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Re: MovieParametericPlot-3D

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51686] Re: MovieParametericPlot-3D
  • From: Roger Bagula <tftn at earthlink.net>
  • Date: Fri, 29 Oct 2004 03:39:10 -0400 (EDT)
  • References: <clproj$a61$1@smc.vnet.net>
  • Reply-to: tftn at earthlink.net
  • Sender: owner-wri-mathgroup at wolfram.com

Yes, you can animate 3d plots.
Here's an old notebook with not pictures for a Bours minimal surface:
(I'm not gauanteeing it is a good one, it is just what sherlock found me 
for "animate"
that had no pictures)

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This notebook can be used on any computer system with Mathematica 3.0,
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Notebook[{
Cell[BoxData[
    \(Clear[t, d, p, f, g, z, x]\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(f[t_] = \((Cos[2*t] - r^2*Cos[4*t]/2)\)/4\)], "Input"],

Cell[BoxData[
    \(1\/4\ \((Cos[2\ t] - 1\/2\ r\^2\ Cos[4\ t])\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(g[t_] = \((Sin[2*t] + r^2*Sin[4*t]/2)\)/4\)], "Input"],

Cell[BoxData[
    \(1\/4\ \((Sin[2\ t] + 1\/2\ r\^2\ Sin[4\ t])\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(x1 = r^2*f[t]\)], "Input"],

Cell[BoxData[
    \(1\/4\ r\^2\ \((Cos[2\ t] - 1\/2\ r\^2\ Cos[4\ t])\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(y1 = r^2*g[t]\)], "Input"],

Cell[BoxData[
    \(1\/4\ r\^2\ \((Sin[2\ t] + 1\/2\ r\^2\ Sin[4\ t])\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(z1 = r^3*Cos[3*t]/3\)], "Input"],

Cell[BoxData[
    \(1\/3\ r\^3\ Cos[3\ t]\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    RowBox[{"M", "=",
      RowBox[{"(", GridBox[{
            {\(\((1 + Cos[aa])\)/2\), \(\(-Sqrt[2]\)*Sin[aa]/2\),
              \(\((1 - Cos[aa])\)/2\)},
            {\(Sqrt[2]*Sin[aa]/2\), \(Cos[aa]\), 
\(\(-Sqrt[2]\)*Sin[aa]/2\)},
            {\(\((1 - Cos[aa])\)/2\), \(Sqrt[2]*Sin[aa]/2\),
              \(\((1 + Cos[aa])\)/2\)}
            }], ")"}]}]], "Input"],

Cell[BoxData[
    \({{1\/2\ \((1 + Cos[\(2\ \[Pi]\ w\)\/25])\),
        \(-\(Sin[\(2\ \[Pi]\ w\)\/25]\/\@2\)\),
        1\/2\ \((1 - Cos[\(2\ \[Pi]\ w\)\/25])\)}, {
        Sin[\(2\ \[Pi]\ w\)\/25]\/\@2, Cos[\(2\ \[Pi]\ w\)\/25],
        \(-\(Sin[\(2\ \[Pi]\ w\)\/25]\/\@2\)\)}, {
        1\/2\ \((1 - Cos[\(2\ \[Pi]\ w\)\/25])\),
        Sin[\(2\ \[Pi]\ w\)\/25]\/\@2,
        1\/2\ \((1 + Cos[\(2\ \[Pi]\ w\)\/25])\)}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(xyz = M . {x1, y1, z1}\)], "Input"],

