RE: [Algorithms] Solid angle calculation

[Nick P. <NPe...@cl...>]

In their prefilter() routine, the authors calculate theta as the angle from
the normal to the (u,v) plane. That's the solid angle... that's all.

The sinc() function is then using that solid angle to do the resampling. As
I flagged, it's pretty useful for that kind of thing.

It seems pretty simple.

Cheers, ....Nick Pelling....

-----Original Message-----
From: Joris Mans [mailto:jor...@pa...]
Sent: 18 September 2002 12:19
To: 'Nick Pelling'; gda...@li...
Subject: RE: [Algorithms] Solid angle calculation


Ok, I understand that, but I fail to see how this function can be used
to calculate the differential solid angle as the formulae found on the
net do not use sinc for that.

Does anyone know?

Joris

> -----Original Message-----
> From: gda...@li... 
> [mailto:gda...@li...] On 
> Behalf Of Nick Pelling
> Sent: Wednesday, September 18, 2002 12:42 PM
> To: gda...@li...
> Subject: RE: [Algorithms] Solid angle calculation
> 
> 
> sinc() is actually a well-known maths function, and is often 
> used in code for rescaling / resampling.
> 
> Search for "sinc function" on Google, and you'll hit loads of 
> maths sites explaining it, such as:
> 
> http://mathworld.wolfram.com/SincFunction.html
> 
> Cheers, .....Nick Pelling.....
> 
> -----Original Message-----
> From: Tom Forsyth [mailto:to...@mu...]
> Sent: 16 September 2002 12:51
> To: Joris Mans; gda...@li...
> Subject: RE: [Algorithms] Solid angle calculation
> 
> 
> I assumed that was a typo, and they mean "sine(theta)". But I 
> didn't worry about it too hard since, using cube-maps and 
> just ignoring the spherical distortion (i.e. every sample is 
> evenly weighted) seemed to work just fine - at least to 
> within the tolerance of my eye :-). It also bins all the 
> angle stuff and uses the SH components directly (since you 
> already have x,y,z to plug into the component calculations), 
> so there's no trig anywhere in any equations. Which is very 
> good news for speed.
> 
> 
> Tom Forsyth - purely hypothetical Muckyfoot bloke.
> 
> This email is the product of your deranged imagination,
> and does not in any way imply existence of the author.
> 
> > -----Original Message-----
> > From: Joris Mans [mailto:jor...@pa...]
> > Sent: 12 September 2002 02:17
> > To: gda...@li...
> > Subject: [Algorithms] Solid angle calculation
> > 
> > 
> > Hi
> > 
> > I am currently trying to understand/implement the 
> integration scheme 
> > used in "An efficient rep. for Irradiance env maps" and I think my 
> > math skills have some holes in them, because I don't understand the 
> > formula for calculating the solid angle.
> > This is the c sample code:
> > 
> > domega = (2*PI/width)*(2*PI/width)*sinc(theta) ;
> > 
> > I understand where the / width comes from since you are 
> integrating in 
> > steps of 1/width over the sphere, but I fail to understand what
> > sinc(theta) means.
> > 
> > FYI:
> > 
> > float sinc(float x) {               /* Supporting sinc function */
> >   if (fabs(x) < 1.0e-4) return 1.0 ;
> >   else return(sin(x)/x) ;
> > }
> > 
> > How does this term calculate the solid angle?
> > 
> > Thanks
> > 
> > Joris
> > 
> > 
> > 
> > -------------------------------------------------------
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> 
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