(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of 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[ 42549, 880]*) (*NotebookOutlinePosition[ 43259, 905]*) (* CellTagsIndexPosition[ 43215, 901]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[ RowBox[{"\n", RowBox[{ \(var = 2\), ";", "\n", \(po1 = 1.5\), ";", "\n", \(po2 = \(-1.5\)\), ";", "\n", \(point = {po1, po2, 0}\), ";", "\n", \(abs = po1*po1 + po2*po2\), ";", "\n", \(spoint = {\((2*po1)\)/\((1 + abs)\), \((2*po2)\)/\((1 + abs)\), \((abs - 1)\)/\((abs + 1)\)}\), ";", "\n", \(p1 = ParametricPlot3D[{Cos[t]*Sin[u], Sin[t]*Sin[u], Cos[u]}, {t, 0, 2 \[Pi]}, {u, 0, \[Pi]}, DisplayFunction\ -> Identity]\), ";", "\n", RowBox[{"p2", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[point]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["$DisplayFunction", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p3", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[spoint]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["$DisplayFunction", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p4", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Line[{{0, 0, 1}, point}]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["$DisplayFunction", "MR"]}]}], "]"}]}], ";", "\n", \(p5\ = \ ParametricPlot3D[{\ t\ , u, 0}, {t, \(-var\), var}, {u, \(-var\), var}, DisplayFunction\ -> Identity]\), ";", "\n", \(Show[p1, p2, p3, p4, p5, DisplayFunction \[Rule] $DisplayFunction, Boxed\ -> False]\), ";"}]}]], "Input"], Cell[BoxData[ RowBox[{ \(po1 = 1.5\), ";", "\n", \(po2 = 0\), ";", "\n", \(point = {po1, po2, 0}\), ";", "\n", \(abs = po1*po1 + po2*po2\), ";", "\n", \(spoint = {\((2*po1)\)/\((1 + abs)\), \((2*po2)\)/\((1 + abs)\), \((abs - 1)\)/\((abs + 1)\)}\), ";", "\n", \(p1 = ParametricPlot3D[{Cos[t]*Sin[u], Sin[t]*Sin[u], Cos[u]}, {t, 0, 1.5 \[Pi]}, {u, 0, \[Pi]}, DisplayFunction\ -> Identity]\), ";", "\n", RowBox[{"p2", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[point]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["$DisplayFunction", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p3", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[spoint]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["$DisplayFunction", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p4", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Line[{{0, 0, 1}, point}]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["$DisplayFunction", "MR"]}]}], "]"}]}], ";", "\n", \(p5\ = \ ParametricPlot3D[{\ t\ , u, 0}, {t, 0, var}, {u, \(-0\), var}, DisplayFunction\ -> Identity]\), ";", "\n", \(p6\ = \ ParametricPlot3D[{\ t\ , u, 0}, {t, \(-var\), 0}, {u, \(-var\), 0}, DisplayFunction\ -> Identity]\), ";", "\n", \(p7\ = \ \ ParametricPlot3D[{\ t\ , u, 0}, {t, \(-var\), 0}, {u, 0, var}, DisplayFunction\ -> Identity]\), ";", "\n", \(Show[p1, p2, p3, p4, p5, p6, p7, DisplayFunction \[Rule] $DisplayFunction, Boxed\ -> False]\), ";"}]], "Input"], Cell[BoxData[ RowBox[{ \(var = 2\), ";", "\n", \(po1 = .5\), ";", "\n", \(po2 = 0\), ";", "\n", \(point = {po1, po2, 0}\), ";", "\n", \(abs = po1*po1 + po2*po2\), ";", "\n", \(spoint = {\((2*po1)\)/\((1 + abs)\), \((2*po2)\)/\((1 + abs)\), \((abs - 1)\)/\((abs + 1)\)}\), ";", "\n", \(p1 = ParametricPlot3D[{Cos[t]*Sin[u], Sin[t]*Sin[u], Cos[u]}, {t, 0, 1.5 \[Pi]}, {u, 