(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 48447, 905] NotebookOptionsPosition[ 31978, 610] NotebookOutlinePosition[ 48532, 907] CellTagsIndexPosition[ 48489, 904] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`high$$ = False, $CellContext`lineType$$ = "D\:4e0a\:306e\:76f4\:7dda", $CellContext`n$$ = 3, $CellContext`pt1$$ = { 0, 0.2}, $CellContext`pt2$$ = {1, 0.1}, $CellContext`pt3$$ = { 0, 0.5}, $CellContext`pt4$$ = 0, $CellContext`pt5$$ = 0, $CellContext`radius$$ = 0.5, $CellContext`type$$ = "\:5186\:9310\:306e\:307f", Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[ Style["\:6bcd\:7dda\:306e\:9577\:3055(\:534a\:5f84\:306f 1 )", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`n$$], 3, "n"}, 2, 12, 1}, { Hold[ Style["\:5b9f\:969b\:306e\:6bd4\:7387\:3067 \:898b\:308b ", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`high$$], False, "Yes"}, {True, False}}, { Hold[ Style["\:8868\:793a\:56f3\:5f62", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`type$$], "\:5186\:9310\:306e\:307f", ""}, { "\:5186\:9310\:306e\:307f", "\:76f4\:7dda,\:6700\:77ed\:8ddd\:96e2\:7dda", "\:5186"}}, { Hold[ Style[ "\:5c55\:958b\:56f3D\:4e0a\:306e\:76f4\:7dda\:3068\:70b9P / \:6700\ \:77ed\:8ddd\:96e2\:7dda", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`lineType$$], "D\:4e0a\:306e\:76f4\:7dda", "type"}, { "D\:4e0a\:306e\:76f4\:7dda", "\:6700\:77ed\:8ddd\:96e2\:7dda", "\:4e21\:65b9"}}, {{ Hold[$CellContext`pt1$$], {0, 0.2}, "\:70b9A"}, {0.1, 0}, { 2 Pi, 0.99999}}, {{ Hold[$CellContext`pt2$$], {1, 0.1}, "\:70b9B"}, {0.1, 0}, { 2 Pi, 0.99999}}, {{ Hold[$CellContext`pt4$$], 0, "\:70b9P"}, 0, 1}, { Hold[ Style["\:5186\:3068\:5186\:4e0a\:306e\:70b9Q", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`pt3$$], {0, 0.5}, "\:4e2d\:5fc3"}, {0.1, 0}, { 2 Pi, 1}}, {{ Hold[$CellContext`radius$$], 0.5, "\:534a\:5f84"}, 0.5, 3}, {{ Hold[$CellContext`pt5$$], 0, "\:70b9Q"}, 0, 0.999999}}, Typeset`size$$ = {540., {510., 519.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`n$1486$$ = 0, $CellContext`high$1487$$ = False, $CellContext`type$1488$$ = 0, $CellContext`lineType$1489$$ = 0, $CellContext`pt1$1490$$ = {0, 0}, $CellContext`pt2$1491$$ = {0, 0}, $CellContext`pt4$1492$$ = 0, $CellContext`pt3$1493$$ = {0, 0}}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`high$$ = False, $CellContext`lineType$$ = "D\:4e0a\:306e\:76f4\:7dda", $CellContext`n$$ = 3, $CellContext`pt1$$ = {0, 0.2}, $CellContext`pt2$$ = { 1, 0.1}, $CellContext`pt3$$ = {0, 0.5}, $CellContext`pt4$$ = 0, $CellContext`pt5$$ = 0, $CellContext`radius$$ = 0.5, $CellContext`type$$ = "\:5186\:9310\:306e\:307f"}, "ControllerVariables" :> { Hold[$CellContext`n$$, $CellContext`n$1486$$, 0], Hold[$CellContext`high$$, $CellContext`high$1487$$, False], Hold[$CellContext`type$$, $CellContext`type$1488$$, 0], Hold[$CellContext`lineType$$, $CellContext`lineType$1489$$, 