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From: AlexLens
Subject: Lens Design: CSG Intersection vs Lathe Object
Date: 14 Jun 2010 12:35:01
Message: <web.4c16590c40a0687f444cd8050@news.povray.org>
Hi all,

I'm playing around with POV-Ray to make two plano-convex lenses, at first with a
CSG intersection, and then with numerically calculated data points rotated 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 actually
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 quadratic
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!!!


//--------------------------------START OF POVRAY CODE-------------------------
#include "colors.inc"
#include "textures.inc"
#include "glass.inc"

global_settings
{
    photons
    {
        spacing .01
        autostop 0
        media 100
    }
}


camera
{
      location <10,1,0>
      angle 60
      look_at <0,1,0>
}


//--------------------------------PLANO CONVEX LENS-----------------------------
#declare R   = 6.0;   //sphere radius
#declare Over= 0.0839202690038387;   //sphere overlappingg
intersection{
 sphere{<0,0,0>,R  translate <0,0,R-Over>}

 plane
 {z,0

 }

  texture
  {
    pigment {color Clear}
    finish
    {
        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 on
    refraction on
    collect off
 }
 hollow
 translate < 0,1,0>

 }

//--------------------------------LIGHT BACK STOP-------------------------------
box
{
    <5,5,.05>,<-5,-5,-.05>
    pigment
    {
        color Black
    }
    finish
    {

     phong 1
     phong_size 1
    }
    photons
    {
        collect on
    }
translate <0,1,-12.05>
}

//--------------------------------LASER LIGHT GRID------------------------------
//Provides grid of lasers to be refracted by lens

#for(j,-.7,.7,.1)
#for(i, -.7,.7,.1)
light_source
{
    <j,1+i,100>
    rgb <1,1,1>
    cylinder
    parallel
    point_at <j,1+i,0>
    //radius 1
    tightness 0
    falloff .01
    photons
    {
        reflection on
        refraction on
    }
}

#end
#end


//--------------------------------SCATTERING MEDIA------------------------------
//makes possible the visualization of light from a side angle
#declare transparent_with_media = material{
texture {pigment { White filter 1 }}
interior{
media {
method 3
intervals 1
samples 50, 1000
scattering {
1 , rgb 1*<0.1, 0.1, 0.1> // isotropic scattering
extinction 0.000001
}
}
}
}

box { <-50,-10,-50> <50,10,50>
material {transparent_with_media}
hollow
photons
{
    pass_through
}
}


Post a reply to this message

From: AlexLens
Subject: Re: Lens Design: CSG Intersection vs Lathe Object
Date: 14 Jun 2010 12:45:01
Message: <web.4c165be84fd62214444cd8050@news.povray.org>
ahh sorry! The interior statement has a negative ior in what I posted, but the
picture was generated with a positive IOR (+1.5).

So, the problem still remains..!


Post a reply to this message

From: Alain
Subject: Re: Lens Design: CSG Intersection vs Lathe Object
Date: 14 Jun 2010 12:56:26
Message: <4c165f3a$1@news.povray.org>

> Hi all,
>
> I'm playing around with POV-Ray to make two plano-convex lenses, at first with a
> CSG intersection, and then with numerically calculated data points rotated 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 actually
> 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 quadratic
> 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!!!
>

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



Alain


Post a reply to this message

From: AlexLens
Subject: Re: Lens Design: CSG Intersection vs Lathe Object
Date: 14 Jun 2010 13:20:00
Message: <web.4c1663914fd62214444cd8050@news.povray.org>
> 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>,
<0.981,0.0108315752>,
<0.980,0.0113940582>,
<0.979,0.0119557865>,
<0.978,0.0125167606>,
<0.977,0.0130769814>,
<0.976,0.0136364496>,
<0.975,0.0141951659>,
<0.974,0.0147531311>,
<0.973,0.0153103457>,
<0.972,0.0158668106>,
<0.971,0.0164225265>,
<0.970,0.0169774941>,
<0.969,0.0175317141>,
<0.968,0.0180851871>,
<0.967,0.0186379140>,
<0.966,0.0191898955>,
<0.965,0.0197411321>,
<0.964,0.0202916247>,
<0.963,0.0208413739>,
<0.962,0.0213903805>,
<0.961,0.0219386451>,
<0.960,0.0224861684>,
<0.959,0.0230329511>,
<0.958,0.0235789940>,
<0.957,0.0241242976>,
<0.956,0.0246688627>,
<0.955,0.0252126900>,
<0.954,0.0257557802>,
<0.953,0.0262981339>,
<0.952,0.0268397518>,
<0.951,0.0273806347>,
<0.950,0.0279207831>,
<0.949,0.0284601978>,
<0.948,0.0289988794>,
<0.947,0.0295368286>,
<0.946,0.0300740461>,
<0.945,0.0306105326>,
<0.944,0.0311462886>,
<0.943,0.0316813149>,
<0.942,0.0322156122>,
<0.941,0.0327491811>,
<0.940,0.0332820222>,
<0.939,0.0338141363>,
<0.938,0.0343455239>,
<0.937,0.0348761858>,
<0.936,0.0354061226>,
<0.935,0.0359353349>,
<0.934,0.0364638234>,
<0.933,0.0369915888>,
<0.932,0.0375186316>,
<0.931,0.0380449526>,
<0.930,0.0385705523>,
<0.929,0.0390954315>,
<0.928,0.0396195907>,
<0.927,0.0401430306>,
<0.926,0.0406657518>,
<0.925,0.0411877551>,
<0.924,0.0417090409>,
<0.923,0.0422296100>,
<0.922,0.0427494629>,
<0.921,0.0432686003>,
<0.920,0.0437870229>,
<0.919,0.0443047312>,
<0.918,0.0448217258>,
<0.917,0.0453380075>,
<0.916,0.0458535768>,
<0.915,0.0463684343>,
<0.914,0.0468825807>,
<0.913,0.0473960166>,
<0.912,0.0479087425>,
<0.911,0.0484207592>,
<0.910,0.0489320671>,
<0.909,0.0494426670>,
<0.908,0.0499525594>,
<0.907,0.0504617450>,
<0.906,0.0509702243>,
<0.905,0.0514779979>,
<0.904,0.0519850665>,
<0.903,0.0524914307>,
<0.902,0.0529970909>,
<0.901,0.0535020480>,
<0.900,0.0540063024>,
<0.899,0.0545098547>,
<0.898,0.0550127056>,
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<0.886,0.0609924156>,
<0.885,0.0614862007>,
<0.884,0.0619792925>,
<0.883,0.0624716916>,
<0.882,0.0629633985>,
<0.881,0.0634544138>,
<0.880,0.0639447381>,
<0.879,0.0644343719>,
<0.878,0.0649233158>,
<0.877,0.0654115703>,
<0.876,0.0658991361>,
<0.875,0.0663860137>,
<0.874,0.0668722036>,
<0.873,0.0673577064>,
<0.872,0.0678425226>,
<0.871,0.0683266529>,
<0.870,0.0688100977>,
<0.869,0.0692928576>,
<0.868,0.0697749332>,
<0.867,0.0702563250>,
<0.866,0.0707370335>,
<0.865,0.0712170594>,
<0.864,0.0716964031>,
<0.863,0.0721750652>,
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<0.861,0.0731303468>,
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<0.859,0.0740829084>,
<0.858,0.0745581706>,
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<0.853,0.0769243166>,
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<0.849,0.0788050674>,
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<0.010,0.2679241923>,
<0.009,0.2679289423>,
<0.008,0.2679331924>,
<0.007,0.2679369424>,
<0.006,0.2679401924>,
<0.005,0.2679429424>,
<0.004,0.2679451924>,
<0.003,0.2679469424>,
<0.002,0.2679481924>,
<0.001,0.2679489424>

  texture
  {
    pigment {color Clear}
    finish
    {
        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>
    rgb <1,1,1>
    cylinder
    parallel
    point_at <j,1+i,0>
    //radius 1
    tightness 0
    falloff .005
    photons
    {
        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
{
    pass_through
}
}


Post a reply to this message

From: "Jérôme M. Berger"
Subject: Re: Lens Design: CSG Intersection vs Lathe Object
Date: 14 Jun 2010 14:05:52
Message: <4c166f80$1@news.povray.org>
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


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From: clipka
Subject: Re: Lens Design: CSG Intersection vs Lathe Object
Date: 14 Jun 2010 14:30:24
Message: <4c167540$1@news.povray.org>
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

From: clipka
Subject: Re: Lens Design: CSG Intersection vs Lathe Object
Date: 14 Jun 2010 14:34:56
Message: <4c167650$1@news.povray.org>
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

From: clipka
Subject: Re: Lens Design: CSG Intersection vs Lathe Object
Date: 14 Jun 2010 15:04:15
Message: <4c167d2f$1@news.povray.org>
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.)


Post a reply to this message

From: AlexLens
Subject: Re: Lens Design: CSG Intersection vs Lathe Object
Date: 14 Jun 2010 15:30:01
Message: <web.4c1682364fd62214444cd8050@news.povray.org>
>  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?


Post a reply to this message

From: AlexLens
Subject: Re: Lens Design: CSG Intersection vs Lathe Object
Date: 14 Jun 2010 15:35:01
Message: <web.4c1683674fd62214444cd8050@news.povray.org>
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?


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