0, \[Pi]}, DisplayFunction\ -> Identity]\), ";", "\n", RowBox[{"p2", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[point]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["$DisplayFunction", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p3", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[spoint]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["$DisplayFunction", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p4", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Line[{{0, 0, 1}, point}]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["$DisplayFunction", "MR"]}]}], "]"}]}], ";", "\n", \(p5\ = \ ParametricPlot3D[{\ t\ , u, 0}, {t, 0, var}, {u, \(-0\), var}, DisplayFunction\ -> Identity]\), ";", "\n", \(p6\ = \ ParametricPlot3D[{\ t\ , u, 0}, {t, \(-var\), 0}, {u, \(-var\), 0}, DisplayFunction\ -> Identity]\), ";", "\n", \(p7\ = \ \ ParametricPlot3D[{\ t\ , u, 0}, {t, \(-var\), 0}, {u, 0, var}, DisplayFunction\ -> Identity]\), ";", "\n", RowBox[{"p8", " ", "=", " ", RowBox[{"Graphics3D", "[", RowBox[{\(Line[{{0, 0, 1}, spoint}]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["$DisplayFunction", "MR"]}]}], "]"}]}], ";", "\n", \(Show[p1, p2, p3, p4, p5, p6, p7, p8, DisplayFunction \[Rule] $DisplayFunction, ViewPoint -> {0.5, \(-1\), .6}, Boxed\ -> False]\), ";"}]], "Input"], Cell[BoxData[ RowBox[{"\n", RowBox[{ \(var = 2\), ";", "\n", \(po1 = 1\), ";", "\n", \(po2 = \(-1.75\)\), ";", "\n", \(pi1\ = \ 2\), ";", "\n", \(pi2\ = \ 0\), ";", "\n", \(point1 = {po1, po2, 0}\), ";", "\n", \(point2 = {pi1, pi2, 0}\), ";", "\n", \(abs = po1*po1 + po2*po2\), ";", "\n", \(spoint = {\((2*po1)\)/\((1 + abs)\), \((2*po2)\)/\((1 + abs)\), \((abs - 1)\)/\((abs + 1)\)}\), ";", "\n", \(p1 = ParametricPlot3D[{Cos[t]*Sin[u], Sin[t]*Sin[u], Cos[u]}, {t, 0, 2 \[Pi]}, {u, 0, \[Pi]}, DisplayFunction\ -> Identity]\), ";", "\n", RowBox[{"p2", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[point1]\), ",", RowBox[{"DisplayFunction", " ", "->", StyleBox["Identity", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p3", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[spoint]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p4", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Line[{{0, 0, 1}, point1}]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}]}], "]"}]}], ";", "\n", \(p5\ = \ ParametricPlot3D[{\ t\ , u, 0}, {t, \(-var\), var}, {u, \(-var\), var}, DisplayFunction\ -> Identity]\), ";", "\n", \(p6\ = \ ParametricPlot3D[{\((t*\((pi1 - po1)\) + po1)\), \((t*\((pi2 - po2)\) + po2)\), 0}, {t, \(-0.1\), 1.1}, DisplayFunction\ -> \ Identity]\), ";", "\n", \(p7 = \ ParametricPlot3D[{ 2*\((t*\((pi1 - po1)\) + po1)\)/ \((1 + \((t*\((pi1 - po1)\) + po1)\)^2 + \((t*\((pi2 - po2)\) + po2)\)^2)\), 2*\((t*\((pi2 - po2)\) + po2)\)/ \((1 + \((t*\((pi1 - po1)\) + po1)\)^2 + \((t*\((pi2 - po2)\) + po2)\)^2)\), \((\((t*\((pi1 - po1)\) + po1)\)^2 + \((t*\((pi2 - po2)\) + po2)\)^2 - 1)\)/ \((1 + \((t*\((pi1 - po1)\) + po1)\)^2 + \((t*\((pi2 - po2)\) + po2)\)^2)\)}, {t, \(-5\), 5}, DisplayFunction\ -> Identity]\), ";", "\n", \(Show[p1, p2, p3, p4, p5, p6, p7, DisplayFunction \[Rule] $DisplayFunction, Boxed\ -> False, ViewPoint -> {1, \(-1\), .75}]\), ";"}]}]], "Input"], Cell[BoxData[ RowBox[{"\n", RowBox[{ \(var = 3\), ";", "\n", \(po1 = \ 