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Sunday, July 17, 2011

About spheres in Mathematica

Plotting a sphere in Mathematica is simple.


What really happens ? Another method to plot a sphere is the following. But let's do a circle in 3D first.

ParametricPlot3D[{Cos[t], Sin[t], 0}, {t, 0, 2 \[Pi]}]

We can then simply rotate this circle as follows:

ParametricPlot3D[{Cos[t] Cos[u], Cos[u] Sin[t], Sin[u]}, {t, 0, 2 \[Pi]}, {u, 0, 2 \[Pi] }]

ParemetricPlot3D generates data we can use in Graphics3D:

sphere = First[ ParametricPlot3D[{Cos[t] Cos[u], Cos[u] Sin[t], Sin[u]}, {t, 0, 2 \[Pi]}, {u, 0, 2 \[Pi] }]]

A very large output was generated. Here is a sample of it:
Show Less\[ThinSpace]Show More\[ThinSpace]Show Full Output\[ThinSpace]Set Size Limit...


Note the difference between Sphere[] a Mathematica function, and the variable sphere which we assigned the first element in the list generated by the ParametricPlot3D function.

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