58795 m .52905 .58984 L s 0 0 1 r .5 Mabswid .80669 .37737 m .80741 .37752 L s .52745 .59214 m .52754 .59234 L s .66414 .31672 m .66487 .31709 L s .80596 .37721 m .80669 .37737 L s .66487 .31709 m .66561 .31747 L s .66561 .31747 m .66634 .31785 L s .80523 .37705 m .80596 .37721 L s .52736 .59194 m .52745 .59214 L s .66634 .31785 m .66708 .31823 L s .8045 .37689 m .80523 .37705 L s .66708 .31823 m .66781 .31861 L s .80376 .37673 m .8045 .37689 L s .52726 .59174 m .52736 .59194 L s .01 w .52736 .59194 Mdot .5 Mabswid .66781 .31861 m .66855 .31899 L s 1 0 0 r .0005 w .37077 .53133 m .36451 .53669 L s .37663 .52555 m .37077 .53133 L s 0 0 1 r .5 Mabswid .80303 .37656 m .80376 .37673 L s 1 0 0 r .0005 w .38201 .51941 m .37663 .52555 L s 0 0 1 r .5 Mabswid .37224 .53047 m .3716 .53108 L s .37288 .52985 m .37224 .53047 L s .3716 .53108 m .37095 .53169 L s .37352 .52923 m .37288 .52985 L s .37095 .53169 m .37029 .5323 L s .37415 .5286 m .37352 .52923 L s .66855 .31899 m .66929 .31937 L s .37029 .5323 m .36963 .5329 L s .37477 .52796 m .37415 .5286 L s .36963 .5329 m .36897 .53349 L s .37539 .52733 m .37477 .52796 L s .36897 .53349 m .3683 .53408 L s .376 .52669 m .37539 .52733 L s .3683 .53408 m .36762 .53467 L s .37661 .52604 m .376 .52669 L s .36762 .53467 m .36695 .53525 L s .37721 .52539 m .37661 .52604 L s .36695 .53525 m .36627 .53582 L s .37781 .52473 m .37721 .52539 L s .80229 .37639 m .80303 .37656 L s .66929 .31937 m .67003 .31975 L s .36627 .53582 m .36558 .53639 L s .3784 .52408 m .37781 .52473 L s .52716 .59153 m .52726 .59174 L s .36558 .53639 m .36489 .53696 L s .37898 .52341 m .3784 .52408 L s .36489 .53696 m .3642 .53752 L s .37956 .52275 m .37898 .52341 L s 1 0 0 r .0005 w .36451 .53669 m .35799 .54159 L s 0 0 1 r .5 Mabswid .3642 .53752 m .36351 .53807 L s .67003 .31975 m .67077 .32013 L s 1 0 0 r .0005 w .67041 .31814 m .67723 .32171 L s 0 0 1 r .5 Mabswid .38013 .52208 m .37956 .52275 L s .80154 .37622 m .80229 .37639 L s .36351 .53807 m .36281 .53862 L s .38069 .5214 m .38013 .52208 L s 1 0 0 r .0005 w .3868 .51296 m .38201 .51941 L s .80243 .37547 m .80933 .37697 L s 0 0 1 r .5 Mabswid .36281 .53862 m .36211 .53916 L s .38125 .52072 m .38069 .5214 L s .67077 .32013 m .67152 .32051 L s .36211 .53916 m .3614 .5397 L s .3818 .52004 m .38125 .52072 L s .8008 .37604 m .80154 .37622 L s .3614 .5397 m .3607 .54023 L s .38234 .51936 m .3818 .52004 L s .52706 .59133 m .52716 .59153 L s .67152 .32051 m .67226 .3209 L s .3607 .54023 m .35999 .54076 L s .38287 .51867 m .38234 .51936 L s .80005 .37586 m .8008 .37604 L s .35999 .54076 m .35928 .54128 L s .3834 .51797 m .38287 .51867 L s .67226 .3209 m .67301 .32128 L s .35928 .54128 m .35856 .54179 L s .38392 .51728 m .3834 .51797 L s .7993 .37568 m .80005 .37586 L s .38443 .51658 m .38392 .51728 L s .35856 .54179 m .35784 .5423 L s .67301 .32128 m .67375 .32167 L s .38494 .51588 m .38443 .51658 L s .35784 .5423 m .35713 .5428 L s .52696 .59112 m .52706 .59133 L s .79855 .37549 m .7993 .37568 L s 1 0 0 r .0005 w .35799 .54159 m .35132 .54598 L s 0 0 1 r .5 Mabswid .67375 .32167 m .6745 .32205 L s .38543 .51517 m .38494 .51588 L s .35713 .5428 m .35641 .5433 L s .38592 .51446 m .38543 .51517 L s 1 0 0 r .0005 w .39091 .50627 m .3868 .51296 L s 0 0 1 r .01 w .35641 .5433 Mdot .5 Mabswid .35641 .5433 m .35568 .54379 L s .6745 .32205 m .67525 .32244 L s .7978 .3753 m .79855 .37549 L s .3864 .51375 m .38592 .51446 L s .35568 .54379 m .35496 .54427 L s .67525 .32244 m .676 .32282 L s .38688 .51304 m .3864 .51375 L s .79704 .37511 m .7978 .3753 L s .52685 .59091 m .52696 .59112 L s .35496 .54427 m .35424 .54475 L s .676 .32282 m .67675 .32321 L s .38734 .51232 m .38688 .51304 L s .35424 .54475 m .35351 .54523 L s .79628 .37491 m .79704 .37511 L s .3878 .5116 m .38734 .51232 L s .67675 .32321 m .6775 .3236 L s .35351 .54523 m .35278 .54569 L s .38825 .51088 m .3878 .5116 L s .79552 .37471 m .79628 .37491 L s 1 0 0 r .0005 w .67723 .32171 m .68416 .32534 L s 0 0 1 r .5 Mabswid .6775 .3236 m .67825 .32399 L s .35278 .54569 m .35205 .54615 L s .52675 .5907 m .52685 .59091 L s .38869 .51016 m .38825 .51088 L s .79476 .37451 m .79552 .37471 L s .67825 .32399 m .67901 .32438 L s .35205 .54615 m .35133 .54661 L s .38912 .50943 m .38869 .51016 L s .67901 .32438 m .67976 .32477 L s .35133 .54661 m .3506 .54706 L s .79399 .3743 m .79476 .37451 L s 1 0 0 r .0005 w .79532 .37365 m .80243 .37547 L s 0 0 1 r .5 Mabswid .38954 .5087 m .38912 .50943 L s .67976 .32477 m .68052 .32516 L s .52663 .59049 m .52675 .5907 L s .3506 .54706 m .34987 .5475 L s .79323 .37409 m .79399 .3743 L s 1 0 0 r .0005 w .35132 .54598 m .34462 .54985 L s 0 0 1 r .5 Mabswid .38995 .50797 m .38954 .5087 L s .68052 .32516 m .68128 .32555 L s 1 0 0 r .0005 w .39426 .4994 m .39091 .50627 L s 0 0 1 r .5 Mabswid .34987 .5475 m .34914 .54794 L s .39036 .50723 m .38995 .50797 L s .79246 .37388 m .79323 .37409 L s .68128 .32555 m .68203 .32594 L s .34914 .54794 m .34841 .54837 L s .39075 .5065 m .39036 .50723 L s .79169 .37366 m .79246 .37388 L s .68203 .32594 m .68279 .32633 L s .52652 .59028 m .52663 .59049 L s 1 0 0 r .0005 w .52686 .58595 m .52806 .58795 L s 0 0 1 r .5 Mabswid .34841 .54837 m .34768 .54879 L s .39114 .50576 m .39075 .5065 L s .79091 .37344 m .79169 .37366 L s .68279 .32633 m .68355 .32672 L s .39151 .50502 m .39114 .50576 L s .34768 .54879 m .34694 .54921 L s .68355 .32672 m .68431 .32711 L s .79014 .37322 m .79091 .37344 L