File:Paraboloid of Revolution.png

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Summary[edit]

DescriptionParaboloid of Revolution.png	A 3D rendering of the paraboloid given parametrically by: ${\displaystyle x={\sqrt {u}}\cos(v)\,}$ ${\displaystyle y={\sqrt {u}}\sin(v)\,}$ ${\displaystyle z=u\,}$
Date	12 April 2007 (upload date)
Source	Self-made, using Mathematica 5.1.
Author	Inductiveload
Permission (Reusing this file)	Public domainPublic domainfalsefalse This work 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.

Mathematica Code[edit]

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]