I'm still thinking about using different multiples for the angles to get a more symmetric power 2-ish Mbulb.
However I noticed a problem with the direct variant, there:
If you just use [r²;2phi;8theta]+c, you don't actually have the "correct" radius for each angle.
So, instead, I thought, an elliptical "radius" could be used.
trying a bit around, I came to a radius formula, entirely dependend on theta, which basically tells you, at which angle of theta the radius is exponentiated how strong, if that makes any sense...
The formula is derived from the parametric coordinates of a rotational ellipsoid, being rotated around the z-axis. It returns values between 2 and 8, with 2 being for theta = 0 (so, the triplex number is a complex number with the second imaginary part = 0) and 8 for theta = +/-pi/2 (which happens at the two poles, where both the real and the first imaginary parts are 0).
The formula is simple:
[Plot]Now, there are two possible ways to use this:
Either, you just take the angles as usual and use the theta-dependend term as power for r or you also take that term as a factor for theta and phi:
1)
![[r^{\sqrt{34-30 \cos{2 \theta}}};2 \phi;8 \theta]](/cgi-bin/mimetex.cgi?[r^{\sqrt{34-30 \cos{2 \theta}}};2 \phi;8 \theta])
2)
![[r^{\sqrt{34-30 \cos{2 \theta}}}; {\sqrt{34-30 \cos{2 \theta}}} \phi; {\sqrt{34-30 \cos{2 \theta}}} \theta]](/cgi-bin/mimetex.cgi?[r^{\sqrt{34-30 \cos{2 \theta}}}; {\sqrt{34-30 \cos{2 \theta}}} \phi; {\sqrt{34-30 \cos{2 \theta}}} \theta])
plots for the change of r, phi and theta (phi and theta as in example 2)
[Plot r][Plot phi][Plot theta]
September 01, 2015, 01:48:52 PM
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