s .68431 .32711 m .68508 .3275 L s .39188 .50427 m .39151 .50502 L s .34694 .54921 m .34621 .54962 L s .78936 .373 m .79014 .37322 L s .5264 .59006 m .52652 .59028 L s 1 0 0 r .0005 w .68416 .32534 m .6912 .32901 L s 0 0 1 r .5 Mabswid .68508 .3275 m .68584 .3279 L s .39224 .50353 m .39188 .50427 L s .78858 .37277 m .78936 .373 L s .34621 .54962 m .34549 .55002 L s .68584 .3279 m .6866 .32829 L s .39259 .50279 m .39224 .50353 L s .7878 .37254 m .78858 .37277 L s .34549 .55002 m .34476 .55042 L s .6866 .32829 m .68737 .32868 L s .52628 .58984 m .5264 .59006 L s .78702 .3723 m .7878 .37254 L s .39292 .50204 m .39259 .50279 L s .68737 .32868 m .68814 .32908 L s .34476 .55042 m .34403 .55081 L s .78624 .37206 m .78702 .3723 L s .68814 .32908 m .6889 .32947 L s 1 0 0 r .0005 w .78805 .37155 m .79532 .37365 L s 0 0 1 r .5 Mabswid .39325 .50129 m .39292 .50204 L s .34403 .55081 m .3433 .5512 L s .6889 .32947 m .68967 .32987 L s .78545 .37182 m .78624 .37206 L s .39357 .50054 m .39325 .50129 L s 1 0 0 r .0005 w .39679 .49242 m .39426 .4994 L s 0 0 1 r .5 Mabswid .52616 .58963 m .52628 .58984 L s 1 0 0 r .0005 w .34462 .54985 m .33802 .55316 L s 0 0 1 r .5 Mabswid .68967 .32987 m .69044 .33026 L s .78466 .37158 m .78545 .37182 L s .3433 .5512 m .34257 .55158 L s .69044 .33026 m .69121 .33066 L s .39388 .49979 m .39357 .50054 L s .78387 .37133 m .78466 .37158 L s .69121 .33066 m .69198 .33105 L s .34257 .55158 m .34185 .55195 L s .78308 .37109 m .78387 .37133 L s .39418 .49903 m .39388 .49979 L s .69198 .33105 m .69275 .33145 L s .52603 .58941 m .52616 .58963 L s 1 0 0 r .0005 w .6912 .32901 m .69832 .33269 L s 0 0 1 r .5 Mabswid .78229 .37083 m .78308 .37109 L s .34185 .55195 m .34113 .55231 L s .69275 .33145 m .69353 .33184 L s .39447 .49828 m .39418 .49903 L s .7815 .37058 m .78229 .37083 L s .69353 .33184 m .6943 .33224 L s .34113 .55231 m .3404 .55267 L s .39475 .49753 m .39447 .49828 L s .7807 .37032 m .7815 .37058 L s .6943 .33224 m .69508 .33263 L s .69508 .33263 m .69585 .33303 L s .5259 .58919 m .52603 .58941 L s .77991 .37006 m .7807 .37032 L s .39502 .49677 m .39475 .49753 L s .3404 .55267 m .33968 .55303 L s .01 w .69585 .33303 Mdot .5 Mabswid .69585 .33303 m .69663 .33342 L s .77911 .3698 m .77991 .37006 L s .69663 .33342 m .69741 .33382 L s .77831 .36953 m .77911 .3698 L s .39528 .49601 m .39502 .49677 L s 1 0 0 r .0005 w .78065 .36919 m .78805 .37155 L s 0 0 1 r .5 Mabswid .33968 .55303 m .33896 .55337 L s .69741 .33382 m .69819 .33422 L s .77751 .36926 m .77831 .36953 L s .52577 .58896 m .5259 .58919 L s .69819 .33422 m .69897 .33461 L s .39552 .49526 m .39528 .49601 L s .77671 .36899 m .77751 .36926 L s .33896 .55337 m .33825 .55371 L s .69897 .33461 m .69975 .33501 L s .7759 .36871 m .77671 .36899 L s .69975 .33501 m .70053 .3354 L s .39576 .4945 m .39552 .49526 L s 1 0 0 r .0005 w .69832 .33269 m .70555 .33638 L s 0 0 1 r .5 Mabswid .7751 .36843 m .7759 .36871 L s .70053 .3354 m .70132 .3358 L s .33825 .55371 m .33753 .55404 L s .77429 .36815 m .7751 .36843 L s .70132 .3358 m .7021 .3362 L s .52564 .58874 m .52577 .58896 L s .01 w .39576 .4945 Mdot .5 Mabswid .39599 .49374 m .39576 .4945 L s .77349 .36787 m .77429 .36815 L s .7021 .3362 m .70289 .33659 L s 1 0 0 r .0005 w .39845 .4854 m .39679 .49242 L s 0 0 1 r .5 Mabswid .33753 .55404 m .33682 .55437 L s .70289 .33659 m .70368 .33699 L s .77268 .36759 m .77349 .36787 L s .39621 .49298 m .39599 .49374 L s .70368 .33699 m .70447 .33738 L s .77187 .3673 m .77268 .36759 L s .70447 .33738 m .70526 .33778 L s .77106 .36701 m .77187 .3673 L s .33682 .55437 m .33611 .55469 L s 1 0 0 r .0005 w .33802 .55316 m .33164 .55592 L s 0 0 1 r .5 Mabswid .5255 .58851 m .52564 .58874 L s .39642 .49222 m .39621 .49298 L s .70526 .33778 m .70605 .33817 L s .77025 .36671 m .77106 .36701 L s .70605 .33817 m .70684 .33857 L s 1 0 0 r .0005 w .77315 .36659 m .78065 .36919 L s 0 0 1 r .5 Mabswid .76944 .36642 m .77025 .36671 L s .70684 .33857 m .70763 .33896 L s .33611 .55469 m .3354 .555 L s .39661 .49146 m .39642 .49222 L s .76863 .36612 m .76944 .36642 L s .70763 .33896 m .70843 .33936 L s .76782 .36581 m .76863 .36612 L s .70843 .33936 m .70922 .33975 L s 1 0 0 r .0005 w .70555 .33638 m .71286 .34007 L s 0 0 1 r .5 Mabswid .767 .36551 m .76782 .36581 L s .52536 .58829 m .5255 .58851 L s .70922 .33975 m .71002 .34015 L s .3968 .4907 m .39661 .49146 L s .3354 .555 m .3347 .55531 L s .76619 .3652 m .767 .36551 L s .71002 .34015 m .71081 .34054 L s 1 0 0 r .0005 w .52543 .58384 m .52686 .58595 L s 0 0 1 r .5 Mabswid .76537 .36489 m .76619 .3652 L s .71081 .34054 m .71161 .34093 L s .76456 .36458 m .76537 .36489 L s .71161 .34093 m .71241 .34133 L s .39698 .48994 m .3968 .4907 L s .3347 .55531 m .334 .55561 L s .71241 .34133 m .71321 .34172 L s .76374 .36427 m .76456 .36458 L s .71321 .34172 m .71401 .34211 L s .76293 .36395 m .76374 .36427 L s .52522 .58806 m .52536 .58829 L s .71401 .34211 m .71481 .3425 L s .76211 .36363 m .76293 .36395 L s .39715 .48918 m .39698 .48994 L s .71481 .3425 m .71562 .34289 L s .76129 .36331 m .76211 .36363 L s .334 .55561 m .3333 .5559 L s .71562 .34289 m .71642 .34328 L s .76047 .36299 m .76129 .36331 L s .71642 .34328 m .71722 .34367 L s 1 0 0 r .0005 w .76559 .36377 m .77315 .36659 L s 0 0 1 r .5 Mabswid .75965 .36266 m .76047 .36299 L s .71722 .34367 m .71803 .34406 L s .39731 .48842 m .39715 .48918 L s .75883 .36233 m .75965 .36266 L s .71803 .34406 m .71883 .34445 L