DescriptionR sin(theta) Surface Plot.png	Polar surface plot of r sin(θ)
Date	26 August 2007
Source	self-made   This diagram was created with Mathematica.
Author	Inductiveload
Permission (Reusing this file)	Public domainPublic domainfalsefalse 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.

Mathematical Function Plot
Description	Ploar Surface Plot of r sin(θ)
Equation	${\displaystyle z=r\sin \left(\theta \right)\,}$
Co-ordinate System	Polar
r Range	0 .. 1
θ Range	-0 .. 2π

Mathematica Code

The rationale for this code can be found on Wikibooks, here. Note the it is slightly modified to allow for antialising.

This uses Chris Hill's antialiasing code to average pixels and produce a less jagged image. The original code can be found here.

dtheta = Pi/20;                                     (*Give a radial gridline \
spacing of Pi/20 radians*)
rmax = 1;                                                     (*Define the \
maximum radius*)
dr = rmax/10;                                        (*Give 10 \
circumferential grid lines*)
f[r_, theta_] := r  Sin[theta]; (*This is the function definition*)

data = Table[
      f[r, theta],
      {theta, 0, 2Pi, dtheta},
      {r, 0, rmax, dr}];

gr1 = ListPlot3D[
    data,
    MeshRange -> {{0, rmax}, {0, 2Pi}},
    TextStyle -> {FontSize -> 60},
    BoxStyle -> {AbsoluteThickness[4]},
    MeshStyle -> {AbsoluteThickness[4]},
    AxesLabel -> {"", "", z},
    ImageSize -> 200,
    DisplayFunction -> Identity]

gr2 = Graphics3D[gr1];

substitution = {r_, theta_, z_} -> {r Cos[theta], r Sin[theta], z};
gr3 = ReplaceAll[gr2, p : Polygon[pts_] :> ReplaceAll[p, substitution]]

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]
    ]

aa[gr3]