AlexLens wrote:
>>  Making a lens out of a lathe works very poorly. The reason is that
>> none of the available spline types will give you a G2-continuous [*]
>> connection on the control points. However G2-continuity is essential
>> to optical surface design.
>>
>>  Since most lenses are modeled with polynomials anyway, I would
>> advise you to use an isosurface with the corresponding polynomial.
>>
>>   Jerome
>>
>> [*]
>> http://en.wikipedia.org/wiki/Geometric_continuity#Geometric_continuity

>> --
>> mailto:jeb### [at] freefr
>> http://jeberger.free.fr
>> Jabber: jeb### [at] jabberfr
> -----------------------------------------------------------------------
--------
> 
> Thanks for the reply!
> 
> I had no clue the cubic splines were not G2 continuous as they usually 
are.  The
> documentation page for the cubic spline makes it seem like it is necess
arily G1
> continuous, however.  I'm guessing that POV-Ray only needs to know the 
first
> derivative to know how a photon would interact with a surface, so this 
method
> still should work.
> 
	Note that you example used quadratic splines, not cubic... However,
even cubic spline is not G2 continuous (it is C2, but the 2nd
derivative is 0 on the control points, which breaks the G2
property). It is indeed G1 and pov will have no problem knowing how
a photon interacts with the surface. The reason you need G2
continuity isn't because of POV, but because of physics: the focal
point is different on either side of a non G2 point and the
difference is then amplified as the light travels away from the
surface, which quickly makes for very big differences.

> As for the Isosurface, I don't have an analytic function to input to PO
V-Ray, so
> maybe that wouldn't work?
> 
	No, if you can't get an analytic function it won't work. Where do
your spline control points come from?

> What do you all recommend as the fastest method to make this lens just 
given the
> numerical data I have?
> 
	I did some research a couple of years ago on how to connect Bezier
curves in a G2 way. I can try to dig it up if you are interested.
However, IIRC the constraints it imposes on the curve mean that you
probably won't be able to use it.

		Jerome
-- 
mailto:jeb### [at] freefr
http://jeberger.free.fr
Jabber: jeb### [at] jabberfr

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