Projecting the disk onto the hemisphere requires "blowing up" the set of
samples in order to prevent samples "sticking" nearby the edge of the
sphere/disk. The surface near the center of the disk grows more than the
surface near the edge, so near the center the samples move farther away.
That results in an uneven distribution.

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Apache wrote:
> IS MY DISTRIBUTION CORRECT?

When viewed from above (+z), a cos theta distribution should look like
uniformly spaced points on a disc. (This isn't hard to show with a little
math.) But neither of your +z views look that way.

Anders

--
#macro E(D)(#if(D<2)D#else#declare I=I+1;mod(pow(.5mod(I 6))*asc(substr(
"X0(1X([\\&Q@TV'YDGU`3F(-V[6Y4aL4XFUTD#N#F8\\A+F1BFO4`#bJN61EM8PFSbFA?C"
I/6 1))2)<1#end)#end#macro R(D,I,T,X,Y)#if(E(D))R(D-1I,T,Y/2X)R(D-1I,T+Y
/2Y/2X)#else box{T T+X+Y pigment{rgb E(2)*9}}#end#end R(10,5z*3-1v*2u*2)

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> Projecting the disk onto the hemisphere requires "blowing up" the set of
> samples in order to prevent samples "sticking" nearby the edge of the
> sphere/disk. The surface near the center of the disk grows more than the
> surface near the edge, so near the center the samples move farther away.
> That results in an uneven distribution.

I'm not sure your understood the projection
sample points evenly on disc (x,y)
then build (x,y,z) with same x,y and z=sqrt(x*x+y*y)
(and we do want an uneven distribution with more points near the center)

M

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The set that POV-Ray uses currently doesn't look like that either. (see my
post, pbi "Re: >1600 radiosity samples: right costheta distribution?"). "My"
distribution has very similar properties to that of POV-Ray, except for the
ordering that I still have to fix.

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Apache wrote:
> 
> The set that POV-Ray uses currently doesn't look like that either. (see my
> post, pbi "Re: >1600 radiosity samples: right costheta distribution?").

You are obviously doing something wrong, i just rendered it and it look
totally different here (it looks indeed uniform although not extremly high
quality).

Christoph

-- 
POV-Ray tutorials, include files, Sim-POV,
HCR-Edit and more: http://www.tu-bs.de/~y0013390/
Last updated 31 Dec. 2002 _____./\/^>_*_<^\/\.______

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I'm nuts .......    I rerendered it and it turned out to be some perspective
distortion :-)

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"Apache" <apa### [at] yahoocom> wrote in
news:3e16ad01$1@news.povray.org 

[...]

Maybe just make a scene that needs >1600 samples, build i.e. 5000 samples 
array, re-compile POV and make few renders involwing old and new 
distribution

-- 
#macro g(U,V)(.4*abs(sin(9*sqrt(pow(x-U,2)+pow(y-V,2))))*pow(1-min(1,(sqrt(
pow(x-U,2)+pow(y-V,2))*.3)),2)+.9)#end#macro p(c)#if(c>1)#local l=mod(c,100
);g(2*div(l,10)-8,2*mod(l,10)-8)*p(div(c,100))#else 1#end#end light_source{
y 2}sphere{z*20 9pigment{function{p(26252423)*p(36455644)*p(66656463)}}}//M

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"Nathan Kopp" <pov### [at] nkoppmailshellcom> wrote in
news:3e1714cf$1@news.povray.org 

> If it realy is O(n), which would be great, couldn't you simply
> generate an appropriate distribution each time, removing the need to
> order them.  If the algorithm produces evenly spaced samples for small
> counts, this would also ensure that small sample counts look their
> best. 

Why not generate array of arrays ?
array for count=3, count=4, count=5 etc... ?

taht would be much faster then generating in real-time, and will not use to 
much memory


-- 
#macro g(U,V)(.4*abs(sin(9*sqrt(pow(x-U,2)+pow(y-V,2))))*pow(1-min(1,(sqrt(
pow(x-U,2)+pow(y-V,2))*.3)),2)+.9)#end#macro p(c)#if(c>1)#local l=mod(c,100
);g(2*div(l,10)-8,2*mod(l,10)-8)*p(div(c,100))#else 1#end#end light_source{
y 2}sphere{z*20 9pigment{function{p(26252423)*p(36455644)*p(66656463)}}}//M

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Rafal 'Raf256' Maj wrote:
> Why not generate array of arrays ?
> array for count=3, count=4, count=5 etc... ?
>
> taht would be much faster then generating in real-time, and will not use
to
> much memory

Uh, it won't? Just the tables for up to 1600 samples would require 3.7 MB in
packed format, and we want to go well beyond that!

Anders

--
#macro E(D)(#if(D<2)D#else#declare I=I+1;mod(pow(.5mod(I 6))*asc(substr(
"X0(1X([\\&Q@TV'YDGU`3F(-V[6Y4aL4XFUTD#N#F8\\A+F1BFO4`#bJN61EM8PFSbFA?C"
I/6 1))2)<1#end)#end#macro R(D,I,T,X,Y)#if(E(D))R(D-1I,T,Y/2X)R(D-1I,T+Y
/2Y/2X)#else box{T T+X+Y pigment{rgb E(2)*9}}#end#end R(10,5z*3-1v*2u*2)

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And that's exactly what I'm planning on.

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