Cell[BoxData[
    \({\(5\
            \((Cos[2\ t] + Cos[3\ t] + 1\/4\ Cos[2\ t]\ Cos[3\ t] +
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            \((1 + Cos[\(2\ \[Pi]\ w\)\/25])\)\)\/\(10 + Cos[p0]\) +
        1\/50\ \((10 + Cos[p0])\)\ \((10 + Cos[p0 + \(2\ \[Pi]\)\/3])\)\
          \((1 - Cos[\(2\ \[Pi]\ w\)\/25])\)\
          \((1\/4\ Sin[3\ t] + 1\/4\ Sin[5\ t])\) -
        \(5\ \@2\
            \((Sin[2\ t] + 1\/4\ Cos[3\ t]\ Sin[2\ t] - Sin[3\ t] -
                1\/4\ Cos[5\ t]\ Sin[3\ t])\)\
            Sin[\(2\ \[Pi]\ w\)\/25]\)\/\(10 + Cos[p0 + \(2\ \[Pi]\)\/3]\),
      \(10\ Cos[\(2\ \[Pi]\ w\)\/25]\
            \((Sin[2\ t] + 1\/4\ Cos[3\ t]\ Sin[2\ t] - Sin[3\ t] -
                1\/4\ Cos[5\ t]\ Sin[3\ t])\)\)\/\(10 +
            Cos[p0 + \(2\ \[Pi]\)\/3]\) +
        \(5\ \@2\
            \((Cos[2\ t] + Cos[3\ t] + 1\/4\ Cos[2\ t]\ Cos[3\ t] +
                1\/4\ Cos[3\ t]\ Cos[5\ t])\)\
            Sin[\(2\ \[Pi]\ w\)\/25]\)\/\(10 + Cos[p0]\) -
        \(\((10 + Cos[p0])\)\ \((10 + Cos[p0 + \(2\ \[Pi]\)\/3])\)\
            \((1\/4\ Sin[3\ t] + 1\/4\ Sin[5\ t])\)\
            Sin[\(2\ \[Pi]\ w\)\/25]\)\/\(25\ \@2\),
      \(5\ \((Cos[2\ t] + Cos[3\ t] + 1\/4\ Cos[2\ t]\ Cos[3\ t] +
                1\/4\ Cos[3\ t]\ Cos[5\ t])\)\
            \((1 - Cos[\(2\ \[Pi]\ w\)\/25])\)\)\/\(10 + Cos[p0]\) +
        1\/50\ \((10 + Cos[p0])\)\ \((10 + Cos[p0 + \(2\ \[Pi]\)\/3])\)\
          \((1 + Cos[\(2\ \[Pi]\ w\)\/25])\)\
          \((1\/4\ Sin[3\ t] + 1\/4\ Sin[5\ t])\) +
        \(5\ \@2\
            \((Sin[2\ t] + 1\/4\ Cos[3\ t]\ Sin[2\ t] - Sin[3\ t] -
                1\/4\ Cos[5\ t]\ Sin[3\ t])\)\
            Sin[\(2\ \[Pi]\ w\)\/25]\)\/\(10 + Cos[p0 + \(2\ \[Pi]\)\/3]\)}
      \)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(nn = Floor[pl*70/13.44370389666515]\)], "Input"],

Cell[BoxData[
    \(180\)], "Output"]
}, Open  ]],

Cell[BoxData[
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          RowBox[{"ParametricPlot3D", "[",
            RowBox[{
            "xyz", ",", \({t, \(-Pi\), Pi}\), ",", \({p0, \(-Pi\), Pi}\),
              ",", " ", \(PlotPoints -> {nn, 20}\), ",",
              \(PlotRange -> All\), ",",
             
              StyleBox[
                \(LightSources\  ->
                  \ {{{0, \ 0, \ 1}, \ RGBColor[0, \ 1, \ 0]}, \n
                    \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {{1, \ 0, \ 0.4}, \
                      RGBColor[1, \ 0, \ 0]}, \n
                    \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {{0, \ 1, \ 0.4}, \
                      RGBColor[0, \ 0, \ 1]}}\),
                "Input\[CenterDot]"],
              StyleBox[",",
                "Input\[CenterDot]"],
              StyleBox[\(Axes -> False\),
                "Input\[CenterDot]"],
              StyleBox[",",
                "Input\[CenterDot]"],
              StyleBox[\(Boxed -> False\),
                "Input\[CenterDot]"]}], "]"}], ",", \({w, 0, 25}\)}],
        "]"}]}]], "Input"]
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]


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Cell[5525, 170, 1110, 26, 75, "Input"]
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End of Mathematica Notebook file.
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news wrote:

>THere is a MovieParametricPlot in 2-D, but is there a MovieParametricPlot in 
>3D also? Or someother way of making it from existing Mathematica functions?
>
>  
>
Respectfully, Roger L. Bagula

tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn at netscape.net
URL :  http://home.earthlink.net/~tftn



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