Image:Paraboloid of Revolution.png

[edit] Summary

Description	A 3D rendering of the paraboloid given parametrically by:
Source	Self-made, using Mathematica 5.1.
Date	12/04/2007
Author	Inductiveload
Permission (Reusing this image)	This image is ineligible for copyright and therefore in the public domain, because it consists entirely of information that is common property and contains no original authorship. العربية | Afrikaans | Български | Bosanski | Česky | Dansk | Deutsch | English | Esperanto | Español | Français | हिन्दी | Italiano | 日本語 | 한국어 | Magyar | Nederlands | ‪Norsk (nynorsk)‬ | Polski | Português | Русский | Svenska | Türkçe | ‪中文(繁體)‬ | ‪中文(简体)‬ | +/-

[edit] Mathematica Code

This code does not require any modules to be loaded. It uses Chris Hill's Anti-aliasing code.

gr = ParametricPlot3D[
      {Sqrt[u]Cos[v], Sqrt[u]Sin[v], u, {EdgeForm[AbsoluteThickness[4]]}},
      {u, 0, 1},
      {v, 0, 2π},
      BoxRatios -> {1, 1, 0.8},
      PlotPoints -> {10, 50},
      Ticks -> False,
      Axes -> False,
      Boxed -> False,
      ImageSize -> 800];

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[[2]] - 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[[2]]/kersiz}}, ImageSize -> is, AspectRatio -> 
      ar]
    ]
finalgraphic = aa[gr]

• Paraboloid