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

[Brett Beeson]

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?)
-   If so, why doesn't the Radiance book formula make sense?
-   What is Cr, Cb and Cg?
-   Does total transmissivity = (1 - Rs)(colour)(trans) ?       


Thanks for reading and thinking!

Cheers,

Brett

Brett Beeson
Sustainable Designer

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