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aurora
05-10-2007, 03:04 PM
Mike Lynch was just one of many people that have been curious about the correlation of Dielectric Absorption - vs - object thickness. My ideas was to preform a simple experiment using spheres of various radius's. