I noticed that if I make a height field like this...

height_field
{
   function nPoints, nPoints {fn_X(x,0,y)}
   smooth
}

as you increase "nPoints" the normals get messed up somehow (visible easily 
if you have specular or reflection enabled) both with and without "smooth". 
Check the attached images, notice how the grid texture becomes better with 
nPoints at 1000, but then the normals get screwed up.  Is it a bug?

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"scott" <sco### [at] scottcom> schreef in bericht 
news:4ba0aea8@news.povray.org...
>I noticed that if I make a height field like this...
>
> height_field
> {
>   function nPoints, nPoints {fn_X(x,0,y)}
>   smooth
> }
>
> as you increase "nPoints" the normals get messed up somehow (visible 
> easily
> if you have specular or reflection enabled) both with and without 
> "smooth".
> Check the attached images, notice how the grid texture becomes better with
> nPoints at 1000, but then the normals get screwed up.  Is it a bug?
>
>
I am probably wrong, but imo, those are not the normals (no normals defined 
here) but just the detail of the grid becoming smaller. Have you tried 
nPoints=10000?

Thomas

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> I am probably wrong, but imo, those are not the normals (no normals 
> defined here)

I only said that because the problem seems to really show up around the 
specular light rather than in the texturing.  Presumably POV needs to 
somehow calculate the normals internally?

> Have you tried nPoints=10000?

Same problem, just smaller scale (see attached the "smooth" version).  IME 
with mesh modellers the appearance indicates incorrectly calculated normals 
(this type of pattern certainly shouldn't be visible with triangles the size 
of a few pixels).  Anyway, the image seems to get *worse* with more 
elements, shouldn't it be getting better?

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Preview of image 'image2.png'

"scott" <sco### [at] scottcom> schreef in bericht 
news:4ba0d4c3@news.povray.org...
> Same problem, just smaller scale (see attached the "smooth" version).  IME
> with mesh modellers the appearance indicates incorrectly calculated 
> normals
> (this type of pattern certainly shouldn't be visible with triangles the 
> size
> of a few pixels).  Anyway, the image seems to get *worse* with more
> elements, shouldn't it be getting better?
>

 I see what you mean. This goes beyond my capabilities. I suppose that the 
function is generating a kind of mesh-like object, but is that comparable to 
a *real* mesh I wonder? Time for the experts to have their say :-)

Thomas

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> I noticed that if I make a height field like this...
>
> height_field
> {
>   function nPoints, nPoints {fn_X(x,0,y)}
>   smooth
> }
>
> as you increase "nPoints" the normals get messed up somehow (visible 
> easily
> if you have specular or reflection enabled) both with and without 
> "smooth".
> Check the attached images, notice how the grid texture becomes better with
> nPoints at 1000, but then the normals get screwed up.  Is it a bug?

I found the problem.  Height_field values *and normals* are stored as 16 bit 
integers internally at parse time, even if you specify a function pattern as 
I did.  Thus when zooming in (or scaling) you will see the discrete nature 
of these values, the same problem if you use an image.  I did a quick hack 
in the source to use floating point rather than integers, and it seems to 
fix this problem at the cost of memory usage.

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Thomas de Groot schrieb:
> "scott" <sco### [at] scottcom> schreef in bericht 
> news:4ba0d4c3@news.povray.org...
>> Same problem, just smaller scale (see attached the "smooth" version).  IME
>> with mesh modellers the appearance indicates incorrectly calculated 
>> normals
>> (this type of pattern certainly shouldn't be visible with triangles the 
>> size
>> of a few pixels).  Anyway, the image seems to get *worse* with more
>> elements, shouldn't it be getting better?
>>
> 
>  I see what you mean. This goes beyond my capabilities. I suppose that the 
> function is generating a kind of mesh-like object, but is that comparable to 
> a *real* mesh I wonder? Time for the experts to have their say :-)

I suspect an aliasing issue with the Y coordinates.

POV-Ray has three limitations applying to this context:

(1) Smooth height fields use precomputed surface normals, which are 
stored with a precision of 3x16 bits. I don't suspect that this has much 
of an influence though, as this still corresponds to a resolution of 
roughly 0.01 degrees, which shouldn't make any visible difference in 
brightness.

(2) The surface normals are not precomputed from the original source, 
but from the Y coordinate data as stored in the height field's internal 
data structure. As this data structure holds the Y coordinate values 
using 16-bit integers, giving a precision of no more than 1/65535, 
terracing effects may occur, which will obviously "kill" the normal 
smoothing algorithm. At a resolution of 10000 by 10000 samples, this 
will happen wherever the slope is less than about 15% (10000/65535).