s .75802 .362 m .75883 .36233 L s 1 0 0 r .0005 w .71286 .34007 m .72024 .34371 L s 0 0 1 r .5 Mabswid .71883 .34445 m .71964 .34484 L s .7572 .36167 m .75802 .362 L s .3333 .5559 m .3326 .55619 L s .71964 .34484 m .72045 .34523 L s .52507 .58783 m .52522 .58806 L s .75638 .36133 m .7572 .36167 L s .72045 .34523 m .72125 .34562 L s .75556 .36099 m .75638 .36133 L s .39745 .48766 m .39731 .48842 L s .72125 .34562 m .72206 .346 L s .01 w .75556 .36099 Mdot .5 Mabswid .75474 .36066 m .75556 .36099 L s .72206 .346 m .72287 .34639 L s .75392 .36031 m .75474 .36066 L s .72287 .34639 m .72368 .34677 L s .7531 .35997 m .75392 .36031 L s .72368 .34677 m .72449 .34716 L s .75228 .35963 m .7531 .35997 L s .72449 .34716 m .7253 .34754 L s .3326 .55619 m .33191 .55647 L s .75146 .35928 m .75228 .35963 L s .7253 .34754 m .72611 .34792 L s .75064 .35893 m .75146 .35928 L s .39759 .4869 m .39745 .48766 L s .72611 .34792 m .72692 .34831 L s .74981 .35858 m .75064 .35893 L s .72692 .34831 m .72774 .34869 L s .74899 .35823 m .74981 .35858 L s .72774 .34869 m .72855 .34907 L s .74817 .35788 m .74899 .35823 L s .72855 .34907 m .72936 .34945 L s .74735 .35753 m .74817 .35788 L s .72936 .34945 m .73018 .34983 L s .52492 .5876 m .52507 .58783 L s .74653 .35718 m .74735 .35753 L s .73018 .34983 m .73099 .3502 L s .74571 .35682 m .74653 .35718 L s .73099 .3502 m .73181 .35058 L s 1 0 0 r .0005 w .3992 .47842 m .39845 .4854 L s 0 0 1 r .5 Mabswid .74489 .35646 m .74571 .35682 L s .73181 .35058 m .73262 .35096 L s .74407 .3561 m .74489 .35646 L s 1 0 0 r .0005 w .758 .36076 m .76559 .36377 L s 0 0 1 r .5 Mabswid .73262 .35096 m .73344 .35133 L s .74325 .35574 m .74407 .3561 L s .73344 .35133 m .73425 .3517 L s .33191 .55647 m .33122 .55674 L s .74244 .35538 m .74325 .35574 L s .73425 .3517 m .73507 .35208 L s .74162 .35502 m .74244 .35538 L s .73507 .35208 m .73589 .35245 L s .7408 .35466 m .74162 .35502 L s .39772 .48614 m .39759 .4869 L s .73589 .35245 m .73671 .35282 L s .73998 .35429 m .7408 .35466 L s 1 0 0 r .0005 w .72024 .34371 m .72771 .34731 L s 0 0 1 r .5 Mabswid .73671 .35282 m .73752 .35319 L s .73916 .35393 m .73998 .35429 L s .73752 .35319 m .73834 .35356 L s .73834 .35356 m .73916 .35393 L s .39783 .48538 m .39772 .48614 L s .33122 .55674 m .33054 .55701 L s .52477 .58737 m .52492 .5876 L s 1 0 0 r .0005 w .75039 .35759 m .758 .36076 L s .72771 .34731 m .73523 .35084 L s 0 0 1 r .5 Mabswid .39794 .48462 m .39783 .48538 L s .33054 .55701 m .32986 .55727 L s 1 0 0 r .0005 w .33164 .55592 m .32558 .5581 L s 0 0 1 r .5 Mabswid .39804 .48386 m .39794 .48462 L s .52461 .58713 m .52477 .58737 L s 1 0 0 r .0005 w .74279 .35427 m .75039 .35759 L s .73523 .35084 m .74279 .35427 L s 0 0 1 r .5 Mabswid .32986 .55727 m .32918 .55752 L s .39812 .48311 m .39804 .48386 L s .32918 .55752 m .32851 .55777 L s .52446 .5869 m .52461 .58713 L s .3982 .48235 m .39812 .48311 L s .32851 .55777 m .32784 .55801 L s .39826 .48159 m .3982 .48235 L s .52429 .58666 m .52446 .5869 L s .39831 .48084 m .39826 .48159 L s .32784 .55801 m .32717 .55824 L s .39836 .48008 m .39831 .48084 L s .52413 .58642 m .52429 .58666 L s .32717 .55824 m .32651 .55847 L s .39839 .47933 m .39836 .48008 L s 1 0 0 r .0005 w .39903 .47154 m .3992 .47842 L s 0 0 1 r .5 Mabswid .32651 .55847 m .32586 .55869 L s .52396 .58619 m .52413 .58642 L s .39841 .47858 m .39839 .47933 L s .32586 .55869 m .32521 .5589 L s 1 0 0 r .0005 w .52374 .58162 m .52543 .58384 L s 0 0 1 r .5 Mabswid .39842 .47783 m .39841 .47858 L s .52379 .58595 m .52396 .58619 L s .32521 .5589 m .32456 .55911 L s .39842 .47708 m .39842 .47783 L s .39841 .47633 m .39842 .47708 L s .52362 .5857 m .52379 .58595 L s .32456 .55911 m .32392 .55931 L s .39839 .47558 m .39841 .47633 L s 1 0 0 r .0005 w .32558 .5581 m .31998 .55972 L s 0 0 1 r .5 Mabswid .32392 .55931 m .32329 .5595 L s .52344 .58546 m .52362 .5857 L s .39836 .47484 m .39839 .47558 L s .32329 .5595 m .32266 .55968 L s .39832 .4741 m .39836 .47484 L s .52327 .58522 m .52344 .58546 L s .32266 .55968 m .32203 .55986 L s .39826 .47335 m .39832 .4741 L s .3982 .47261 m .39826 .47335 L s .52308 .58497 m .52327 .58522 L s .32203 .55986 m .32141 .56004 L s 1 0 0 r .0005 w .39792 .46483 m .39903 .47154 L s 0 0 1 r .5 Mabswid .39812 .47188 m .3982 .47261 L s .32141 .56004 m .3208 .56021 L s .5229 .58473 m .52308 .58497 L s .39804 .47114 m .39812 .47188 L s .3208 .56021 m .32019 .56037 L s .39794 .47041 m .39804 .47114 L s .52271 .58448 m .5229 .58473 L s .39783 .46968 m .39794 .47041 L s .32019 .56037 m .31959 .56052 L s .52252 .58423 m .52271 .58448 L s .39772 .46895 m .39783 .46968 L s .31959 .56052 m .319 .56067 L s .39759 .46822 m .39772 .46895 L s .52233 .58398 m .52252 .58423 L s .319 .56067 m .31841 .56081 L s .39745 .4675 m .39759 .46822 L s 1 0 0 r .0005 w .5218 .57932 m .52374 .58162 L s 0 0 1 r .5 Mabswid .52213 .58373 m .52233 .58398 L s 1 0 0 r .0005 w .31998 .55972 m .31493 .5608 L s 0 0 1 r .5 Mabswid .31841 .56081 m .31783 .56094 L s .3973 .46678 m .39745 .4675 L s .39713 .46606 m .3973 .46678 L s .31783 .56094 m .31725 .56107 L s .52193 .58348 m .52213 .58373 L s 1 0 0 r .0005 w .3959 .45836 m .39792 .46483 L s 0 0 1 r .5 Mabswid .39696 .46534 m .39713 .46606 L s .31725 .56107 m .31669 .56119 L s .52173 .58322 m .52193 .58348 L s .39678 .46463 m .39696 .46534 L s .31669 .56119 m .31612 .56131 L s .39659 .46392 m .39678 .46463 L s .52152 .58297 m .52173 .58322 L s .39638 .46321 m .39659 .46392 L s .31612 .56131 m .31557 .56141 L s .52131 .58271 m .52152 .58297 L s .39617 .4625 m .39638 .46321 L s .31557 .56141 m .31502 .56152 L s .39594 .4618 m .39617 .4625 L s .5211 .58246 m .52131 .58271 L s .31502 .56152 m .31448 .56161 L s .3957 .4611 m .39594 .4618 L s .52089 .5822 m .5211 .58246 L s .39546 .46041 m .3957 .4611 L s .31448 .56161 m .31395 .5617 L s .3952 .45972 m .39546 .46041 L s .52067 .58194 m .52089 .5822 L s .31395 .5617 m .31342 .56179 L s .39493 .45903 m .3952 .45972 L s 1 0 0 r .0005 w .39298 .45218 m .3959 .45836 L s 0 0 1 r .5 Mabswid .52045 .58168 m .52067 .58194 L s .39465 .45834 m .39493 .45903 L s .31342 .56179 m .31291 .56186 L s 1 0 0 r .0005 w .31493 .5608 m .31052 .56135 L s 0 0 1 r .5 Mabswid .39436 .45766 m .39465 .45834 L s .52022 .58142 m .52045 .58168 L s .31291 .56186 m .3124 .56193 L s 1 0 0 r .0005 w .51959 .57692 m .5218 .57932 L s 0 0 1 r .5 Mabswid .39406 .45699 m .39436 .45766 L s .51999 .58116 m .52022 .58142 L s .3124 .56193 m .31189 .562 L s .39375 .45631 m .39406 .45699 L s .39343 .45564 m .39375 .45631 L s .31189 .562 m .3114 .56206 L s .51976 .5809 m .51999 .58116 L s .39309 .45498 m .39343 .45564 L s .3114 .56206 m .31091 .56211 L s .51953 .58063 m .51976 .5809 L s .39275 .45431 m .39309 .45498 L s .3924 .45366 m .39275 .45431 L s .31091 .56211 m .31044 .56216 L s .51929 .58037 m .51953 .58063 L s .39203 .453 m .3924 .45366 L s 1 0 0 r .0005 w .38919 .44636 m .39298 .45218 L s 0 0 1 r .5 Mabswid .31044 .56216 m .30997 .5622 L s .51905 .5801 m .51929 .58037 L s .39166 .45235 m .39203 .453 L s .39128 .45171 m .39166 .45235 L s .30997 .5622 m .30951 .56223 L s .51881 .57984 m .51905 .5801 L s .39088 .45107 m .39128 .45171 L s .30951 .56223 m .30905 .56226 L s .51857 .57957 m .51881 .57984 L s .39048 .45043 m .39088 .45107 L s .39006 .4498 m .39048 .45043 L s .30905 .56226 m .30861 .56229 L s .51832 .5793 m .51857 .57957 L s 1 0 0 r .0005 w .31052 .56135 m .30684 .56141 L s 0 0 1 r .5 Mabswid .38964 .44917 m .39006 .4498 L s .01 w .30861 .56229 Mdot .5 Mabswid .30861 .56229 m .30818 .5623 L s .51806 .57903 m .51832 .5793 L s .38921 .44855 m .38964 .44917 L s 1 0 0 r .0005 w .51708 .57446 m .51959 .57692 L s 0 0 1 r .5 Mabswid .38876 .44793 m .38921 .44855 L s .30818 .5623 m .30775 .56231 L s .51781 .57876 m .51806 .57903 L s .38831 .44732 m .38876 .44793 L s .30775 .56231 m .30733 .56232 L s 1 0 0 r .0005 w .3846 .44094 m .38919 .44636 L s 0 0 1 r .5 Mabswid .51755 .57849 m .51781 .57876 L s .38784 .44671 m .38831 .44732 L s .38737 .44611 m .38784 .44671 L s .30733 .56232 m .30692 .56232 L s .51729 .57822 m .51755 .57849 L s .38688 .44551 m .38737 .44611 L s .30692 .56232 m .30652 .56232 L s .51702 .57795 m .51729 .57822 L s .38639 .44492 m .38688 .44551 L s .38589 .44433 m .38639 .44492 L s .30652 .56232 m .30613 .56231 L s .51676 .57768 m .51702 .57795 L s .38538 .44375 m .38589 .44433 L s .30613 .56231 m .30574 .56229 L s .38485 .44317 m .38538 .44375 L s .51649 .5774 m .51676 .57768 L s .38432 .4426 m .38485 .44317 L s .30574 .56229 m .30537 .56227 L s .51621 .57713 m .51649 .5774 L s .01 w .38432 .4426 Mdot .5 Mabswid .38378 .44203 m .38432 .4426 L s .38323 .44147 m .38378 .44203 L s 1 0 0 r .0005 w .37925 .43596 m .3846 .44094 L s 0 0 1 r .5 Mabswid .51594 .57685 m .51621 .57713 L s .30537 .56227 m .305 .56225 L s .38268 .44091 m .38323 .44147 L s 1 0 0 r .0005 w .30684 .56141 m .30395 .56102 L s 0 0 1 r .5 Mabswid .51566 .57658 m .51594 .57685 L s .305 .56225 m .30465 .56222 L s .38211 .44036 m .38268 .44091 L s 1 0 0 r .0005 w .51427 .57193 m .51708 .57446 L s 0 0 1 r .5 Mabswid .38154 .43981 m .38211 .44036 L s .51537 .5763 m .51566 .57658 L s .30465 .56222 m .3043 .56218 L s .38096 .43927 m .38154 .43981 L s .38037 .43873 m .38096 .43927 L s .51509 .57602 m .51537 .5763 L s .3043 .56218 m .30396 .56214 L s .37978 .4382 m .38037 .43873 L s .5148 .57575 m .51509 .57602 L s .37917 .43767 m .37978 .4382 L s .30396 .56214 m .30363 .5621 L s .37856 .43715 m .37917 .43767 L s .5145 .57547 m .5148 .57575 L s .30363 .5621 m .30331 .56205 L s .37794 .43663 m .37856 .43715 L s 1 0 0 r .0005 w .37323 .43146 m .37925 .43596 L s 0 0 1 r .5 Mabswid .37732 .43612 m .37794 .43663 L s .51421 .57519 m .5145 .57547 L s .30331 .56205 m .303 .56199 L s .37668 .43562 m .37732 .43612 L s .51391 .57491 m .51421 .57519 L s .37604 .43512 m .37668 .43562 L s .303 .56199 m .3027 .56193 L s .37539 .43462 m .37604 .43512 L s .51361 .57463 m .51391 .57491 L s .37474 .43413 m .37539 .43462 L s .3027 .56193 m .30241 .56187 L s .37408 .43365 m .37474 .43413 L s .5133 .57435 m .51361 .57463 L s .37341 .43317 m .37408 .43365 L s .30241 .56187 m .30213 .5618 L s .37273 .4327 m .37341 .43317 L s .51299 .57407 m .5133 .57435 L s .37205 .43223 m .37273 .4327 L s .30213 .5618 m .30186 .56172 L s 1 0 0 r .0005 w .51115 .56934 m .51427 .57193 L s .30395 .56102 m .30192 .56021 L s 0 0 1 r .5 Mabswid .51268 .57378 m .51299 .57407 L s 1 0 0 r .0005 w .36659 .42746 m .37323 .43146 L s 0 0 1 r .5 Mabswid .37136 .43177 m .37205 .43223 L s .37066 .43131 m .37136 .43177 L s .30186 .56172 m .3016 .56164 L s .51236 .5735 m .51268 .57378 L s .36995 .43086 m .37066 .43131 L s .36924 .43042 m .36995 .43086 L s .3016 .56164 m .30135 .56156 L s .01 w .51236 .5735 Mdot .5 Mabswid .51205 .57322 m .51236 .5735 L s .36853 .42998 m .36924 .43042 L s .3678 .42955 m .36853 .42998 L s .51172 .57294 m .51205 .57322 L s .30135 .56156 m .3011 .56147 L s .36707 .42912 m .3678 .42955 L s .36634 .4287 m .36707 .42912 L s .5114 .57265 m .51172 .57294 L s .3011 .56147 m .30087 .56138 L s .3656 .42829 m .36634 .4287 L s .36485 .42788 m .3656 .42829 L s 1 0 0 r .0005 w .35944 .424 m .36659 .42746 L s 0 0 1 r .5 Mabswid .51106 .57237 m .5114 .57265 L s .30087 .56138 m .30065 .56128 L s .36409 .42748 m .36485 .42788 L s .36333 .42708 m .36409 .42748 L s .51073 .57208 m .51106 .57237 L s .36257 .42669 m .36333 .42708 L s .30065 .56128 m .30044 .56118 L s .3618 .42631 m .36257 .42669 L s .51039 .57179 m .51073 .57208 L s .36102 .42593 m .3618 .42631 L s .30044 .56118 m .30024 .56108 L s .36024 .42556 m .36102 .42593 L s .51004 .57151 m .51039 .57179 L s .35945 .4252 m .36024 .42556 L s .01 w .26254 .42275 Mdot .5 Mabswid .26254 .42275 m .26332 .42248 L s 1 0 0 r .0005 w .26254 .42275 m .26984 .42038 L s 0 0 1 r .5 Mabswid .35866 .42484 m .35945 .4252 L s .30024 .56108 m .30005 .56097 L s .26332 .42248 m .26409 .42221 L s .50969 .57122 m .51004 .57151 L s 1 0 0 r .0005 w .50769 .56673 m .51115 .56934 L s 0 0 1 r .5 Mabswid .35786 .42449 m .35866 .42484 L s .26409 .42221 m .26487 .42195 L s 1 0 0 r .0005 w .35184 .42108 m .35944 .424 L s 0 0 1 r .5 Mabswid .35706 .42414 m .35786 .42449 L s .26487 .42195 m .26566 .42169 L s .30005 .56097 m .29987 .56085 L s .35625 .4238 m .35706 .42414 L s .50934 .57093 m .50969 .57122 L s .26566 .42169 m .26645 .42143 L s 1 0 0 r .0005 w .30192 .56021 m .30079 .55905 L s 0 0 1 r .5 Mabswid .35543 .42347 m .35625 .4238 L s .26645 .42143 m .26725 .42118 L s .35462 .42314 m .35543 .42347 L s .26725 .42118 m .26804 .42094 L s .29987 .56085 m .29969 .56073 L s .50898 .57065 m .50934 .57093 L s .35379 .42282 m .35462 .42314 L s .26804 .42094 m .26885 .4207 L s .35297 .42251 m .35379 .42282 L s .26885 .4207 m .26966 .42046 L s .50862 .57036 m .50898 .57065 L s .35213 .42221 m .35297 .42251 L s .26966 .42046 m .27047 .42023 L s .29969 .56073 m .29953 .56061 L s 1 0 0 r .0005 w .26984 .42038 m .27746 .41838 L s 0 0 1 r .5 Mabswid .3513 .42191 m .35213 .42221 L s .27047 .42023 m .27128 .42001 L s .35046 .42161 m .3513 .42191 L s .27128 .42001 m .2721 .41979 L s .50825 .57007 m .50862 .57036 L s .34961 .42132 m .35046 .42161 L s .2721 .41979 m .27293 .41957 L s 1 0 0 r .0005 w .34389 .4187 m .35184 .42108 L s 0 0 1 r .5 Mabswid .29953 .56061 m .29939 .56049 L s .34876 .42104 m .34961 .42132 L s .27293 .41957 m .27375 .41936 L s .27375 .41936 m .27458 .41915 L s .34791 .42077 m .34876 .42104 L s .50788 .56978 m .50825 .57007 L s .27458 .41915 m .27542 .41895 L s .34706 .4205 m .34791 .42077 L s .29939 .56049 m .29925 .56035 L s .27542 .41895 m .27626 .41875 L s .3462 .42024 m .34706 .4205 L s .27626 .41875 m .2771 .41856 L s .34533 .41999 m .3462 .42024 L s .50751 .56949 m .50788 .56978 L s .2771 .41856 m .27794 .41838 L s .34446 .41974 m .34533 .41999 L s 1 0 0 r .0005 w .27746 .41838 m .28537 .41678 L s 0 0 1 r .5 Mabswid .27794 .41838 m .27879 .41819 L s .29925 .56035 m .29912 .56022 L s .34359 .4195 m .34446 .41974 L s .27879 .41819 m .27964 .41802 L s .34272 .41927 m .34359 .4195 L s .50713 .5692 m .50751 .56949 L s .27964 .41802 m .2805 .41785 L s .34184 .41904 m .34272 .41927 L s .2805 .41785 m .28136 .41768 L s 1 0 0 r .0005 w .33568 .41687 m .34389 .4187 L s 0 0 1 r .5 Mabswid .34096 .41882 m .34184 .41904 L s .28136 .41768 m .28222 .41752 L s .29912 .56022 m .299 .56008 L s .34008 .41861 m .34096 .41882 L s .28222 .41752 m .28308 .41736 L s .50674 .56891 m .50713 .5692 L s .33919 .4184 m .34008 .41861 L s .28308 .41736 m .28395 .41721 L s .3383 .4182 m .33919 .4184 L s .28395 .41721 m .28482 .41707 L s .33741 .41801 m .3383 .4182 L s .28482 .41707 m .28569 .41692 L s .33652 .41782 m .33741 .41801 L s .299 .56008 m .29889 .55994 L s .28569 .41692 m .28657 .41679 L s .50635 .56862 m .50674 .56891 L s .33562 .41764 m .33652 .41782 L s 1 0 0 r .0005 w .28537 .41678 m .29351 .41559 L s 0 0 1 r .5 Mabswid .28657 .41679 m .28745 .41666 L s .33472 .41747 m .33562 .41764 L s 1 0 0 r .0005 w .50389 .56409 m .50769 .56673 L s 0 0 1 r .5 Mabswid .28745 .41666 m .28833 .41653 L s .33382 .41731 m .33472 .41747 L s .28833 .41653 m .28921 .41641 L s .33292 .41715 m .33382 .41731 L s .28921 .41641 m .2901 .4163 L s 1 0 0 r .0005 w .32728 .41559 m .33568 .41687 L s 0 0 1 r .5 Mabswid .33201 .41699 m .33292 .41715 L s .2901 .4163 m .29098 .41619 L s .50596 .56833 m .50635 .56862 L s .29889 .55994 m .2988 .5598 L s .33111 .41685 m .33201 .41699 L s .29098 .41619 m .29187 .41609 L s .3302 .41671 m .33111 .41685 L s .29187 .41609 m .29277 .41599 L s .32929 .41658 m .3302 .41671 L s .29277 .41599 m .29366 .4159 L s .32838 .41645 m .32929 .41658 L s .29366 .4159 m .29456 .41581 L s .32747 .41633 m .32838 .41645 L s .29456 .41581 m .29546 .41573 L s .01 w .32747 .41633 Mdot .5 Mabswid .32655 .41622 m .32747 .41633 L s .29546 .41573 m .29636 .41565 L s .50556 .56803 m .50596 .56833 L s 1 0 0 r .0005 w .29351 .41559 m .30184 .41486 L s 0 0 1 r .5 Mabswid .32564 .41612 m .32655 .41622 L s .29636 .41565 m .29726 .41558 L s .2988 .5598 m .29871 .55965 L s .32472 .41601 m .32564 .41612 L s .29726 .41558 m .29816 .41551 L s .3238 .41592 m .32472 .41601 L s .29816 .41551 m .29907 .41545 L s .32289 .41583 m .3238 .41592 L s .29907 .41545 m .29997 .4154 L s .32197 .41574 m .32289 .41583 L s .29997 .4154 m .30088 .41535 L s 1 0 0 r .0005 w .3188 .41484 m .32728 .41559 L s 0 0 1 r .5 Mabswid .32105 .41567 m .32197 .41574 L s .30088 .41535 m .30179 .41531 L s .32013 .41559 m .32105 .41567 L s .30179 .41531 m .3027 .41527 L s .31921 .41553 m .32013 .41559 L s .3027 .41527 m .30361 .41523 L s .31829 .41546 m .31921 .41553 L s .30361 .41523 m .30452 .41521 L s 1 0 0 r .0005 w .30079 .55905 m .30058 .55757 L s 0 0 1 r .5 Mabswid .31737 .41541 m .31829 .41546 L s .30452 .41521 m .30544 .41518 L s .50516 .56774 m .50556 .56803 L s .31646 .41536 m .31737 .41541 L s .30544 .41518 m .30635 .41517 L s .31554 .41531 m .31646 .41536 L s .30635 .41517 m .30727 .41516 L s .31462 .41527 m .31554 .41531 L s .30727 .41516 m .30819 .41515 L s .3137 .41524 m .31462 .41527 L s .30819 .41515 m .3091 .41515 L s .31278 .41521 m .3137 .41524 L s .3091 .41515 m .31002 .41516 L s .31186 .41519 m .31278 .41521 L s .31002 .41516 m .31094 .41517 L s .31094 .41517 m .31186 .41519 L s 1 0 0 r .0005 w .30184 .41486 m .31029 .4146 L s 0 0 1 r .5 Mabswid .29871 .55965 m .29864 .55949 L s 1 0 0 r .0005 w .31029 .4146 m .3188 .41484 L s 0 0 1 r .5 Mabswid .50476 .56745 m .50516 .56774 L s .29864 .55949 m .29857 .55934 L s .50435 .56716 m .50476 .56745 L s .29857 .55934 m .29852 .55918 L s .50393 .56687 m .50435 .56716 L s .29852 .55918 m .29848 .55901 L s .50351 .56657 m .50393 .56687 L s .50309 .56628 m .50351 .56657 L s .29848 .55901 m .29845 .55885 L s .50266 .56599 m .50309 .56628 L s .29845 .55885 m .29843 .55868 L s 1 0 0 r .0005 w .49974 .56144 m .50389 .56409 L s 0 0 1 r .5 Mabswid .50223 .5657 m .50266 .56599 L s .29843 .55868 m .29842 .55851 L s .50179 .5654 m .50223 .5657 L s .29842 .55851 m .29842 .55833 L s .50135 .56511 m .50179 .5654 L s .29842 .55833 m .29843 .55815 L s .50091 .56482 m .50135 .56511 L s 1 0 0 r .0005 w .30058 .55757 m .3013 .55585 L s 0 0 1 r .5 Mabswid .50046 .56452 m .50091 .56482 L s .29843 .55815 m .29846 .55797 L s .50001 .56423 m .50046 .56452 L s .29846 .55797 m .29849 .55778 L s .49955 .56394 m .50001 .56423 L s .29849 .55778 m .29854 .5576 L s .49909 .56365 m .49955 .56394 L s .29854 .5576 m .29859 .55741 L s .49862 .56335 m .49909 .56365 L s .29859 .55741 m .29866 .55721 L s 1 0 0 r .0005 w .49523 .55881 m .49974 .56144 L s 0 0 1 r .5 Mabswid .49815 .56306 m .49862 .56335 L s .49768 .56277 m .49815 .56306 L s .29866 .55721 m .29874 .55702 L s .4972 .56247 m .49768 .56277 L s .29874 .55702 m .29883 .55682 L s .49672 .56218 m .4972 .56247 L s .29883 .55682 m .29894 .55662 L s .49623 .56189 m .49672 .56218 L s .29894 .55662 m .29905 .55642 L s .49574 .5616 m .49623 .56189 L s .29905 .55642 m .29917 .55621 L s .49525 .5613 m .49574 .5616 L s 1 0 0 r .0005 w .3013 .55585 m .30295 .55393 L s 0 0 1 r .5 Mabswid .49475 .56101 m .49525 .5613 L s .29917 .55621 m .29931 .556 L s .49424 .56072 m .49475 .56101 L s .29931 .556 m .29946 .55579 L s .49374 .56043 m .49424 .56072 L s 1 0 0 r .0005 w .49035 .55621 m .49523 .55881 L s 0 0 1 r .5 Mabswid .29946 .55579 m .29961 .55558 L s .49322 .56014 m .49374 .56043 L s .29961 .55558 m .29978 .55537 L s .49271 .55985 m .49322 .56014 L s .29978 .55537 m .29996 .55515 L s .49219 .55956 m .49271 .55985 L s .49166 .55927 m .49219 .55956 L s .29996 .55515 m .30015 .55494 L s .49114 .55898 m .49166 .55927 L s .30015 .55494 m .30036 .55472 L s .4906 .55869 m .49114 .55898 L s .30036 .55472 m .30057 .5545 L s .49007 .5584 m .4906 .55869 L s .30057 .5545 m .3008 .55428 L s .48953 .55811 m .49007 .5584 L s 1 0 0 r .0005 w .30295 .55393 m .30552 .55187 L s 0 0 1 r .5 Mabswid .3008 .55428 m .30103 .55405 L s .48898 .55782 m .48953 .55811 L s 1 0 0 r .0005 w .48509 .55365 m .49035 .55621 L s 0 0 1 r .5 Mabswid .48843 .55754 m .48898 .55782 L s .30103 .55405 m .30128 .55383 L s .48788 .55725 m .48843 .55754 L s .30128 .55383 m .30154 .5536 L s .48733 .55696 m .48788 .55725 L s .30154 .5536 m .30181 .55337 L s .48677 .55668 m .48733 .55696 L s .30181 .55337 m .30209 .55315 L s .4862 .55639 m .48677 .55668 L s .48563 .55611 m .4862 .55639 L s .30209 .55315 m .30238 .55292 L s .48506 .55582 m .48563 .55611 L s .30238 .55292 m .30268 .55269 L s .48448 .55554 m .48506 .55582 L s .30268 .55269 m .303 .55245 L s .4839 .55526 m .48448 .55554 L s 1 0 0 r .0005 w .47946 .55117 m .48509 .55365 L s 0 0 1 r .5 Mabswid .303 .55245 m .30332 .55222 L s .48332 .55498 m .4839 .55526 L s 1 0 0 r .0005 w .30552 .55187 m .30897 .54974 L s 0 0 1 r .01 w .30332 .55222 Mdot .5 Mabswid .30332 .55222 m .30365 .55199 L s .48273 .55469 m .48332 .55498 L s .48214 .55441 m .48273 .55469 L s .30365 .55199 m .304 .55176 L s .48154 .55413 m .48214 .55441 L s .304 .55176 m .30435 .55152 L s .48094 .55385 m .48154 .55413 L s .30435 .55152 m .30472 .55129 L s .48034 .55358 m .48094 .55385 L s .30472 .55129 m .30509 .55105 L s .47973 .5533 m .48034 .55358 L s .30509 .55105 m .30547 .55082 L s .47912 .55302 m .47973 .5533 L s .4785 .55274 m .47912 .55302 L s .30547 .55082 m .30586 .55058 L s 1 0 0 r .0005 w .47345 .54878 m .47946 .55117 L s 0 0 1 r .5 Mabswid .47788 .55247 m .4785 .55274 L s .30586 .55058 m .30627 .55035 L s .47726 .5522 m .47788 .55247 L s .30627 .55035 m .30668 .55011 L s .01 w .47726 .5522 Mdot .5 Mabswid .47663 .55192 m .47726 .5522 L s 1 0 0 r .0005 w .30897 .54974 m .31325 .54758 L s 0 0 1 r .5 Mabswid .30668 .55011 m .3071 .54987 L s .476 .55165 m .47663 .55192 L s .3071 .54987 m .30753 .54964 L s .47536 .55138 m .476 .55165 L s .47472 .55111 m .47536 .55138 L s .30753 .54964 m .30796 .5494 L s .47407 .55084 m .47472 .55111 L s .30796 .5494 m .30841 .54916 L s .47342 .55058 m .47407 .55084 L s .30841 .54916 m .30887 .54893 L s .47276 .55031 m .47342 .55058 L s .30887 .54893 m .30933 .54869 L s 1 0 0 r .0005 w .46707 .54649 m .47345 .54878 L s 0 0 1 r .5 Mabswid .4721 .55005 m .47276 .55031 L s .30933 .54869 m .30981 .54846 L s .47143 .54979 m .4721 .55005 L s .47076 .54953 m .47143 .54979 L s .30981 .54846 m .31029 .54822 L s .47008 .54927 m .47076 .54953 L s .31029 .54822 m .31079 .54799 L s .4694 .54901 m .47008 .54927 L s .31079 .54799 m .31129 .54775 L s 1 0 0 r .0005 w .31325 .54758 m .31833 .54546 L s 0 0 1 r .5 Mabswid .46872 .54875 m .4694 .54901 L s .31129 .54775 m .3118 .54752 L s .46802 .5485 m .46872 .54875 L s .3118 .54752 m .31232 .54728 L s .46733 .54825 m .46802 .5485 L s .31232 .54728 m .31285 .54705 L s .46663 .548 m .46733 .54825 L s .46592 .54775 m .46663 .548 L s 1 0 0 r .0005 w .46033 .54434 m .46707 .54649 L s 0 0 1 r .5 Mabswid .31285 .54705 m .31339 .54682 L s .46521 .5475 m .46592 .54775 L s .31339 .54682 m .31393 .54659 L s .4645 .54725 m .46521 .5475 L s .31393 .54659 m .31449 .54636 L s .46378 .54701 m .4645 .54725 L s .31449 .54636 m .31505 .54613 L s .46306 .54677 m .46378 .54701 L s .31505 .54613 m .31562 .5459 L s .46233 .54653 m .46306 .54677 L s .4616 .54629 m .46233 .54653 L s .31562 .5459 m .3162 .54567 L s 1 0 0 r .0005 w .31833 .54546 m .32412 .54342 L s 0 0 1 r .5 Mabswid .46086 .54605 m .4616 .54629 L s .3162 .54567 m .31679 .54544 L s .46012 .54581 m .46086 .54605 L s .31679 .54544 m .31738 .54522 L s .45937 .54558 m .46012 .54581 L s 1 0 0 r .0005 w .45323 .54235 m .46033 .54434 L s 0 0 1 r .5 Mabswid .31738 .54522 m .31799 .54499 L s .45862 .54535 m .45937 .54558 L s .31799 .54499 m .3186 .54477 L s .45787 .54512 m .45862 .54535 L s .45711 .54489 m .45787 .54512 L s .3186 .54477 m .31922 .54454 L s .45635 .54467 m .45711 .54489 L s .31922 .54454 m .31985 .54432 L s .45559 .54444 m .45635 .54467 L s .31985 .54432 m .32049 .5441 L s .45482 .54422 m .45559 .54444 L s .32049 .5441 m .32113 .54388 L s .45404 .544 m .45482 .54422 L s .32113 .54388 m .32178 .54367 L s .45326 .54378 m .45404 .544 L s 1 0 0 r .0005 w .32412 .54342 m .33056 .54151 L s 0 0 1 r .5 Mabswid .45248 .54356 m .45326 .54378 L s .32178 .54367 m .32244 .54345 L s 1 0 0 r .0005 w .4458 .54054 m .45323 .54235 L s 0 0 1 r .5 Mabswid .4517 .54335 m .45248 .54356 L s .32244 .54345 m .32311 .54324 L s .45091 .54314 m .4517 .54335 L s .32311 .54324 m .32379 .54302 L s .45011 .54293 m .45091 .54314 L s .32379 .54302 m .32447 .54281 L s .44931 .54272 m .45011 .54293 L s .32447 .54281 m .32516 .5426 L s .44851 .54251 m .44931 .54272 L s .32516 .5426 m .32585 .5424 L s .44771 .54231 m .44851 .54251 L s .4469 .54211 m .44771 .54231 L s .32585 .5424 m .32656 .54219 L s .44609 .54191 m .4469 .54211 L s .32656 .54219 m .32727 .54199 L s .44527 .54171 m .44609 .54191 L s .32727 .54199 m .32799 .54179 L s 1 0 0 r .0005 w .43806 .53892 m .4458 .54054 L s 0 0 1 r .5 Mabswid .44445 .54152 m .44527 .54171 L s 1 0 0 r .0005 w .33056 .54151 m .33758 .53977 L s 0 0 1 r .5 Mabswid .32799 .54179 m .32871 .54159 L s .44363 .54132 m .44445 .54152 L s .32871 .54159 m .32945 .54139 L s .4428 .54113 m .44363 .54132 L s .44197 .54095 m .4428 .54113 L s .32945 .54139 m .33019 .54119 L s .44114 .54076 m .44197 .54095 L s .33019 .54119 m .33093 .541 L s .4403 .54058 m .44114 .54076 L s .33093 .541 m .33168 .54081 L s .43946 .54039 m .4403 .54058 L s .33168 .54081 m .33244 .54062 L s .43862 .54021 m .43946 .54039 L s .33244 .54062 m .33321 .54044 L s .43778 .54004 m .43862 .54021 L s .33321 .54044 m .33398 .54025 L s 1 0 0 r .0005 w .43005 .53752 m .43806 .53892 L s 0 0 1 r .5 Mabswid .43693 .53986 m .43778 .54004 L s .33398 .54025 m .33476 .54007 L s .43607 .53969 m .43693 .53986 L s 1 0 0 r .0005 w .33758 .53977 m .34509 .53823 L s 0 0 1 r .5 Mabswid .43522 .53952 m .43607 .53969 L s .33476 .54007 m .33554 .53989 L s .43436 .53935 m .43522 .53952 L s .33554 .53989 m .33633 .53972 L s .4335 .53919 m .43436 .53935 L s .33633 .53972 m .33713 .53954 L s .43263 .53903 m .4335 .53919 L s .33713 .53954 m .33793 .53937 L s .43177 .53887 m .43263 .53903 L s .33793 .53937 m .33873 .5392 L s .4309 .53871 m .43177 .53887 L s .33873 .5392 m .33955 .53904 L s .43003 .53855 m .4309 .53871 L s .33955 .53904 m .34036 .53888 L s .42915 .5384 m .43003 .53855 L s 1 0 0 r .0005 w .42178 .53636 m .43005 .53752 L s 0 0 1 r .5 Mabswid .34036 .53888 m .34119 .53872 L s .42827 .53825 m .42915 .5384 L s .42739 .5381 m .42827 .53825 L s .34119 .53872 m .34202 .53856 L s 1 0 0 r .0005 w .34509 .53823 m .35301 .53692 L s 0 0 1 r .5 Mabswid .42651 .53796 m .42739 .5381 L s .34202 .53856 m .34285 .53841 L s .42562 .53781 m .42651 .53796 L s .34285 .53841 m .34369 .53826 L s .42473 .53767 m .42562 .53781 L s .34369 .53826 m .34454 .53811 L s .42384 .53754 m .42473 .53767 L s .34454 .53811 m .34538 .53796 L s .42295 .5374 m .42384 .53754 L s .34538 .53796 m .34624 .53782 L s .42205 .53727 m .42295 .5374 L s .34624 .53782 m .3471 .53769 L s 1 0 0 r .0005 w .41331 .53545 m .42178 .53636 L s 0 0 1 r .5 Mabswid .42115 .53714 m .42205 .53727 L s .3471 .53769 m .34796 .53755 L s .42025 .53701 m .42115 .53714 L s .34796 .53755 m .34883 .53742 L s .41935 .53689 m .42025 .53701 L s .34883 .53742 m .3497 .53729 L s .01 w .41935 .53689 Mdot .5 Mabswid .41845 .53677 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Cell[BoxData[ \(TraditionalForm\`\[Kappa]\_c\)]], " ", "= 2", StyleBox["\[Pi] if and only if c is \tan ovaloid contained in a plane.", FontSlant->"Italic"], "\n\nWe do not go further into this theorem here, but since the proof is \ based on the Gauss map of space curves, so we introduce here some ", StyleBox["dg-", FontFamily->"Courier New", FontWeight->"Bold"], "commands related to the Gauss map.