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File:Moebius Surface 1 Display Small.png

Moebius_Surface_1_Display_Small.png(180 × 140 pixels, file size: 16 KB, MIME type: image/png)
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Description A moebius strip parametrized by the following equations:
x = \cos u + v\cos\frac{nu}{2}\cos u
y = \sin u + v\cos\frac{nu}{2}\sin u
z = v\sin\frac{nu}{2},

where n=1.

This plot is for display purposes by itself as a thumbnail. If you are looking for the image that is part of the sequence from n=0 to 1, see below for the other verison, along with a larger version (800px) of this image
Date 19 June 2007
Source Self-made, with Mathematica 5.1
Icon Mathematical Plot.svg
This mathematical image was created with Mathematica.
Author Inductiveload
( Reusing this file)
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Icon Mathematical Plot.svg      Mathematical Function Plot
Description Moebius Strip, 1 half-turn (n=1)
Equation :x = \cos u + v\cos\frac{nu}{2}\cos u
y = \sin u + v\cos\frac{nu}{2}\sin u
z = v\sin\frac{nu}{2}
Co-ordinate System Cartesian ( Parametric Plot)
u Range 0 .. 4π
v Range 0 .. 0.3

Mathematica Code

Nuvola apps important.svg Please be aware that at the time of uploading (15:27, 19 June 2007 (UTC)), this code may take a significant amount of time to execute on a consumer-level computer. Integrated circuit icon.svg
Antialias Icon.svg This uses Chris Hill's antialiasing code to average pixels and produce a less jagged image. The original code can be found here. Icon Mathematical Plot.svg

This code requires the following packages:

MoebiusStrip[r_:1] =
      {u, v, n},
      r {Cos[u] + v Cos[n u/2]Cos[u],
          Sin[u] + v Cos[n u/2]Sin[u],
          v Sin[n u/2],

aa[gr_] := Module[{siz, kersiz, ker, dat, as, ave, is, ar},
    is = ImageSize /. Options[gr, ImageSize];
    ar = AspectRatio /. Options[gr, AspectRatio];
    If[! NumberQ[is], is = 288];
    kersiz = 4;
    img = ImportString[ExportString[gr, "PNG", ImageSize -> (
      is kersiz)], "PNG"];
    siz = Reverse@Dimensions[img[[1, 1]]][[{1, 2}]];
    ker = Table[N[1/kersiz^2], {kersiz}, {kersiz}];
    dat = N[img[[1, 1]]];
    as = Dimensions[dat];
    ave = Partition[Transpose[Flatten[ListConvolve[ker, dat[[All, All, #]]]] \
& /@ Range[as[[3]]]], as[] - kersiz + 1];
    ave = Take[ave, Sequence @@ ({1, Dimensions[ave][[#]], 
    kersiz} & /@ Range[Length[Dimensions[ave]] - 1])];
    Show[Graphics[Raster[ave, {{0, 0}, siz/kersiz}, {0, 255}, ColorFunction ->
     RGBColor]], PlotRange -> {{0, siz[[1]]/kersiz}, {
  0, siz[]/kersiz}}, ImageSize -> is, AspectRatio -> ar]

deg = 1;
gr = ParametricPlot3D[Evaluate[MoebiusStrip[][u, v, deg]],
      {u, 0, 4π},
      {v, 0, .3},
      PlotPoints -> {99, 3},
      PlotRange -> {{-1.3, 1.3}, {-1.3, 1.3}, {-0.7, 0.7}},
      Boxed -> False,
      Axes -> False,
      ImageSize -> 220,
      PlotRegion -> {{-0.22, 1.15}, {-0.5, 1.4}},
      DisplayFunction -> Identity
finalgraphic = aa[gr];

Export["Moebius Surface " <> ToString[deg] <> ".png", finalgraphic]
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