trans - georg vs greg vs book

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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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" <[email protected]>
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
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

Hi Brett,

regarding your trans question and to confuse you even more:
There's no such thing as "Specular transmittance" for scattering
materials. All "transmittance" values [0..1] are integrals over the BRTF
times incident radiance, with the BRTF limited by [0...infinity] . In
case of an ideal specular BRTF (ideal glass), a "specular transmittance"
is readily defined, but for all other cases it is necessary to specify
over which solid angle the BRTF was integrated (that's why there's a
*diffuse* transmittance under all circumstances, - that integral
extends over the hemisphere). Specularwise it gets all very ugly and has
been an efficient source for a lot of confusion. IMHO, the easiest way
is to stick to the BRTF and even then it is worth clearly separating
between an ideal BRTF (which may be a delta function) and
measurements/simulations (which both deal with folded, aka integrated,
BRTFs, so no delta-functions). This holds also true for "trans", whose
BRTF gets more "peakish" (delta-like) with lower roughness values.

http://www.pab-opto.de/pers/phd/apian_phd.pdf (in German, sorry for
that) lists the transmittance defs on (acrobat page numbering) page 31
and the trans BRTF on page 131.

-Peter

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