2\), ";", "\n", \(po2 = \(-1.75\)\), ";", "\n", \(pi1\ = \ 1\), ";", "\n", \(pi2\ = \ \(-1.75\)\), ";", "\n", \(pii1\ = \ 0\), ";", "\n", \(pii2\ = \ \(-1.75\)\), ";", "\n", \(piii1\ = \ \(-1\)\), ";", "\n", \(piii2\ = \ \(-1.75\)\), ";", "\n", \(piv1\ = \ \(-2\)\), ";", "\n", \(piv2\ = \ \(-1.75\)\), ";", "\n", \(point1 = {po1, po2, 0}\), ";", "\n", \(point2 = {pi1, pi2, 0}\), ";", "\n", \(abs = po1*po1 + po2*po2\), ";", "\n", \(spoint = {\((2*po1)\)/\((1 + abs)\), \((2*po2)\)/\((1 + abs)\), \((abs - 1)\)/\((abs + 1)\)}\), ";", "\n", \(abs1 = pi1^2 + pi2^2\), ";", "\n", \(spoint1 = {\((2*pi1)\)/\((1 + abs1)\), \((2*pi2)\)/\((1 + abs1)\), \((abs1 - 1)\)/\((abs1 + 1)\)}\), ";", "\n", \(abs2 = pii1^2 + pii2^2\), ";", "\n", \(spoint2 = {\((2*pii1)\)/\((1 + abs2)\), \((2*pii2)\)/\((1 + abs2)\), \((abs2 - 1)\)/\((abs2 + 1)\)}\), ";", "\n", \(abs3 = piii1^2 + piii2^2\), ";", "\n", \(spoint3 = {\((2*piii1)\)/\((1 + abs3)\), \((2*piii2)\)/\((1 + abs3)\), \((abs3 - 1)\)/\((abs3 + 1)\)}\), ";", "\n", \(abs4 = piv1^2 + piv2^2\), ";", "\n", \(spoint4 = {\((2*piv1)\)/\((1 + abs4)\), \((2*piv2)\)/\((1 + abs4)\), \((abs4 - 1)\)/\((abs4 + 1)\)}\), ";", "\n", \(p1 = ParametricPlot3D[{Cos[t]*Sin[u], Sin[t]*Sin[u], Cos[u]}, {t, 0, 2 \[Pi]}, {u, 0, \[Pi]}, DisplayFunction\ -> Identity, Axes -> None]\), ";", "\n", RowBox[{"p2", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[point1]\), ",", RowBox[{"DisplayFunction", " ", "->", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", "\n", RowBox[{"p3", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[spoint]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", "\n", RowBox[{"p4", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Line[{{0, 0, 1}, point1}]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", "\n", \(p5\ = \ ParametricPlot3D[{\ t\ , u, 0}, {t, \(-var\), var}, {u, \(-var\), var}, DisplayFunction\ -> Identity, Axes -> None]\), ";", "\n", \(p6\ = \ ParametricPlot3D[{\((t*\((piv1 - po1)\) + po1)\), \((t*\((piv2 - po2)\) + po2)\), 0}, {t, \(-0.3\), 1.3}, DisplayFunction\ -> \ Identity, Axes -> None]\), ";", "\n", \(p7 = \ ParametricPlot3D[{ 2*\((t*\((pi1 - po1)\) + po1)\)/ \((1 + \((t*\((pi1 - po1)\) + po1)\)^2 + \((t*\((pi2 - po2)\) + po2)\)^2)\), 2*\((t*\((pi2 - po2)\) + po2)\)/ \((1 + \((t*\((pi1 - po1)\) + po1)\)^2 + \((t*\((pi2 - po2)\) + po2)\)^2)\), \((\((t*\((pi1 - po1)\) + po1)\)^2 + \((t*\((pi2 - po2)\) + po2)\)^2 - 1)\)/ \((1 + \((t*\((pi1 - po1)\) + po1)\)^2 + \((t*\((pi2 - po2)\) + po2)\)^2)\)}, {t, \(-25\), 25}, DisplayFunction\ -> Identity, Axes -> None]\), ";", "\n", RowBox[{"p8", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[{pii1, pii2, 0}]\), ",", RowBox[{"DisplayFunction", " ", "->", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", " ", "\n", RowBox[{"p9", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[spoint2]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", "\n", RowBox[{"p10", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Line[{{0, 0, 1}, {pii1, pii2, 0}}]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", "\n", RowBox[{"p11", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[{piii1, piii2, 0}]\), ",", RowBox[{"DisplayFunction", " ", "->", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", "\n", RowBox[{"p12", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[spoint3]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", "\n", RowBox[{"p13", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Line[{{0, 