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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Am 14.06.2010 21:30, schrieb AlexLens:

> Right now I am trying to intersect it with a plane to bound the flat side of the
> lens.  Is that how you would close this?

No, you'll really need to close the lathe object itself, by placing both 
the first and last point on the axis.

> Also, are some of my settings unnecessary, it seems to be taking longer than I
> would expect it to..maybe this method overall is not the best way to implement
> this lens from data points?

I'd suggest linear spline; with that many data points, it shouldn't make 
any noticeable difference in precision, and you'll have a much easier 
job closing it with a plane.

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AlexLens wrote:

> What do you all recommend as the fastest method to make this lens just given the
> numerical data I have?

I'd check first whether the (closed) lathe provides result
which are good enough for your purposes. Although not having
G2 properties for the spline has the mentioned problems, the
effect may be small since you have a lot of data points and
the focal point changes in between might be limited by that.

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