0], Hold[$CellContext`pt1$$, $CellContext`pt1$1490$$, {0, 0}], Hold[$CellContext`pt2$$, $CellContext`pt2$1491$$, {0, 0}], Hold[$CellContext`pt4$$, $CellContext`pt4$1492$$, 0], Hold[$CellContext`pt3$$, $CellContext`pt3$1493$$, {0, 0}]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`xmax = 2 Pi; $CellContext`rmax = $CellContext`n$$; $CellContext`f := Sqrt[$CellContext`n$$^2 - 1] ( 1 - $CellContext`x); $CellContext`\[Theta]1 := Part[$CellContext`pt1$$, 1] $CellContext`n$$; $CellContext`\[Theta]2 := Part[$CellContext`pt2$$, 1] $CellContext`n$$; $CellContext`r1 := $CellContext`rmax - Part[$CellContext`pt1$$, 2] $CellContext`n$$; $CellContext`r2 := $CellContext`rmax - Part[$CellContext`pt2$$, 2] $CellContext`n$$; $CellContext`\[Theta]3 := Part[$CellContext`pt3$$, 1] $CellContext`n$$; $CellContext`r3 := $CellContext`rmax - Part[$CellContext`pt3$$, 2] $CellContext`n$$; $CellContext`x1 := $CellContext`r1 Cos[$CellContext`\[Theta]1/$CellContext`n$$]; $CellContext`x2 := \ $CellContext`r2 Cos[$CellContext`\[Theta]2/$CellContext`n$$]; $CellContext`y1 := \ $CellContext`r1 Sin[$CellContext`\[Theta]1/$CellContext`n$$]; $CellContext`y2 := \ $CellContext`r2 Sin[$CellContext`\[Theta]2/$CellContext`n$$]; $CellContext`x3 := \ $CellContext`r3 Cos[$CellContext`\[Theta]3/$CellContext`n$$]; $CellContext`y3 := \ $CellContext`r3 Sin[$CellContext`\[Theta]3/$CellContext`n$$]; $CellContext`\[Alpha] := N[ ArcTan[ Sin[$CellContext`\[Theta]1/$CellContext`n$$ - \ $CellContext`\[Theta]2/$CellContext`n$$] ($CellContext`y1 - $CellContext`y2), Sin[$CellContext`\[Theta]1/$CellContext`n$$ - \ $CellContext`\[Theta]2/$CellContext`n$$] (-$CellContext`x1 + \ $CellContext`x2)]]; $CellContext`h := ($CellContext`r1 $CellContext`r2) (Abs[ Sin[$CellContext`\[Theta]1/$CellContext`n$$ - $CellContext`\ \[Theta]2/$CellContext`n$$]]/ Sqrt[$CellContext`r1^2 + $CellContext`r2^2 - (( 2 $CellContext`r1) $CellContext`r2) Cos[$CellContext`\[Theta]1/$CellContext`n$$ - \ $CellContext`\[Theta]2/$CellContext`n$$]]); $CellContext`\[Beta] := ArcCos[$CellContext`h/$CellContext`n$$]; $CellContext`mesh := Which[$CellContext`n$$ <= 3, 8 $CellContext`n$$ - 1, Inequality[8, Greater, $CellContext`n$$, GreaterEqual, 4], 4 $CellContext`n$$ - 1, $CellContext`n$$ >= 8, 2 $CellContext`n$$ - 1]; $CellContext`p := $CellContext`pt4$$; $CellContext`q := \ $CellContext`pt5$$; Which[Part[$CellContext`pt1$$, 1] - Part[$CellContext`pt2$$, 1] > Pi/$CellContext`n$$, {$CellContext`theta2 := Part[$CellContext`pt2$$, 1] $CellContext`n$$ + 2 Pi, $CellContext`theta1 := Part[$CellContext`pt1$$, 1] $CellContext`n$$}, Part[$CellContext`pt1$$, 1] - Part[$CellContext`pt2$$, 1] < (- Pi)/$CellContext`n$$, {$CellContext`theta2 := Part[$CellContext`pt2$$, 1] $CellContext`n$$, $CellContext`theta1 := Part[$CellContext`pt1$$, 1] $CellContext`n$$ + 2 Pi}, Abs[Part[$CellContext`pt1$$, 1] - Part[$CellContext`pt2$$, 1]] <= Pi/$CellContext`n$$, {$CellContext`theta1 := Part[$CellContext`pt1$$, 1] $CellContext`n$$, $CellContext`theta2 := Part[$CellContext`pt2$$, 1] $CellContext`n$$}]; $CellContext`X1 := $CellContext`r1 Cos[$CellContext`theta1/$CellContext`n$$]; $CellContext`X2 := \ $CellContext`r2 Cos[$CellContext`theta2/$CellContext`n$$]; $CellContext`Y1 := \ $CellContext`r1 Sin[$CellContext`theta1/$CellContext`n$$]; $CellContext`Y2 := \ $CellContext`r2 Sin[$CellContext`theta2/$CellContext`n$$]; $CellContext`alpha := N[ ArcTan[ Sin[$CellContext`theta1/$CellContext`n$$ - \ $CellContext`theta2/$CellContext`n$$] ($CellContext`Y1 - $CellContext`Y2), Sin[$CellContext`theta1/$CellContext`n$$ - \ $CellContext`theta2/$CellContext`n$$] (-$CellContext`X1 + $CellContext`X2)]]; \ $CellContext`geoh := ($CellContext`r1 $CellContext`r2) (Abs[ Sin[$CellContext`theta1/$CellContext`n$$ - \ $CellContext`theta2/$CellContext`n$$]]/ Sqrt[$CellContext`r1^2 + $CellContext`r2^2 - (( 2 $CellContext`r1) $CellContext`r2) Cos[$CellContext`theta1/$CellContext`n$$ - \ $CellContext`theta2/$CellContext`n$$]]); $CellContext`beta := ArcCos[$CellContext`geoh/$CellContext`n$$]; $CellContext`ptAB3D := Graphics3D[{ PointSize[Large], Black, Point[{($CellContext`r1/$CellContext`n$$) Cos[$CellContext`\[Theta]1], ($CellContext`r1/$CellContext`n$$) Sin[$CellContext`\[Theta]1], Part[$CellContext`pt1$$, 2] Sqrt[$CellContext`n$$^2 - 1]}], Blue, Point[{($CellContext`r2/$CellContext`n$$) Cos[$CellContext`\[Theta]2], ($CellContext`r2/$CellContext`n$$) Sin[$CellContext`\[Theta]2], Part[$CellContext`pt2$$, 2] Sqrt[$CellContext`n$$^2 - 1]}], Black, Text[ "A", {($CellContext`r1/$CellContext`n$$) Cos[$CellContext`\[Theta]1], ($CellContext`r1/$CellContext`n$$) Sin[$CellContext`\[Theta]1], Part[$CellContext`pt1$$, 2] Sqrt[$CellContext`n$$^2 - 1]}], Text[ "B", {($CellContext`r2/$CellContext`n$$) Cos[$CellContext`\[Theta]2], ($CellContext`r2/$CellContext`n$$) Sin[$CellContext`\[Theta]2], Part[$CellContext`pt2$$, 2] Sqrt[$CellContext`n$$^2 - 1]}]}]; $CellContext`line3D := If[Mod[$CellContext`\[Theta]1 - $CellContext`\[Theta]2, 2 Pi] != 0, {$CellContext`OP := $CellContext`h/ Cos[$CellContext`t - $CellContext`\[Alpha]]; ParametricPlot3D[{($CellContext`OP/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t], \ ($CellContext`OP/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t], ( 1 - $CellContext`OP/$CellContext`n$$) Sqrt[$CellContext`n$$^2 - 1]}, {$CellContext`t, $CellContext`\[Alpha] - $CellContext`\ \[Beta], $CellContext`\[Alpha] + $CellContext`\[Beta]}, PlotStyle -> { Thick, Green}]}, $CellContext`oline3D]; $CellContext`oline3D := Graphics3D[{Thick, Green, Line[{{ Cos[$CellContext`\[Theta]1], Sin[$CellContext`\[Theta]1], 0}, {0, 0, Sqrt[$CellContext`n$$^2 - 1]}, {-Cos[$CellContext`\[Theta]1], - Sin[$CellContext`\[Theta]1], 0}}]}]; $CellContext`ptOnLine3D := If[Mod[$CellContext`\[Theta]1 - $CellContext`\[Theta]2, 2 Pi] != 0, {$CellContext`t1 := $CellContext`p ($CellContext`\[Alpha] - \ $CellContext`\[Beta]) + ( 1 - $CellContext`p) ($CellContext`\[Alpha] + $CellContext`\ \[Beta]); $CellContext`OP1 := $CellContext`h/ Cos[$CellContext`t1 - $CellContext`\[Alpha]]; Graphics3D[{ PointSize[Large], Purple, Point[{($CellContext`OP1/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t1], \ ($CellContext`OP1/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t1], ( 1 - $CellContext`OP1/$CellContext`n$$) Sqrt[$CellContext`n$$^2 - 1]}], Black, Text[ "P", {($CellContext`OP1/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t1], \ ($CellContext`OP1/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t1], ( 1 - $CellContext`OP1/$CellContext`n$$) Sqrt[$CellContext`n$$^2 - 1]}]}]}, Graphics3D[{ PointSize[Large], Purple, Point[{{(1 - 2 $CellContext`p) Cos[$CellContext`\[Theta]1], (1 - 2 $CellContext`p) Sin[$CellContext`\[Theta]1], (1 - Abs[1 - 2 $CellContext`p]) Sqrt[$CellContext`n$$^2 - 1]}}]}]]; $CellContext`geoline3D := If[Mod[$CellContext`\[Theta]1 - $CellContext`\[Theta]2, 2 Pi] != 0, {$CellContext`d := $CellContext`geoh/ Cos[$CellContext`s - $CellContext`alpha]; ParametricPlot3D[{($CellContext`d/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`s], \ ($CellContext`d/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`s], ( 1 - $CellContext`d/$CellContext`n$$) Sqrt[$CellContext`n$$^2 - 1]}, {$CellContext`s, $CellContext`alpha - $CellContext`beta, \ $CellContext`alpha + $CellContext`beta}, PlotStyle -> { Thick, Purple}]}, $CellContext`oline3D]; $CellContext`segment3D := \ ($CellContext`OQ := $CellContext`h/ Cos[$CellContext`t - $CellContext`\[Alpha]]; Which[$CellContext`\[Theta]1 - $CellContext`\[Theta]2 > \ $CellContext`n$$ Pi, {$CellContext`\[Theta]max := $CellContext`\[Theta]2 + ( 2 $CellContext`n$$) Pi, $CellContext`\[Theta]min := $CellContext`\[Theta]1}, \ $CellContext`\[Theta]2 - $CellContext`\[Theta]1 > $CellContext`n$$ Pi, {$CellContext`\[Theta]max := $CellContext`\[Theta]1 + ( 2 $CellContext`n$$) Pi, $CellContext`\[Theta]min := $CellContext`\[Theta]2}, Abs[$CellContext`\[Theta]1 - $CellContext`\[Theta]2] <= \ $CellContext`n$$ Pi, {$CellContext`\[Theta]max := Max[$CellContext`\[Theta]1, $CellContext`\[Theta]2], \ $CellContext`\[Theta]min := Min[$CellContext`\[Theta]1, $CellContext`\[Theta]2]}]; ParametricPlot3D[{($CellContext`OQ/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t], \ ($CellContext`OQ/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t], ( 1 - $CellContext`OQ/$CellContext`n$$) Sqrt[$CellContext`n$$^2 - 1]}, {$CellContext`t, \ $CellContext`\[Theta]min/$CellContext`n$$, \ $CellContext`\[Theta]max/$CellContext`n$$}, PlotStyle -> {Thick, Red}]); $CellContext`ptAB2D := Graphics[{ PointSize[Large], Black, Point[{$CellContext`r1 Cos[$CellContext`\[Theta]1/$CellContext`n$$], $CellContext`r1 Sin[$CellContext`\[Theta]1/$CellContext`n$$]}], Blue, Point[{$CellContext`r2 