> You only provide code for the intersection case. You forgot to provide
> that for the lathe.

> Alain

Thanks for the fast response!
These files take a long time to run so I will try and create a less
computationally intensive case that still illustrates this problem.

In the meantime, here is the lathe code, it's a bit long so I didn't initially
post it:

//--------------------------------BEGINNING OF POV-RAY CODE---------------------
#include "colors.inc"
#include "textures.inc"
#include "glass.inc"

global_settings
{
    photons
    {
        spacing .001
        autostop 0
        media 500
        max_trace_level 2
    }
}


camera
{
      angle 60
      location <20,1,2>
      look_at <0,1,0>


}

//--------------------------------PLANO-CONVEX LENS LATHE-----------------------
lathe
{
  quadratic_spline
   1000,
  <1.000,0.0000000000>,
<0.999,0.0005769655>,
<0.998,0.0011531620>,
<0.997,0.0017285902>,
<0.996,0.0023032509>,
<0.995,0.0028771448>,
<0.994,0.0034502728>,
<0.993,0.0040226356>,
<0.992,0.0045942339>,
<0.991,0.0051650685>,
<0.990,0.0057351401>,
<0.989,0.0063044496>,
<0.988,0.0068729975>,
<0.987,0.0074407848>,
<0.986,0.0080078121>,
<0.985,0.0085740802>,
<0.984,0.0091395898>,
<0.983,0.0097043417>,
<0.982,0.0102683366>,
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<0.980,0.0113940582>,
<0.979,0.0119557865>,
<0.978,0.0125167606>,
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    {
        ambient 0

        diffuse 0
        specular 0
        roughness 0
        reflection 0

    }

  }
 interior
 {
    ior 1.5
    dispersion 1
    fade_power 0
    fade_distance 0
    fade_color <1,1,1>

 }
 photons
 {
    target
    reflection off
    refraction on
    collect off
 }
hollow
scale 1
sturm

rotate <-90,0,0>
translate <0,1,0>

}


//--------------------------------LIGHT BACK STOP-------------------------------
box
{
    <5,5,.05>,<-5,-5,-.05>
    pigment
    {
        color Black
    }
    finish
    {
    ambient 1
    phong 1
    phong_size .1
    }
    photons
    {
        reflection off
        collect on
    }
translate <0,1,-4.05>
}

//--------------------------------LASER LIGHT GRID------------------------------


#for(j,-.4,.4,.05)
#for(i, -.4,.4,.05)
light_source
{
    <j,1+i,100>
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    {
        reflection off
        refraction on
    }
}

#end
#end

//--------------------------------SCATTERING MEDIA------------------------------
#declare transparent_with_media = material{
texture {pigment { White filter 1 }}
interior{
media {
method 3
intervals 1
samples 100, 1000
scattering {
1 , rgb 1*<0.1, 0.1, 0.1> // isotropic scattering
extinction 0.000001
}
}
}
}

box { <-100,-10,-100> <100,100,100>
material {transparent_with_media}
hollow
photons
{
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}
}

Post a reply to this message

AlexLens wrote:
> Hi all,
> 
> I'm playing around with POV-Ray to make two plano-convex lenses, at fir
st with a
> CSG intersection, and then with numerically calculated data points rota
ted with
> a quadratic spline lathe.
> 
> The problem I'm having now is the plano-convex lens made from a sphere
> intersected with a plane converges light as expected:
> 
> Image 1)    http://img193.imageshack.us/i/planoconvexjpg.jpg/
> 
> But then when I make the lens with a lathe of 1000 data points, it actu
ally
> DIVERGES light, when it should be functionally the same:
> 
> Image 2)   http://img507.imageshack.us/i/planoconvexnumericallin.jpg/
> 
> Here is the POV-Ray source code for the first image (CSG intersections)

> 
> The code for Image 2 is the same as Image 1 except with a lathe with qu
adratic
> spline replacing the CSG intersection.
> 
> Please let me know what you all think could be the reason for this, and
 any
> random tips as well as I'm pretty new to POV-Ray.
> 
> Thanks!!!
> 
	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

Post a reply to this message

Attachments:
Download 'us-ascii' (1 KB)

Am 14.06.2010 19:14, schrieb AlexLens:
>
> In the meantime, here is the lathe code, it's a bit long so I didn't initially
> post it:

What version of POV-Ray are we talking about?

Post a reply to this message

Am 14.06.2010 20:30, schrieb clipka:
> Am 14.06.2010 19:14, schrieb AlexLens:
>>
>> In the meantime, here is the lathe code, it's a bit long so I didn't
>> initially
>> post it:
>
> What version of POV-Ray are we talking about?

(Ah, forget that question - I see you are using #for, so obviously it 
must be 3.7 beta.)

Post a reply to this message

Am 14.06.2010 19:14, schrieb AlexLens:

> In the meantime, here is the lathe code, it's a bit long so I didn't initially
> post it:

Here's your problem:

> //--------------------------------PLANO-CONVEX LENS LATHE-----------------------
> lathe
> {
>    quadratic_spline
>     1000,
>    <1.000,0.0000000000>,
> <0.999,0.0005769655>,
> <0.998,0.0011531620>,
...
> <0.002,0.2679481924>,
> <0.001,0.2679489424>
>
...
> }

Quote from the docs, section 3.4.1.7, "Lathe" (emphasis added):

"The curve is *not* automatically closed, i.e. the first and last points 
are not automatically connected. You will have to do this yourself if 
you want a closed curve. The curve thus defined is rotated about the 
y-axis to form the lathe object, centered at the origin."

As you do not explicitly close the curve, all you get is a surface (the 
curved side), not a solid body - which pretty much messes up reflection 
computations. (When the rays encounter the curved surface, POV-Ray 
thinks they would be /entering/ the object there rather than leaving it, 
having pretty much the same effect as using a planar-convex lens with an 
ior of 0.666 rather than 1.5.)

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>  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 necessarily 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.

As for the Isosurface, I don't have an analytic function to input to POV-Ray, so
maybe that wouldn't work?

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

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clipka <ano### [at] anonymousorg> wrote:
> Am 14.06.2010 19:14, schrieb AlexLens:
>
> > In the meantime, here is the lathe code, it's a bit long so I didn't initially
> > post it:
>
> Here's your problem:
>
> > //--------------------------------PLANO-CONVEX LENS LATHE-----------------------
> > lathe
> > {
> >    quadratic_spline
> >     1000,
> >    <1.000,0.0000000000>,
> > <0.999,0.0005769655>,
> > <0.998,0.0011531620>,
> ...
> > <0.002,0.2679481924>,
> > <0.001,0.2679489424>
> >
> ...
> > }
>
> Quote from the docs, section 3.4.1.7, "Lathe" (emphasis added):
>
> "The curve is *not* automatically closed, i.e. the first and last points
> are not automatically connected. You will have to do this yourself if
> you want a closed curve. The curve thus defined is rotated about the
> y-axis to form the lathe object, centered at the origin."
>
> As you do not explicitly close the curve, all you get is a surface (the
> curved side), not a solid body - which pretty much messes up reflection
> computations. (When the rays encounter the curved surface, POV-Ray
> thinks they would be /entering/ the object there rather than leaving it,
> having pretty much the same effect as using a planar-convex lens with an
> ior of 0.666 rather than 1.5.)
--------------------------------------------------------------------------------
clipka, thanks a lot!

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?

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?

Post a reply to this message

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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