File:Sine of distance from origin negative.png

DescriptionSine of distance from origin negative.png	A 3D surface plot of the negative of the sine of distance from the origin: ${\displaystyle u=-\sin \left({\sqrt {x^{2}+y^{2}}}\right)}$. This represents the displacement for a point source in 2D, with no attenuation due to distance.
Date	13 June 2007
Source	Self-Made with Mathematica   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	Negative of the sine of the distance from the origin
Equation	${\displaystyle u=-\sin \left({\sqrt {x^{2}+y^{2}}}\right)}$
Co-ordinate System	Cartesian
X Range	-2π .. 2π
Y Range	-2π .. 2π

Mathematica Code[edit]

Please be aware that at the time of uploading (21:24, 13 June 2007 (UTC)), this code may take a significant amount of time to execute on a consumer-level computer.

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

\!\(gr = Plot3D[\[IndentingNewLine]Sin[Sqrt[x^2 + 
      y^2]], \[IndentingNewLine]{x, \(-2\)\ Pi, 2  Pi}, \[IndentingNewLine]{
      y, \(-2\)\ Pi, 2  
      Pi}, \[IndentingNewLine]PlotPoints -> 600, \[IndentingNewLine]Mesh -> 
      False, \[IndentingNewLine]BoxRatios -> {4,
             4, 1}, \[IndentingNewLine]Axes -> True, \[IndentingNewLine]Boxed \
-> True, \[IndentingNewLine]AxesLabel -> {"\<x\>", "\<y\>", 
      "\<u\>"}, \[IndentingNewLine]Ticks -> {\[IndentingNewLine]{\
\[IndentingNewLine]{\(-2\) 
      Pi, \(-2\) π, 0.01, {AbsoluteThickness[4]}}, \[IndentingNewLine]{\(-
      Pi\), \(-π\), 0.01, {AbsoluteThickness[4]}}, \[IndentingNewLine]{0, 0, 
      0.01, {AbsoluteThickness[4]}}, \[IndentingNewLine]{Pi, π, 0.01, {
      AbsoluteThickness[
      4]}}, \[IndentingNewLine]{2  
        Pi, 2  π, 0.01, {AbsoluteThickness[4]}}\[IndentingNewLine]}, \
\[IndentingNewLine]{\[IndentingNewLine]{\(-2\) 
        Pi, \(-2\) π, 0.01, {AbsoluteThickness[
          4]}}, \[IndentingNewLine]{\(-Pi\), \(-π\), 
            0.01, {AbsoluteThickness[
      4]}}, \[IndentingNewLine]{0, 0, 0.01, {
        AbsoluteThickness[4]}}, \[IndentingNewLine]{Pi, π, 0.01, \
{AbsoluteThickness[4]}}, \[IndentingNewLine]{2  Pi, 2  π, 0.01, {
            AbsoluteThickness[
            4]}}\[IndentingNewLine]}, \
\[IndentingNewLine]{\[IndentingNewLine]{\(-1\), \(-1\), 
                  0.01, {AbsoluteThickness[4]}}, \[IndentingNewLine]{0, 0, 
          0.01, {AbsoluteThickness[
          4]}}, \[IndentingNewLine]{1, 1, 0.01, {
            AbsoluteThickness[4]}}\[IndentingNewLine]}\[IndentingNewLine]}, \
\[IndentingNewLine]TextStyle -> {FontSize -> 
            40}, \[IndentingNewLine]BoxStyle -> {AbsoluteThickness[4]}, \
\[IndentingNewLine]ImageSize -> 200, \[IndentingNewLine]]\[IndentingNewLine]\
\[IndentingNewLine]
  aa[gr_] := Module[{siz, kersiz, ker, dat, as, ave, is,
                   ar}, \[IndentingNewLine]is = ImageSize /. Options[gr, \
ImageSize]; \[IndentingNewLine]ar = AspectRatio /. Options[gr, 
      AspectRatio]; \[IndentingNewLine]If[\(! NumberQ[is]\), is = 288]; \
\[IndentingNewLine]kersiz = 
                      4; \[IndentingNewLine]img = \
ImportString[ExportString[gr, "\<PNG\>", ImageSize -> \((is\ 
      kersiz)\)], 
        "\<PNG\>"]; \[IndentingNewLine]siz = Reverse@\(Dimensions[img[\([1, 
                1]\)]]\)[\([{1, 2}]\)]; \[IndentingNewLine]ker = 
      Table[N[1/
        kersiz\^2], {kersiz}, {kersiz}]; \[IndentingNewLine]dat = N[img[\([
          1, 1]\)]]; \[IndentingNewLine]as = Dimensions[
      dat]; \[IndentingNewLine]ave = 
          Partition[Transpose[\(Flatten[ListConvolve[ker, dat[\([All, 
      All, #]\)]]] &\) /@ Range[as[\([3]\)]]], as[\([2]\)] - kersiz + 
      1]; \[IndentingNewLine]ave = 
      Take[ave, 
        Sequence @@ \((\({1, \(Dimensions[ave]\)[\([#]\)], kersiz} &\) /@
                   Range[Length[Dimensions[
                    ave]] - 1])\)]; \
\[IndentingNewLine]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]\[IndentingNewLine]]\[IndentingNewLine]
  finalgraphic = aa[gr]\)