Cos[$CellContext`\[Theta]2/$CellContext`n$$], $CellContext`r2 Sin[$CellContext`\[Theta]2/$CellContext`n$$]}], Black, Text[ "A", {$CellContext`r1 Cos[$CellContext`\[Theta]1/$CellContext`n$$], $CellContext`r1 Sin[$CellContext`\[Theta]1/$CellContext`n$$]}, {-2, 0}], Text[ "B", {$CellContext`r2 Cos[$CellContext`\[Theta]2/$CellContext`n$$], $CellContext`r2 Sin[$CellContext`\[Theta]2/$CellContext`n$$]}, {-2, 0}]}]; $CellContext`geoptAB2D := Graphics[{ PointSize[Large], Black, Point[{$CellContext`r1 Cos[$CellContext`theta1/$CellContext`n$$], $CellContext`r1 Sin[$CellContext`theta1/$CellContext`n$$]}], Red, Point[{$CellContext`r2 Cos[$CellContext`theta2/$CellContext`n$$], $CellContext`r2 Sin[$CellContext`theta2/$CellContext`n$$]}], Black, Text[ "A", {$CellContext`r1 Cos[$CellContext`theta1/$CellContext`n$$], $CellContext`r1 Sin[$CellContext`theta1/$CellContext`n$$]}, {-2, 0}], Text[ "B", {$CellContext`r2 Cos[$CellContext`theta2/$CellContext`n$$], $CellContext`r2 Sin[$CellContext`theta2/$CellContext`n$$]}, {-2, 0}]}]; $CellContext`basic3D := ($CellContext`ratio := If[$CellContext`high$$, {2, 2, Sqrt[$CellContext`n$$^2 - 1]}, Automatic]; RevolutionPlot3D[$CellContext`f, {$CellContext`x, 0, 1}, BoxRatios -> $CellContext`ratio]); $CellContext`basic2D := { Graphics[{Blue, Table[ Line[{{0, 0}, {$CellContext`n$$ Cos[($CellContext`k 2) ( Pi/$CellContext`n$$)], $CellContext`n$$ Sin[($CellContext`k 2) ( Pi/$CellContext`n$$)]}}], {$CellContext`k, 0, $CellContext`n$$ - 1}]}], ParametricPlot[{$CellContext`r Cos[$CellContext`t], $CellContext`r Sin[$CellContext`t]}, {$CellContext`r, 0, $CellContext`rmax}, {$CellContext`t, 0, 2 Pi}, PlotStyle -> Gray, Mesh -> {15, $CellContext`mesh}]}; $CellContext`circle2D := Graphics[{ PointSize[0.015], Purple, Point[{$CellContext`r3 Cos[$CellContext`\[Theta]3/$CellContext`n$$], $CellContext`r3 Sin[$CellContext`\[Theta]3/$CellContext`n$$]}], Blue, Thick, Circle[{$CellContext`x3, $CellContext`y3}, \ $CellContext`radius$$]}]; $CellContext`ptOnCircle3D := If[$CellContext`radius$$ <= $CellContext`r3, {$CellContext`\[Delta]t2 := ArcSin[$CellContext`radius$$/$CellContext`r3]; \ $CellContext`rplus2 := $CellContext`r3 Cos[$CellContext`t3 - $CellContext`\[Theta]3/$CellContext`n$$] + Sign[ Sin[((-2) Pi) $CellContext`q]] Sqrt[$CellContext`radius$$^2 - $CellContext`r3^2 Sin[$CellContext`t3 - \ $CellContext`\[Theta]3/$CellContext`n$$]^2]; $CellContext`t3 := $CellContext`\ \[Theta]3/$CellContext`n$$ + $CellContext`\[Delta]t2 Cos[(2 Pi) $CellContext`q]; Graphics3D[{ PointSize[Large], Red, Point[{($CellContext`rplus2/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t3], \ ($CellContext`rplus2/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t3], Sqrt[$CellContext`n$$^2 - 1] ( 1 - $CellContext`rplus2/$CellContext`n$$)}], Black, Text[ "Q", {($CellContext`rplus2/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t3], \ ($CellContext`rplus2/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t3], Sqrt[$CellContext`n$$^2 - 1] ( 1 - $CellContext`rplus2/$CellContext`n$$)}]}]}, \ {$CellContext`rplus3 := $CellContext`r3 Cos[$CellContext`t3 - $CellContext`\[Theta]3/$CellContext`n$$] + Sqrt[$CellContext`radius$$^2 - $CellContext`r3^2 Sin[$CellContext`t3 - \ $CellContext`\[Theta]3/$CellContext`n$$]^2]; $CellContext`t3 := $CellContext`\ \[Theta]3/$CellContext`n$$ + (2 $CellContext`q - 1) Pi; Graphics3D[{ PointSize[Large], Red, Point[{($CellContext`rplus3/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t3], \ ($CellContext`rplus3/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t3], Sqrt[$CellContext`n$$^2 - 1] ( 1 - $CellContext`rplus3/$CellContext`n$$)}], Black, Text[ "Q", {($CellContext`rplus3/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t3], \ ($CellContext`rplus3/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t3], Sqrt[$CellContext`n$$^2 - 1] ( 1 - $CellContext`rplus3/$CellContext`n$$)}]}]}]; \ $CellContext`ptOnCircle2D := If[$CellContext`radius$$ <= $CellContext`r3, {$CellContext`\[Delta]t3 := ArcSin[$CellContext`radius$$/$CellContext`r3]; \ $CellContext`rplus3 := $CellContext`r3 Cos[$CellContext`t4 - $CellContext`\[Theta]3/$CellContext`n$$] + Sign[ Sin[((-2) Pi) $CellContext`q]] Sqrt[$CellContext`radius$$^2 - $CellContext`r3^2 Sin[$CellContext`t4 - \ $CellContext`\[Theta]3/$CellContext`n$$]^2]; $CellContext`t4 := $CellContext`\ \[Theta]3/$CellContext`n$$ + $CellContext`\[Delta]t3 Cos[(2 Pi) $CellContext`q]; Graphics[{ PointSize[Large], Red, Point[{$CellContext`rplus2 Cos[$CellContext`t4], $CellContext`rplus2 Sin[$CellContext`t4]}], Black, Text[ "Q", {$CellContext`rplus2 Cos[$CellContext`t4], $CellContext`rplus2 Sin[$CellContext`t4]}, {-2, 0}]}]}, {$CellContext`rplus4 := $CellContext`r3 Cos[$CellContext`t4 - $CellContext`\[Theta]3/$CellContext`n$$] + Sqrt[$CellContext`radius$$^2 - $CellContext`r3^2 Sin[$CellContext`t4 - \ $CellContext`\[Theta]3/$CellContext`n$$]^2]; $CellContext`t4 := $CellContext`\ \[Theta]3/$CellContext`n$$ + Pi (2 $CellContext`q - 1); Graphics[{ PointSize[Large], Red, Point[{$CellContext`rplus4 Cos[$CellContext`t4], $CellContext`rplus4 Sin[$CellContext`t4]}], Black, Text[ "Q", {$CellContext`rplus4 Cos[$CellContext`t4], $CellContext`rplus4 Sin[$CellContext`t4]}, {-2, 0}]}]}]; $CellContext`circle3D := ($CellContext`rplus := \ $CellContext`r3 Cos[$CellContext`t - $CellContext`\[Theta]3/$CellContext`n$$] + Sqrt[$CellContext`radius$$^2 - $CellContext`r3^2 Sin[$CellContext`t - $CellContext`\[Theta]3/$CellContext`n$$]^2]; \ $CellContext`rminus := $CellContext`r3 Cos[$CellContext`t - $CellContext`\[Theta]3/$CellContext`n$$] - Sqrt[$CellContext`radius$$^2 - $CellContext`r3^2 Sin[$CellContext`t - $CellContext`\[Theta]3/$CellContext`n$$]^2]; \ $CellContext`pluscircle := ParametricPlot3D[{($CellContext`rplus/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t], \ ($CellContext`rplus/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t], Sqrt[$CellContext`n$$^2 - 1] ( 1 - $CellContext`rplus/$CellContext`n$$)}, {$CellContext`t, \ $CellContext`\[Theta]3/$CellContext`n$$ - $CellContext`\[Delta]t, \ $CellContext`\[Theta]3/$CellContext`n$$ + $CellContext`\[Delta]t}, PlotStyle -> {Thick, Blue}]; $CellContext`minuscircle := ParametricPlot3D[{($CellContext`rminus/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t], \ ($CellContext`rminus/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t], Sqrt[$CellContext`n$$^2 - 1] ( 1 - $CellContext`rminus/$CellContext`n$$)}, {$CellContext`t, \ $CellContext`\[Theta]3/$CellContext`n$$ - $CellContext`\[Delta]t, \ $CellContext`\[Theta]3/$CellContext`n$$ + $CellContext`\[Delta]t}, PlotStyle -> {Thick, Blue}]; $CellContext`wholecircle := ParametricPlot3D[{($CellContext`rplus/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t], \ ($CellContext`rplus/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t], Sqrt[$CellContext`n$$^2 - 1] ( 1 - $CellContext`rplus/$CellContext`n$$)}, {$CellContext`t, 0, 2 Pi}, PlotStyle -> {Thick, Blue}]; $CellContext`center := Graphics3D[{ PointSize[Large], Purple, Point[{($CellContext`r3/$CellContext`n$$) Cos[$CellContext`\[Theta]3], ($CellContext`r3/$CellContext`n$$) Sin[$CellContext`\[Theta]3], Part[$CellContext`pt3$$, 2] Sqrt[$CellContext`n$$^2 - 1]}]}]; If[$CellContext`radius$$ <= $CellContext`r3, {$CellContext`\[Delta]t := ArcSin[$CellContext`radius$$/$CellContext`r3]; \ $CellContext`pluscircle, $CellContext`minuscircle, $CellContext`center}, \ {$CellContext`wholecircle, $CellContext`center}]); $CellContext`line2D := If[Part[$CellContext`pt1$$, 1] != Part[$CellContext`pt2$$, 1], PolarPlot[$CellContext`h/ Cos[$CellContext`t - $CellContext`\[Alpha]], {$CellContext`t, \ $CellContext`\[Alpha] - $CellContext`\[Beta], $CellContext`\[Alpha] + \ $CellContext`\[Beta]}, PlotStyle -> {Thick, Green}], Graphics[{Thick, Green, Line[{{$CellContext`n$$ Cos[ Part[$CellContext`pt1$$, 1]], $CellContext`n$$ Sin[ Part[$CellContext`pt1$$, 1]]}, {(-$CellContext`n$$) Cos[ Part[$CellContext`pt1$$, 1]], (-$CellContext`n$$) Sin[ Part[$CellContext`pt1$$, 1]]}}]}]]; $CellContext`ptOnLine2D := If[ Part[$CellContext`pt1$$, 1] != Part[$CellContext`pt2$$, 1], {$CellContext`t2 := $CellContext`p ($CellContext`\[Alpha] - \ $CellContext`\[Beta]) + ( 1 - $CellContext`p) ($CellContext`\[Alpha] + $CellContext`\ \[Beta]); Graphics[{ PointSize[Large], Purple, Point[{($CellContext`h/ Cos[$CellContext`t2 - $CellContext`\[Alpha]]) Cos[$CellContext`t2], ($CellContext`h/ Cos[$CellContext`t2 - $CellContext`\[Alpha]]) Sin[$CellContext`t2]}], Black, Text[ "P", {($CellContext`h/ Cos[$CellContext`t2 - $CellContext`\[Alpha]]) Cos[$CellContext`t2], ($CellContext`h/ Cos[$CellContext`t2 - $CellContext`\[Alpha]]) Sin[$CellContext`t2]}, {-2, 