[Radiance-general] trans - georg vs greg vs book

[Greg Ward]

Hi Brett,

You see, my clever plan in designing the "trans" material arguments  
was a lifetime of guaranteed consultancy, advising others in how to  
set its parameters.  Unfortunately, Georg has really undermined this  
plan by creating the excellent diagram you refer to, explaining how  
trans actually works, leading me to consider changing the parameters  
just to keep everyone guessing.

> From: "Brett Beeson" <brettbeeson at fastmail.fm>
> Date: January 9, 2006 2:44:01 PM PST
>
> Hi all,
>
> We've all gone over trans several times and there appears to be much
> confusion about the parameters.  I present an inconsistency when  
> working
> from
>
> (1) Radiance book
> (2) Georg's diagram
> (http://www.schorsch.com/rayfront/manual/transdef.html)
> (3) Greg Ward's emailed example (Desktop Radiance Digest v2n7, Sep  
> 1994,
> in RADIANCE_HOME/doc/digest/v2n7).
>
> Clearing up of the inconsistency will help me and many others!
>
> To summarise my understanding the trans arguments
>
> A1,A2,A3 - colour components.  As shown by "colour" diamond in Georg's
> diagram. Fraction of light NOT absorbed for each component.=
> A4, A5 - specular reflection, roughness (ignore, 0 for following
> examples)
> A6 - trans ("trans" diamond on georg's diagram).  (ie, fraction
> non-absorbed light transmitted through material.)
> A7 - specular proportion of transmitted light (ignore)
>
> According to the Radiance Book:
>
> A1 = Cr / (1-Rs)(1-A6)
>
> *I assume that A6 = "trans" diamond on georg's diagram.*
>
> Greg's example:
>
> Requirement: grey trans material.  Transmission factor of 60% (ie
> *total* amount of light going through).  Specular component of 10%:
>
> void trans opale
> 0
> 0
> 7 .6 .6 .6 0 0 1 .1666
>
> ie
> A1 = 0.6
> A6 = 1
>
> We adapt a number of his formulae to show this meets the requirements.
>> From Georg's diagram (note no reflection, as per Greg's example)
>
> Diffuse reflectance Rd = (1 - Rs)(colour)(1 - trans)
>                        = (1 - 0 )(0.6   )(1 - 1    )
>                        = 1 x 0.6 x 0
>                        = 0 (ie no diffuse reflectance, => 40% is
>                        absorbed)
>
>
> Diffuse transmittance Td = (1 - Rs)(colour)(trans)(1 - Tspec)
>                          = (1 - 0 )(0.6   )(1    )(1 - 0.1666)
>                          = 50%
>
> Specular transmittance Ts = (1 - Rs)(colour)(trans)(Tspec)
>                           = (1 - 0 )(0.6   )(1    )(0.1666)
> 			  = 10%
>
> That's great and seems to make sense.
>
> But - the inconsistency:
>
> Plug this example into Radiance book's formula.  (Stiil assume Rs=0.)
>
> A1 = Cr / (1 - Rs)(1 - A6)
> A1 = Cr / (1 - 0 )(1 - A6)
> A1 = Cr / (1 - A6)
>
> * Now consider what happens as A6 approaches 1.  A1 tends to  
> infinity -
> clearly not correct.*
>
> My questions are then:
>
> -   Is A6 = trans (in the diamond in Georg's diagram) as both Greg and
> Georg appear to show.  (ie. is A6 the fraction the non-absorbed light
> that is not diffusely reflected?)

Yes.

> -   If so, why doesn't the Radiance book formula make sense?

It does, but not for surfaces that are 100% specular or 100%  
transmissive.

> -   What is Cr, Cb and Cg?

These are the diffuse reflection values for red, green, and blue, and  
they will be 0 if either A4 or A6 are 1.0 due to energy balance  
constraints.

> -   Does total transmissivity = (1 - Rs)(colour)(trans) ?

Yes.

Basically, the problem you point out has to do with the formulation  
in RwR, which relies on a non-zero value for the diffuse reflection.   
If either A4 or A6 are 1.0,  then it follows that the diffuse  
reflection (Cr,Cg,Cb) must be zero for energy to balance, and the  
formulae for A1 to A3 give you 0/0, which is indeterminate (not  
infinity).

This is the main reason why trans has the confusing specification it  
does (besides keeping me employed) -- its parameterization has well- 
defined physical ranges.  All parameters except the roughness (A5)  
should be between 0 and 1.0, and any combination of parameter values  
in this range yields a physically valid model.

I hope this clears up your confusion.  If not, my rates are really  
quite reasonable....

-Greg