I used metallographic techniques to determine the volume fraction of
space which is filled by the surface.  The nonzero volume fraction at a
threshold of zero explains the plateaus we saw in the Mega 0.0-0.4
noise3d function.

I ran the same file in both Mega 0.4 and Mega 0.5.

Note that simply switching the version statement in Mega 0.5 did not
give me the old noise3d function. Thus, the "original" noise3d is lost
in version 0.5.


#version unofficial MegaPov 0.4;  /0.5;
#include "colors.inc"
#include "textures.inc"
#include "stones.inc"
#include "metals.inc"

camera{
        location <0,40,-27.5>
        look_at 0 //  <9,24,2>
        angle 25
        }
background {White}
light_source {<0, 390, 0> color White}
#declare rag=.01;

#declare threshy=0;
#while (threshy<1)

#declare B=
isosurface{
        function{ noise3d(x/rag,y/rag,z/rag)}//&(y-.00001)&(-y-.001)}
         accuracy .001
         threshold threshy //  .40    //  8
         contained_by      {  box{<-10,0,-10>,<10,0.00001,10>}       }
          bounded_by      {  box{-10,10}       }
        pigment{Red + Green/2.5}
        finish{ambient 0.15}
          }

#declare minxyz=<-10,0,-10>;// +<min_extent(B);
#declare maxxyz=<10,0,10>;// +max_extent(B);
#declare nnxmax=60;
#declare nnzmax=nnxmax;

#declare nymin=100000;
#declare numsects=0;
#declare nnx=0;
#declare nnz=0;
#while(nnx<nnxmax)
#while(nnz<nnzmax)

#declare testy=<0,0,0>;
#declare Norm=<0,0,0>;

#declare
trial=trace(B,<minxyz.x+(maxxyz.x-minxyz.x)/nnxmax*nnx,-1000,minxyz.z+(maxxyz.z-minxyz.z)/nnzmax*nnz>,y,Norm);

#if (Norm.x = 0 & Norm.y = 0 & Norm.z = 0)
                //we found an open path!
        #else
                        #declare numsects=numsects+1; //nymin=trial.y;

#end

#declare nnz=nnz+1;
#end
#declare nnz=0;
#declare nnx=nnx+1;
#end
                        //#debug "\n"
                       #debug str(threshy,5,3)
                        #debug  "   "
                        #debug str(numsects/nnzmax/nnzmax,5,4)
                        #debug "\n"

#declare threshy=threshy+0.025;
//nnxmax=nnxmax+1;
#end
object {B}

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Attachments:
Download 'noise3d.jpg' (39 KB)

Preview of image 'noise3d.jpg'

Greg M. Johnson <gre### [at] my-dejanewscom> wrote...
> I used metallographic techniques to determine the volume fraction of
> space which is filled by the surface.  The nonzero volume fraction at a
> threshold of zero explains the plateaus we saw in the Mega 0.0-0.4
> noise3d function.
>
> I ran the same file in both Mega 0.4 and Mega 0.5.
>
> Note that simply switching the version statement in Mega 0.5 did not
> give me the old noise3d function. Thus, the "original" noise3d is lost
> in version 0.5.

That is odd.

This is very interesting info, although I think that your graphs might be
mis-labeled (maybe the red line should be 0.4 and the black line 0.5).

-Nathan

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Nathan Kopp wrote:

> This is very interesting info, although I think that your graphs might be
> mis-labeled (maybe the red line should be 0.4 and the black line 0.5).

"The nonzero volume fraction at a threshold of zero explains the plateaus we
saw in the Mega 0.0-0.4 noise3d function."

--
David Fontaine     <dav### [at] faricynet>     ICQ 55354965
Please visit my website: http://www.faricy.net/~davidf/

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David Fontaine <dav### [at] faricynet> wrote...
> Nathan Kopp wrote:
>
> > This is very interesting info, although I think that your graphs might
be
> > mis-labeled (maybe the red line should be 0.4 and the black line 0.5).
>
> "The nonzero volume fraction at a threshold of zero explains the plateaus
we
> saw in the Mega 0.0-0.4 noise3d function."
>

Yes, I read that, but I still stick with my original opinion.  I think that
the flat, clipped, sections of the red line are what explain the plateaus
from the original noise3d.  The non-zero volume fraction at a zero thershold
for the black line would demonstrate that the range of noise3d is not yet
perfect, but it is missing in the other direction.

-Nathan

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>> "The nonzero volume fraction at a threshold of zero explains the plateaus
>we
>> saw in the Mega 0.0-0.4 noise3d function."
>>
>
>Yes, I read that, but I still stick with my original opinion.  I think that
>the flat, clipped, sections of the red line are what explain the plateaus
>from the original noise3d.
>

If the graph shows how much space is filled when a certain threshold is
used, e.g. it shows how many output-values of that value is used, the red
line should not be the one for version 0.5. Let's say the threshold is 0.
Then the graph at x-value 0 would show zero if the function had no plateaus,
because if it _had_ such plateaus, then space would be filled at threshold
zero. If the function had no plateaus, there would be no (very few)
output-values at zero. Therefore, no space should be filled. My point is:
the graphs must be correct.

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Simen Kvaal <sim### [at] studentmatnatuiono> wrote...
>
> If the graph shows how much space is filled when a certain threshold is
> used, e.g. it shows how many output-values of that value is used, the red
> line should not be the one for version 0.5. Let's say the threshold is 0.
> Then the graph at x-value 0 would show zero if the function had no
plateaus,
> because if it _had_ such plateaus, then space would be filled at threshold
> zero. If the function had no plateaus, there would be no (very few)
> output-values at zero. Therefore, no space should be filled. My point is:
> the graphs must be correct.
>

Doh.  You are correct.  I was looking at the problem totally backwards.

-Nathan

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It DOES beg the question, however, as to whether we could get a function which
is linear, or

volumefractfilled= threshold.


Nathan Kopp wrote:

> Simen Kvaal <sim### [at] studentmatnatuiono> wrote...
> >
> > If the graph shows how much space is filled when a certain threshold is
> > used, e.g. it shows how many output-values of that value is used, the red
> > line should not be the one for version 0.5. Let's say the threshold is 0.
> > Then the graph at x-value 0 would show zero if the function had no
> plateaus,
> > because if it _had_ such plateaus, then space would be filled at threshold
> > zero. If the function had no plateaus, there would be no (very few)
> > output-values at zero. Therefore, no space should be filled. My point is:
> > the graphs must be correct.
> >
>
> Doh.  You are correct.  I was looking at the problem totally backwards.
>
> -Nathan

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Nathan Kopp wrote:

> Yes, I read that, but I still stick with my original opinion.  I think that
> the flat, clipped, sections of the red line are what explain the plateaus
> from the original noise3d.  The non-zero volume fraction at a zero thershold
> for the black line would demonstrate that the range of noise3d is not yet
> perfect, but it is missing in the other direction.

Oh! Of course. I think you're right.

--
David Fontaine     <dav### [at] faricynet>     ICQ 55354965
Please visit my website: http://www.faricy.net/~davidf/

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