Le 31/08/2013 23:24, Schrodinger nous fit lire :
> I have been trying to plot the d-orbitals for a while on pov-ray because I like
> the better quality. To plot the d-orbitals I used the square of the real
> component of the spherical harmonic. For l = 2 and m = 2 the spherical harmonic
> is Y_{2,2} = \sqrt{15/32\pi}e^{i2\phi}\sin ^2(\theta). Thus we would be plotting
> [Re(Y_{2,2}(\theta,\phi))]^2. The povray code I have thus far looks like this.

> camera { location  <2*R, 2*R, 2*R> look_at <0, 0, 0>}

beware, the ratio of the camera is not adapted to the resolution, it
might distort/compress the view.

Consider adding before look_at:

direction -z
up y
right image_width/image_height*x

> This kind of looks like a d-orbital with the four lobes but it is still not
> right. First the tops of the four lobes are open rather than round and the
> spacing should be greater between them so there are actually angular nodes.
> Right now I'm not sure if this is a problem with povray's internal functions
> that I used in the equation or my math or both. Anyone have some Idea were I'm
> going wrong here? I know there is a built in function to plot a d_{z^2} orbital
> and I would like the results to look like that however I cannot find the code
> that is used to produce it anywhere to use as a reference.

If it's open, maybe you are looking to only a part of it. scale it down...
but indeed, there is no part of your function that depend on r, so it's
just describing an infinite fold.

(f_ph is the Phi elevation/latitude of polar coordinate, f_th is the
longitude, in a sphere/earth with the pole at +/-y ; where is f_r )

From old thread in povray.advanced-users, 13 December 2001, Mike Williams:

> One of the d orbitals is available as the f_quantum(x,y,z,0) function.
> 
> #include "functions.inc"
> isosurface {
>   function {f_quantum(x,y,z,0)}
>         max_gradient 2
>         contained_by {sphere {0,8}}
>         pigment {rgb 1}
> }

but it's the d_z² orbital and it would need a "scale R/8" to match your
scene.

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