Showing the points on a surface about a circle in the plane
- To: mathgroup at smc.vnet.net
- Subject: [mg74848] Showing the points on a surface about a circle in the plane
- From: "ahallam at iastate.edu" <ahallam at iastate.edu>
- Date: Sun, 8 Apr 2007 05:04:16 -0400 (EDT)
What I would like to do with Plot3D and ParametricPlot3D is show a surface in three dimensions, a circle in the plane and the points on the surface above the circle. This is what I have in mind where I have a square in the plane. I simply don't know of a way to handle the circle. If there were am ImplicitPlot3D, I can think so some options. I am not sure how to send code so that it is readable so I am simply pasting as is. Someone can yell at me and tell me this is wrong and how to do it correctly and then I will. \!\(\* RowBox[{\(Clear[f, x1, x2];\), "\n", \(c = 0;\), "\[IndentingNewLine]", \(A = 10;\), "\[IndentingNewLine]", \(=CE=B11 = 1/4;\), "\[IndentingNewLine]", \(= =CE=B12 = 1/2;\), "\[IndentingNewLine]", \(f[x1_, x2_] := A*x1^=CE=B11*x2^=CE= =B12;\), "\ \[IndentingNewLine]", \(Print[ "\<This is f[x1, x2]\>"]\), "\[IndentingNewLine]", \(f[ x1, x2]\), "\n", "\[IndentingNewLine]", \(fv = Table[f[x1, x2], {x1, 20, 24}, {x2, 20, 24}];\), "\[IndentingNewLine]", "fv ", "\[IndentingNewLine]", \(Print["\<This is the minimum value of the function\>"];\), "\[IndentingNewLine]", \(fvmin = Min[fv] // N \), "\[IndentingNewLine]", \(Print["\<This is the maximum value of the function\>"];\), "\[IndentingNewLine]", \ (fvmax = \ Max[fv] // N\), "\[IndentingNewLine]", \(x1g = {20, 24}; x2g = {20, 24}; zg = {fvmin, fvmax};\), "\[IndentingNewLine]", RowBox[{ RowBox[{"p1", "=", RowBox[{"Plot3D", "[", " ", RowBox[{\(f[x1, x2]\), ",", \({x1, .1, 30}\), ",", \({x2, . 1, 30}\), ",", " ", \(AxesLabel -> {\*"\"\<\!\(x\_1\)\>\"", \ \*"\"\<\!\(x\_2\)\>\"", \*"\"\<f(\!\(x\_1\),\!\(x\_2\))\>\""}\), ",", \ \(TextStyle -> {FontFamily -> "\<Helvetica\>", FontSize -> 18}\), ", ", " ", \(ColorFunction -> \ Hue\), ",", RowBox[{"ViewPoint", "->", RowBox[{"{", RowBox[{\(-1.5\), StyleBox[",", "MR"], StyleBox["2.5", "MR"], StyleBox[",", "MR"], StyleBox[\(-1\), "MR"]}], StyleBox["}", "MR"]}]}], ",", " ", \(ImageSize -> \ 600\), ",", " ", RowBox[{ StyleBox["Boxed", "MR"], " ", "->", " ", "True"}], ",", \(BoxRatios -> {1, 1, 0=2E6}\), ", ", \(DisplayFunction -> Identity\)}], "]"}]}], ";"}], " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"p2", "=", RowBox[{"Plot3D", "[", " ", RowBox[{\(f[x1, x2]\), ",", \({x1, 20, 24}\), ",", \({x2, 20, 24}\), ",", " ", \(AxesLabel -> {\*"\"\<\!\(x\_1\)\>\"", \ \*"\"\<\!\(x\_2\)\>\"", \*"\"\<f(\!\(x\_1\),\!\(x\_2\))\>\""}\), ",", " ", \ \(ColorFunction -> \((GrayLevel[#^3] &)\)\), StyleBox[",", FontWeight->"Bold"], " ", \(TextStyle -> { FontFamily -> "\<Helvetica\>", FontSize -> 18}\), ",", \(ViewPoint\ -> \ {6, 3, \ \(-1\)}\), ",", " ", \(ImageSize -> \ 600\), ",", " ", RowBox[{ StyleBox["Boxed", "MR"], " ", "->", " ", "True"}], ",", \(BoxRatios -> {1, 1, 0.6}\), ",", \ \(DisplayFunction -> Identity\)}], "]"}]}], ";"}], " ", "\ [IndentingNewLine]", RowBox[{ RowBox[{"Neigh1", "=", " ", RowBox[{"Plot3D", "[", RowBox[{"c", ",", \({x1, 20, 24}\), ",", \({x2, 20, 24}\), ",", " ", \(ColorFunction -> \((GrayLevel[#^3] &)\) \), StyleBox[",", FontWeight->"Bold"], RowBox[{"ViewPoint", "->", RowBox[{"{", RowBox[{\(-1.5\), StyleBox[",", "MR"], StyleBox["2.5", "MR"], StyleBox[",", "MR"], StyleBox["0", "MR"]}], StyleBox["}", "MR"]}]}], ",", \(DisplayFunction\ -> \ Identity \)}], "] "}]}], ";"}], "\[IndentingNewLine]", \(tx1 = Graphics3D[{\ \ CMYKColor[ .8, 0, .3, .1], \ PointSize[ 0.015], Point[\ {22, 22, 0}]\ , \ PointSize[0.015], Point[\ {22, 22, f[22, 22]}]\ , \[IndentingNewLine]CMYKColor[ .1, 0, .3, .9], \ Text["\<\>", \ {\(-3.9\), 0.5, 20}, \ \ TextStyle -> {FontSize -> 24, FontWeight -> "\<Bold\>"}]\[IndentingNewLine]\ }];\), " ", "\[IndentingNewLine]", \(Show[\ p1, p2, Neigh1, tx1, \ Ticks -> {Automatic, Automatic, \ \ \ {\ {25, "\<25\>", .02, {Thickness[ .004]}\ }, {50, "\<50\>", . 02, { Thickness[ .004]}\ }, \[IndentingNewLine]{75, "\<75\>", . 02, \ {Thickness[ .004]}\ }, { 125, "\<125\>", .02, {Thickness[ .004]}\ }, {fvmin, \*"\"\<\!\(f\ \_min\)\>\"", .02, { Thickness[ .004]}\ }, {fvmax, \*"\"\<\!\(f\_max\)\> \"", .02, \ {Thickness[ .004]}\ }\ \ }\ \ \ }, ViewPoint\ -> \ {6, 3, \ 3}, FaceGrids -> {{{1, 0, 0}, {x2g, zg}}, {{0, 1, 0}, {x1g, zg}}, {{0, 0, \(-1\)}, { x1g, x2g}}}, DefaultFont -> {"\<Helvetica\>", 20}, \ DisplayFunction\ -> \ $DisplayFunction, \ ImageSize\ -> \ 600];\)}]\)