0}]}]}, Graphics[{ PointSize[Large], Purple, Point[{($CellContext`n$$ (1 - 2 $CellContext`p)) Cos[ Part[$CellContext`pt1$$, 1]], ($CellContext`n$$ (1 - 2 $CellContext`p)) Sin[ Part[$CellContext`pt1$$, 1]]}]}]]; $CellContext`geoline2D := PolarPlot[$CellContext`geoh/ Cos[$CellContext`u - $CellContext`alpha], {$CellContext`u, \ $CellContext`alpha - $CellContext`beta, $CellContext`alpha + \ $CellContext`beta}, PlotStyle -> { Thick, Purple}]; $CellContext`mycircle3D := {$CellContext`basic3D, \ $CellContext`circle3D, $CellContext`ptOnCircle3D}; $CellContext`myline3D := Switch[$CellContext`lineType$$, "D\:4e0a\:306e\:76f4\:7dda", {$CellContext`basic3D, \ $CellContext`line3D, $CellContext`ptAB3D, $CellContext`ptOnLine3D}, "\:6700\:77ed\:8ddd\:96e2\:7dda", {$CellContext`basic3D, \ $CellContext`geoline3D, $CellContext`ptAB3D}, "\:4e21\:65b9", {$CellContext`basic3D, $CellContext`geoline3D, \ $CellContext`line3D, $CellContext`ptAB3D, $CellContext`ptOnLine3D}]; \ $CellContext`mycircle2D := {$CellContext`basic2D, $CellContext`circle2D, \ $CellContext`ptOnCircle2D}; $CellContext`myline2D := Switch[$CellContext`lineType$$, "D\:4e0a\:306e\:76f4\:7dda", {$CellContext`basic2D, \ $CellContext`line2D, $CellContext`ptAB2D, $CellContext`ptOnLine2D}, "\:6700\:77ed\:8ddd\:96e2\:7dda", {$CellContext`basic2D, \ $CellContext`geoline2D, $CellContext`ptAB2D, $CellContext`geoptAB2D}, "\:4e21\:65b9", {$CellContext`basic2D, $CellContext`geoline2D, \ $CellContext`line2D, $CellContext`ptAB2D, $CellContext`ptOnLine2D, \ $CellContext`geoptAB2D}]; $CellContext`cone := Switch[$CellContext`type$$, "\:5186", Show[$CellContext`mycircle3D], "\:76f4\:7dda,\:6700\:77ed\:8ddd\:96e2\:7dda", Show[$CellContext`myline3D], "\:5168\:3066", Show[$CellContext`mycircle3D, $CellContext`myline3D], "\:5186\:9310\:306e\:307f", Show[$CellContext`basic3D]]; $CellContext`development := Switch[$CellContext`type$$, "\:5186", Show[$CellContext`mycircle2D], "\:76f4\:7dda,\:6700\:77ed\:8ddd\:96e2\:7dda", Show[$CellContext`myline2D], "\:5168\:3066", Show[$CellContext`mycircle2D, $CellContext`myline2D], "\:5186\:9310\:306e\:307f", Show[$CellContext`basic2D]]; GraphicsColumn[{$CellContext`cone, $CellContext`development}]), "Specifications" :> { Style[ "\:6bcd\:7dda\:306e\:9577\:3055(\:534a\:5f84\:306f 1 )", Bold], {{$CellContext`n$$, 3, "n"}, 2, 12, 1}, Delimiter, Style[ "\:5b9f\:969b\:306e\:6bd4\:7387\:3067 \:898b\:308b ", Bold], {{$CellContext`high$$, False, "Yes"}, {True, False}}, Delimiter, Style[ "\:8868\:793a\:56f3\:5f62", Bold], {{$CellContext`type$$, "\:5186\:9310\:306e\:307f", ""}, { "\:5186\:9310\:306e\:307f", "\:76f4\:7dda,\:6700\:77ed\:8ddd\:96e2\:7dda", "\:5186"}, ControlType -> PopupMenu}, Delimiter, Style[ "\:5c55\:958b\:56f3D\:4e0a\:306e\:76f4\:7dda\:3068\:70b9P / \:6700\ \:77ed\:8ddd\:96e2\:7dda", Bold], {{$CellContext`lineType$$, 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