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oblate spheriod
From http://en.wikipedia.org/wiki/Oblate_spheroidal_coordinates I'm given the formulas to compute cartesian coordinates from oblate spheroidal coordinates.
[tex]
\begin{array}{l}
x = a\cosh \mu \,\,\cos \nu \,\,\cos \phi \\
y = a\cosh \mu \,\,\cos \nu \,\,\sin \phi \\
z = a\cosh \mu \,\,\sin \nu \\
\end{array}
[/tex]
But I've got a few questions:
I've written a short block of code to plot an oblate spheroid:
What is μ ? I don't see it defined on Wikipedia's page. I image it is a number that describes how oblate the object is. So I imagine there should be a number I can set it to that gives me a sphere. My guess would be that mu can range from 0 to 1, with one of those limits giving me a sphere.
So I tried it. I see that μ = 0 gives me a straight line, meaning completely oblate, and the larger I set this number, the more spherical the shape becomes. But it seems to become a sphere at μ = 2, contrary to my guess. Any value larger than 2 gives me a larger sphere. Does anyone know exactly what μ is, and what it's range is?
Also, I see Earth described as an oblate spheroid. What is its μ value?
Thanks!
From http://en.wikipedia.org/wiki/Oblate_spheroidal_coordinates I'm given the formulas to compute cartesian coordinates from oblate spheroidal coordinates.
[tex]
\begin{array}{l}
x = a\cosh \mu \,\,\cos \nu \,\,\cos \phi \\
y = a\cosh \mu \,\,\cos \nu \,\,\sin \phi \\
z = a\cosh \mu \,\,\sin \nu \\
\end{array}
[/tex]
But I've got a few questions:
I've written a short block of code to plot an oblate spheroid:
Code:
mu = 0.5
For a = 0 To 100
For nu = 0 To (2*pi) Step 0.02
For phi = 0 To (2*pi) Step 0.02
x = a * cosh(mu) * Cos(nu) * Cos(phi)
y = a * cosh(mu) * Cos(nu) * Sin(phi)
z = a * sinh(mu) * Sin(nu)
Call PlotPoint(x, z)
Next phi
Next nu
Next a
What is μ ? I don't see it defined on Wikipedia's page. I image it is a number that describes how oblate the object is. So I imagine there should be a number I can set it to that gives me a sphere. My guess would be that mu can range from 0 to 1, with one of those limits giving me a sphere.
So I tried it. I see that μ = 0 gives me a straight line, meaning completely oblate, and the larger I set this number, the more spherical the shape becomes. But it seems to become a sphere at μ = 2, contrary to my guess. Any value larger than 2 gives me a larger sphere. Does anyone know exactly what μ is, and what it's range is?
Also, I see Earth described as an oblate spheroid. What is its μ value?
Thanks!