File:R sin(theta) Surface Plot.png
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![File:R sin(theta) Surface Plot.png](https://upload.wikimedia.org/wikipedia/commons/thumb/5/55/R_sin%28theta%29_Surface_Plot.png/740px-R_sin%28theta%29_Surface_Plot.png?20070826155343)
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DescriptionR sin(theta) Surface Plot.png | Polar surface plot of r sin(θ) | |||
Date | ||||
Source |
self-made ![]() This diagram was created with Mathematica. |
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Author | Inductiveload | |||
Permission (Reusing this file) |
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![]() | |
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Description | Ploar Surface Plot of r sin(θ) |
Equation | |
Co-ordinate System | Polar |
r Range | 0 .. 1 |
θ Range | -0 .. 2π |
Mathematica Code
[edit]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]
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 15:53, 26 August 2007 | ![]() | 800 × 648 (72 KB) | Inductiveload (talk | contribs) | |
15:05, 26 August 2007 | ![]() | 800 × 648 (100 KB) | Inductiveload (talk | contribs) | {{Information |Description=Polar surface plot of r sin(θ) |Source=self-made {{Mathematica}} |Date=26/08/2007 |Author= Inductiveload |Permission = {{PD-self}} }} {| class=prettytable !colspan=2|[[Image:Icon Mathematical Plot.s |
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