Worse yet: As the surface normal depends not on the absolute Y 
coordinates, but rather on coordinate differences, the normals' 
precision directly corresponds not on absolute precision of the Y 
coordinates, but on their precision /relative/ to the Y coordinate 
differences. That is, aliasing problems will already kick in much 
earlier; for instance, even at a resolution of just 1000 by 1000 
samples, a slope of 15% would theoretically give "raw" coordinate 
difference values of 9.83025 (65535*0.15/1000), which due to aliasing of 
the absolute Y values will in practice result in raw Y coordinate 
difference values alternating between 9 and 10; at the default height 
field "aspect ratio" of 1:1:1, this translates to Y coordinate 
difference values of approx. 0.000137 and 0.000153 respectively (9/65535 
and 10/65535), which in turn correspond to normal angles of approx. 7.82 
and 8.68 degrees (atan(1000*9/65535) and atan(1000*10/65535)), respectively.

So at a resolution of 1000x1000 samples, the normals on a 15% slope will 
exhibit "quantization noise" with an amplitude of 0.86 degrees, which 
may already cause visible artifacts in highlights (especially since this 
type of artifacts is likely to exhibit a certain banding structure). At 
more shallow slopes, the noise only gets a little bit worse, but it 
doesn't get much better at steeper slopes too soon eithger: At a slope 
of 100% (45 degrees), for instance, the noise is still at approx. 0.437 
degrees.

It appears to me that the noise roughly follows the formula 
0.5*(1+cos(slope_angle*2))*(image_resolution/65535), with the result 
giving the normal jitter in radians. I guess some mathematically 
inclined will even be able to show why that is - I'm not in that mood 
myself right now :-).

(3) The function is not evaluated directly by the height field code, but 
instead first sampled and stored as a function image; for function 
images, a similar limitation applies: Again, these happen to be limited 
to a depth of 16 bit (per channel in case of pigment functions).


As far as workarounds go, I currently know none, except for using a 
totally different primitive; if you don't need a solid, the parametric 
primitive may be the way to go, using f(u,v)=u and f(u,v)=v for the x 
and z coordinates respectively. If you absolutely need a solid, you may 
want to try the isosurface primitive, using f(x,y,z)=y-g(x,z) (with g 
being your own function) and the default threshold of 0. Or you can use 
SDL to create a mesh primitive from the function.

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> As far as workarounds go, I currently know none, except for using a 
> totally different primitive; if you don't need a solid, the parametric 
> primitive may be the way to go, using f(u,v)=u and f(u,v)=v for the x and 
> z coordinates respectively. If you absolutely need a solid, you may want 
> to try the isosurface primitive, using f(x,y,z)=y-g(x,z) (with g being 
> your own function) and the default threshold of 0. Or you can use SDL to 
> create a mesh primitive from the function.

Thanks for the detailed analysis, after a rough look through the source for 
the height field I assumed something similar was happening - I couldn't 
believe it when I saw the normals were stored as 16 bit integers!  I guess 
the code was written in a time where every byte counted.  The code seems to 
be written in such a way that changing it to use floating point numbers is 
straightforward (I guess the original author suspected that in the future 
someone might want to change it).

I had used an isosurface originally but it was painfully slow to render. 
I'll take a look at the parametric primitive, I always forget about that 
one.  Thanks.

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> I had used an isosurface originally but it was painfully slow to render. 
> I'll take a look at the parametric primitive, I always forget about that 
> one.  Thanks.

OK scrap that, parametric is *really* slow.  I'm going to make a mesh2 using 
a macro...

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scott schrieb:

> Thanks for the detailed analysis, after a rough look through the source 
> for the height field I assumed something similar was happening - I 
> couldn't believe it when I saw the normals were stored as 16 bit 
> integers!  I guess the code was written in a time where every byte 
> counted.

As indicated in my post, the normals' precision isn't the bottleneck - 
it's the limitation to 16 bit of the values from which the normals are 
computed.

As for memory consumption, with POV-Ray we're still living in a time 
where every byte does count. I recently tried to render an (admittedly 
pathological) scene and faild because POV-Ray would have had to generate 
more radiosity samples than my physical memory (6 GB) could hold. Trying 
to stabilize the system after it had started swapping was no fun, with 
every mouse click or keyboard press literally taking minutes to be 
processed >_<

... and that was even with a custom POV-Ray version that featured a 
smaller radiosity sample memory footprint than standard beta...

 > The code seems to be written in such a way that changing it to
> use floating point numbers is straightforward (I guess the original 
> author suspected that in the future someone might want to change it).

Or maybe he just had particularly good programming habits. Or someone 
already changed it from bytes to shorts. Or the original author wanted 
to provide a simple way to change the type on other platforms where a 
short int might be something else than 16 bit - after all, POV-Ray has 
been developed with such portability issues in mind.

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scott schrieb:

> OK scrap that, parametric is *really* slow.  I'm going to make a mesh2 
> using a macro...

Did you try using the precompute keyword for the parametric?

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