Mathematical Function Plot
Description
Sine of the distance from the origin
Equation
u
=
sin
(
x
2
+
y
2
)
{\displaystyle u=\sin \left({\sqrt {x^{2}+y^{2}}}\right)}
Co-ordinate System
Cartesian
X Range
-2π .. 2π
Y Range
-2π .. 2π
Mathematica Code
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]\)
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