0, 1}, {piii1, piii2, 0}}]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", "\n", RowBox[{"p14", " ", "=", " ", RowBox[{"Graphics3D", "[", RowBox[{\(Point[{piv1, piv2, 0}]\), ",", RowBox[{"DisplayFunction", " ", "->", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", "\n", RowBox[{"p15", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[spoint4]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", "\n", RowBox[{"p16", "\t", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Line[{{0, 0, 1}, {piv1, piv2, 0}}]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", "\n", RowBox[{"p17", " ", "=", " ", RowBox[{"Graphics3D", "[", RowBox[{\(Point[{pi1, pi2, 0}]\), ",", RowBox[{"DisplayFunction", " ", "->", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", "\n", RowBox[{"p18", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[spoint1]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", "\n", RowBox[{"p19", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Line[{{0, 0, 1}, {pi1, pi2, 0}}]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}], ",", \(Axes -> None\)}], "]"}]}], ";", " ", "\n", \(Show[p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, DisplayFunction \[Rule] $DisplayFunction, Boxed\ -> False]\), ";"}]}]], "Input"], Cell[BoxData[ RowBox[{"\n", RowBox[{ \(var = 2\), ";", "\n", \(po1 = 1.5\), ";", "\n", \(po2 = 0\), ";", "\n", \(pi1\ = \ 1.5\), ";", "\n", \(pi2\ = \ 2\), ";", "\n", \(point1 = {po1, po2, 0}\), ";", "\n", \(point2 = {pi1, pi2, 0}\), ";", "\n", \(abs = po1*po1 + po2*po2\), ";", "\n", \(spoint = {\((2*po1)\)/\((1 + abs)\), \((2*po2)\)/\((1 + abs)\), \((abs - 1)\)/\((abs + 1)\)}\), ";", "\n", \(p1 = ParametricPlot3D[{Cos[t]*Sin[u], Sin[t]*Sin[u], Cos[u]}, {t, 0, 1.5*\[Pi]}, {u, 0, \[Pi]}, DisplayFunction\ -> Identity]\), ";", "\n", RowBox[{"p2", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[point1]\), ",", RowBox[{"DisplayFunction", " ", "->", StyleBox["Identity", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p3", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[spoint]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p4", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Line[{{0, 0, 1}, point1}]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}]}], "]"}]}], ";", "\n", \(p5\ = \ ParametricPlot3D[{\ t\ , u, 0}, {t, \(-var\), var}, {u, \(-var\), var}, DisplayFunction\ -> Identity]\), ";", "\n", \(p6\ = \ ParametricPlot3D[{\((t*\((pi1 - po1)\) + po1)\), \((t*\((pi2 - po2)\) + po2)\), 0}, {t, \(-1\), 1}, DisplayFunction\ -> \ Identity]\), ";", "\n", \(p7\ = \ ParametricPlot3D[{t, u, 1 - t/po1}, {t, 0, po1}, {u, 0, 2}, DisplayFunction\ -> Identity]\), ";", "\n", \(Show[p1, p2, p3, p4, p5, p6, p7, DisplayFunction \[Rule] $DisplayFunction, Boxed\ -> False, ViewPoint -> {1, \(-0.5\), .75}]\), ";"}]}]], "Input"], Cell[BoxData[ RowBox[{"\n", RowBox[{ \(var = 2\), ";", "\n", \(po1 = 1.5\), ";", "\n", \(po2 = 0\), ";", "\n", \(pi1\ = \ 1.5\), ";", "\n", \(pi2\ = \ 2\), ";", "\n", \(point1 = {po1, po2, 0}\), ";", "\n", \(point2 = {pi1, pi2, 0}\), ";", "\n", \(abs = po1*po1 + po2*po2\), ";", "\n", \(spoint = {\((2*po1)\)/\((1 + abs)\), \((2*po2)\)/\((1 + abs)\), \((abs - 1)\)/\((abs + 1)\)}\), ";", "\n", \(p1 = ParametricPlot3D[{Cos[t]*Sin[u], Sin[t]*Sin[u], Cos[u]}, {t, 0, 2*\[Pi]}, {u, 0, \[Pi]}, DisplayFunction\ -> Identity]\), ";", "\n", RowBox[{"p2", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[point1]\), ",", RowBox[{"DisplayFunction", " ", "->", StyleBox["Identity", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p3", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[spoint]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p4", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Line[{{0, 0, 1}, point1}]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}]}], "]"}]}], ";", "\n", \(p5\ = \ ParametricPlot3D[{\ t\ , u, 0}, {t, \(-var\), var}, {u, \(-var\), var}, DisplayFunction\ -> Identity]\), ";", "\n", \(p6\ = \ ParametricPlot3D[{\((t*\((pi1 - po1)\) + po1)\), \((t*\((pi2 - po2)\) + po2)\), 0}, {t, \(-1\), 1}, DisplayFunction\ -> \ Identity]\), ";", "\n", \(p7\ = \ ParametricPlot3D[{t, u, 1 - t/po1}, {t, 0, po1}, {u, \(-2\), 2}, DisplayFunction\ -> Identity]\), ";", "\n", \(Show[p1, p2, p3, p4, p5, p6, p7, DisplayFunction \[Rule] $DisplayFunction, Boxed\ -> False, ViewPoint -> {1, \(-0.25\), 1}]\), ";"}]}]], "Input"], Cell[BoxData[ RowBox[{"\n", RowBox[{ \(var = 2\), ";", "\n", \(po1 = 1.5\), ";", "\n", \(po2 = 0\), ";", "\n", \(pi1\ = \ 1.5\), ";", "\n", \(pi2\ = \ 2\), ";", "\n", \(pii1\ = \ 1.5\), ";", "\n", \(pii2\ = \ 1\), ";", "\n", \(piii1\ = \ 1.5\), ";", "\n", \(piii2\ = \ \(-1\)\), ";", "\n", \(piv1\ = \ 1.5\), ";", "\n", \(piv2\ = \ \(-2\)\), ";", "\n", \(point1 = {po1, po2, 0}\), ";", "\n", \(point2 = {pi1, pi2, 0}\), ";", "\n", \(abs = po1*po1 + po2*po2\), ";", "\n", \(spoint = {\((2*po1)\)/\((1 + abs)\), \((2*po2)\)/\((1 + abs)\), \((abs - 1)\)/\((abs + 1)\)}\), ";", "\n", \(abs1 = pi1^2 + pi2^2\), ";", "\n", \(spoint1 = {\((2*pi1)\)/\((1 + abs1)\), \((2*pi2)\)/\((1 + abs1)\), \((abs1 - 1)\)/\((abs1 + 1)\)}\), ";", "\n", \(abs2 = pii1^2 + pii2^2\), ";", "\n", \(spoint2 = {\((2*pii1)\)/\((1 + abs2)\), \((2*pii2)\)/\((1 + abs2)\), \((abs2 - 1)\)/\((abs2 + 1)\)}\), ";", "\n", \(abs3 = piii1^2 + piii2^2\), ";", "\n", \(spoint3 = {\((2*piii1)\)/\((1 + abs3)\), \((2*piii2)\)/\((1 + abs3)\), \((abs3 - 1)\)/\((abs3 + 1)\)}\), ";", "\n", \(abs4 = piv1^2 + piv2^2\), ";", "\n", \(spoint4 = {\((2*piv1)\)/\((1 + abs4)\), \((2*piv2)\)/\((1 + abs4)\), \((abs4 - 1)\)/\((abs4 + 1)\)}\), ";", "\n", \(p1 = ParametricPlot3D[{Cos[t]*Sin[u], Sin[t]*Sin[u], Cos[u]}, {t, 0, 2*\[Pi]}, {u, 0, \[Pi]}, DisplayFunction\ -> Identity]\), ";", "\n", RowBox[{"p2", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[point1]\), ",", RowBox[{"DisplayFunction", " ", "->", StyleBox["Identity", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p3", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Point[spoint]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}]}], "]"}]}], ";", "\n", RowBox[{"p4", " ", "=", RowBox[{"Graphics3D", "[", RowBox[{\(Line[{{0, 0, 1}, point1}]\), ",", RowBox[{"DisplayFunction", " ", "->", " ", StyleBox["Identity", "MR"]}]}], "]"}]}], ";", "\n", \(p5\ = \ ParametricPlot3D[{\ t\ , u, 0}, {t, \(-var\), var}, {u, \(-var\), var}, DisplayFunction\ -> Identity]\), ";", "\n", \(p6\ = \ ParametricPlot3D[{\((t*\((pi1 - 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