File:Sphere (Shaded).png

DescriptionSphere (Shaded).png	A rendering of a parametrically plotted sphere.
Date	16 February 2007
Source	Own work, drawn in 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.
Other versions	Wireframe Sphere

Parameterisation[edit]

• x₀, y₀, z₀ are constants relating to the position of the sphere
• r is a positive constant governing the radius
• The parameters u and v run from 0 to 2π.

${\displaystyle x=x_{0}+r\sin {u}\cos {v}\,}$

${\displaystyle y=y_{0}+r\sin {u}\sin {v}\,}$

${\displaystyle z=z_{0}+r\cos {u}\,}$

Mathematica source[edit]

 r = 1
 x0 = 0
 y0 = 0
 z0 = 0

 sphere = ParametricPlot3D[
     {x0 + r Sin[u]Cos[v],
      y0 + r Sin[u]Sin[v],
      z0 + r Cos[u]},
    {u, 0, 2Pi},
    {v, 0, 2Pi},
    Boxed -> False,
    Axes -> False,
    PlotPoints -> 50,
    ImageSize -> 800]

This image was then antialised with Chris Hill's code, and the background was erased.