How to get a perfect sphere with subd?

[emile_francois]

How to get a perfect sphere with subd ? rebuild mesh ? how ?
would like to have a “lens” cuted from a perfect sphere

thanks !!

[Normand (Jakob Normand)]

Hi @emile_francois
Increase the number of subdivisions in the prompt to get closer to a perfect sphere - although it’ll always be an approximation, you can get quite close.

But if you need a perfect sphere, and the goal is some sort of optical lens, why not just use a nurbs sphere and work from there? My initial thought is, that nurbs are a better fit for something needing that sort of precision.
HTH, Jakob

[emile_francois]

Thanks for your answer @Normand !
I tried by an other way : extrude with subd crv followin the half circle curve. But i don’t know how to close the half-sphere ?

[emile_francois]

Can we start with a nurbs sphere and tranform it into subd to continue ?

[encephalon]

question remains, why would you want to use subD for this? when nurbs would give you exactly what you want.

if you somehow persist on using SubD, here is probably the most simple spherical subd sphere one can get without having to subdivide, honestly i think subdividing it makes it just too complex and is not needed. it might not be a hundred percent but certainly way better than Rhinos own SubD Sphere which is by all means not a sphere at all…, @chuck not sure if you are involved i saw you fiddling on the quadsphere once can that get any better?

my result may be close enough or a good starting point. there are 2 lines in the circle with different length leading to 2 sets of vertex points, those at the center of 4 and those at the center of 3 faces. the key is to get a perfect proportion other than equal between these, keep in mind that i made it manually.

SubD Sphere.3dm (3.9 MB)

[laurent_delrieu]

Hello
For an aspherical miror i used a curve and a revolution. Could be quite the same for a lens.

Simulation of European Extremely Large Telescope ("ELT")

ELT telescope is really huge and exceptional. I tried to model the mirror and then simulate the rays. I don’t think I have the last coefficient for the optics has some of the last coefficients are not the same on the ESO website, but as I need all parameters (see image at the end) I can’t use them. The ray converge to a 10 mm radius, I don’t know if it is correct or if there is a slight error somewhere. Three mirror are aspheric so there are defined by coefficients that link the Z to the radius …

[emile_francois]

sorry i have a lot of question …
I am looking for a perfect surface reflexion, i drew with a curvature curve following the perfect sphere, but cannot get a perfect zebra on the same surface, weird no ?

So i matched curves to draw the half oh the total curve to make a revolve, but the surface isn’t perfect… any tips ? @laurent_delrieu
Lot of thanks !!

[laurent_delrieu]

A perfect zebra needs a very fine render mesh. It will be the same if you just want a render of the effect of the lens. Meshes are used in render tools.
But if you have a custom reflexion refraction tool it could use the surface from Rhino. Hard to say.

If you want to say what it gives with rays. Post a surface I will make some simulations.

[chuck (Chuck Welsh)]

@encephalon I’m not a SubD expert, and have not looked into them very much. I do know that the conversion to non-rational cubic NURBS patches is exact except at extraordinary vertices, so you can’t make a perfect sphere. @pierrec would be a better person for this than I am.

[pierrec (Pierre Cuvilliers)]

@encephalon I can confirm what Chuck said, there is no way to make a perfect sphere in SubD. You cannot make a perfect circle with a SubD curve either, so rotating a SubD approximation of a circle around another one will not give you a perfect SubD sphere either. This might be why you are seeing imperfect reflection lines in your example.

This is true for all software using Catmull-Clark subdivion as its basis for SubD, and as far as I know is true for other subdivision schemes as well.

SubD just cannot represent that shape, just like a non-rational NURBS cannot be a circle. In fact a SubD face is exactly a degree 3, single span, non-rational NURBS surface (except at extraordinary nodes, but that is just a local phenomenon that does not change what I said above).

Rational NURBS surfaces sound like a much better modelling basis for optical surfaces. Why do you want to use a SubD instead?

[emile_francois]

First : thanks to all for answers. I get a perfect zebra on sphere with a torus that i close like a sphere. it works.
Now i have an other question to continue :
i am in top view, and i would like to delete some part of this round sudb objet. but when i delete parts, the circle is deformed. how to keep a perfect circle whitout the global closed subd objet ?

thanks

[pascal (Pascal Golay)]

Hi Emile - in SubD you cannot- the open ends will always straighten out.

-Pascal