\n\n ", StyleBox["The Gauss map \[Gamma] of a space curve", PageWidth->PaperWidth, FontFamily->"Times New Roman"], " ", StyleBox["c", FontSlant->"Italic"], ": ", StyleBox["I ", FontSlant->"Italic"], "\[LongRightArrow] ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^3\)]], StyleBox[" is a mapping to the unit sphere ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], Cell[BoxData[ \(TraditionalForm\`S\^\(\(\ \)\(2\)\) \[Subset] \[DoubleStruckCapitalR]\ \^3\)]], StyleBox["defined by\n ", PageWidth->PaperWidth, FontFamily->"Times New Roman"], "\n ", StyleBox["\[Gamma] ", FontSlant->"Italic"], ": ", StyleBox["I ", FontSlant->"Italic"], "\[LongRightArrow] ", Cell[BoxData[ \(TraditionalForm\`S\^\(\(\ \)\(2\)\) \[Subset] \[DoubleStruckCapitalR]\ \^3\)]], "; ", StyleBox["\[Gamma]", FontSlant->"Italic"], "(", StyleBox["t", FontSlant->"Italic"], ")=", Cell[BoxData[ \(TraditionalForm\`e\_1\)]], "(", StyleBox["t", FontSlant->"Italic"], ") ", StyleBox["t\[Element] I,\n \n", FontSlant->"Italic"], "where the starting point of the unit vector ", StyleBox["\[Gamma]", FontSlant->"Italic"], "(", StyleBox["t", FontSlant->"Italic"], ") is set to the origin O of ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^3\)]], ". Therefore, the image of the Gauss map of a space curve is a curve \ contained in the unit sphere. If we draw a surface by the usual ", StyleBox["ParametricPlot3D", FontFamily->"Courier New", FontWeight->"Bold"], ", then curves on the surface cannot be expressed rightly. So we use here \ ", StyleBox["dgWireFrame", FontFamily->"Courier New", FontWeight->"Bold"], " to draw a colorful wireframe of a surface with a kind of hidden curves \ expression, to make a curve on the surface clearer." }], "Text"], Cell[CellGroupData[{ Cell[TextData[StyleBox["?dgWireFrame", AspectRatioFixed->True]], "Input", CellLabel->"In[14]:="], Cell[BoxData[ \("dgWireFrame[f[u,v],{u,u0,u1},{v,v0,v1},{m1,m2},{n1,n2},viewpnt,opts] \ returns a wireframe graphics of the surface f[u,v], u0<=u<=u1, v0<=v<=v1, \ with (n1+1) u-curves and (m1+1) v-curves. (m1*m2+1) is the plotpoints of \ each u-curve, and (n1*n2+1) is of each v-curve. The wireframe is shown with \ RGBColor similar to that of surfaces plotted by ParametricPlot3d. viewpnt \ shoul be the viewpoint from which the wiewframe is observed, by default \ {1.3,-2.4,2}. opts are options for Show"\)], "Print", CellTags->"Info3352742147-4748773"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["graph11=dgWireFrame[\n", AspectRatioFixed->True], "{Cos[u]*(Cos[v]+2),Sin[u]*(Cos[v]+2),Sin[v]}", StyleBox[",\n{u,0,2Pi},{v,", AspectRatioFixed->True], "0,2Pi", StyleBox["},{24,8},{10,4},", AspectRatioFixed->True], "{1.3,-2.4,2.},Boxed->False", StyleBox["]", AspectRatioFixed->True] }], "Input", CellLabel->"In[15]:="], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .7782 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 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r .66531 .44476 m .67 .44754 L s .77 .397 .985 r .23218 .39232 m .24238 .40794 L s .23218 .39232 m .23725 .38654 L s .805 .507 .915 r .26878 .43565 m .28419 .4471 L s .805 .533 .87 r .28419 .4471 m .28852 .44248 L s .68 .383 .255 r .70473 .20921 m .71387 .21321 L s .635 .223 .77 r .27657 .2552 m .27203 .26743 L s .815 .543 .255 r .79991 .29632 m .80692 .30213 L s .51 .193 .41 r .45105 .17878 m .44708 .17843 L s .73 .573 .7 r .3687 .44127 m .38244 .44568 L s .68 .57 .63 r .38244 .44568 m .38728 .443 L s .92 .663 .485 r .81019 .38459 m .81551 .39034 L s .85 .613 .72 r .75919 .44095 m .76371 .44547 L s .79 .437 .97 r .24238 .40794 m .2547 .42248 L s .625 .463 .83 r .66044 .44211 m .66531 .44476 L s .8 .473 .95 r .2547 .42248 m .26878 .43565 L s .825 .54 .265 r .79009 .27651 m .79256 .29065 L s .53 .443 .75 r .57902 .4212 m .57392 .42257 L s .585 .2 .605 r .34143 .21051 m .35076 .20663 L s .68 .57 .63 r .38728 .443 m .3922 .44037 L s .68 .383 .255 r .70473 .20921 m .71127 .21585 L s .685 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s .835 .437 .955 r .27543 .35402 m .28295 .34906 L s .83 .55 .86 r .33335 .40893 m .34015 .40522 L s .965 .653 .545 r .76363 .34744 m .77136 .35231 L s .73 .287 .795 r .30473 .26133 m .31424 .25678 L s .865 .52 .36 r .71997 .23689 m .72185 .25094 L s .825 .407 .945 r .27634 .33132 m .28295 .34906 L s .85 .5 .925 r .30206 .38333 m .31382 .39886 L s .815 .583 .775 r .66635 .4042 m .65549 .41557 L s .765 .397 .38 r .6276 .19021 m .63043 .19888 L s .865 .61 .74 r .70685 .40398 m .71372 .40762 L s .86 .52 .35 r .73167 .25523 m .74137 .2598 L s .845 .443 .95 r .28295 .34906 m .29169 .36661 L s .28295 .34906 m .29094 .34421 L s .85 .473 .945 r .29169 .36661 m .30206 .38333 L s .83 .55 .855 r .34015 .40522 m .3471 .40163 L s .715 .3 .57 r .44057 .1868 m .43817 .19536 L s .74 .293 .785 r .31424 .25678 m .3241 .25238 L s .865 .61 .745 r .69977 .40047 m .70685 .40398 L s .75 .553 .785 r .59651 .39945 m .59043 .40954 L s .965 .653 .55 r .75562 .34262 m .76363 .34744 L s .81 .567 .81 r .39541 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