File:Vector Field on a Sphere.png

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Original file(1,200 × 1,200 pixels, file size: 439 KB, MIME type: image/png)

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This image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}.


It is recommended to name the SVG file “Vector Field on a Sphere.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

Summary

Description
English: The vector field represented by plotted over the unit sphere. Vectors have been uniformly scaled down to 0.2 times their original length for aesthetics. Originally created as an image for the example problem on the divergence theorem page to replace the less relevant image here.
Date
Source Own work
Author Glosser.ca
Other versions
This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}.


It is recommended to name the SVG file “Vector Field on a Sphere.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

Licensing

Public domain 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.

Mathematica 7.0 Source

scaling = 0.2;
stepSize = 1/10;

makeVectors[data_, f_] := Map[{Arrowheads[0.01], Arrow[{#, # + scaling*f @@ #}]} &, data]
upperHemi[x_, y_] := Sqrt[1 - x^2 - y^2]
lowerHemi[x_, y_] := -Sqrt[1 - x^2 - y^2]
f[x_, y_, z_] := {2 x, y^2, z^2}

upperPoints = 
  Flatten[Table[{x, y, upperHemi[x, y]}, {x, -1, 1, 
     stepSize}, {y, -Sqrt[1 - x^2], Sqrt[1 - x^2], stepSize}], 1] ;
lowerPoints = 
  Flatten[Table[{x, y, lowerHemi[x, y]}, {x, -1, 1, 
     stepSize}, {y, -Sqrt[1 - x^2], Sqrt[1 - x^2], stepSize}], 1];

upperVectors = makeVectors[upperPoints, f];
lowerVectors = makeVectors[lowerPoints, f];

Graphics3D[{{Opacity[0.8], Sphere[]}, {Opacity[0.7], 
   upperVectors~Join~lowerVectors}}, ViewPoint -> {Back, Top}, 
 Axes -> True, AxesLabel -> {x, y, z}, LabelStyle -> Directive[Large],
  ImageSize -> {1200, 1200}]

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5 November 2011

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Date/TimeThumbnailDimensionsUserComment
current18:53, 4 November 2011Thumbnail for version as of 18:53, 4 November 20111,200 × 1,200 (439 KB)Rayhem

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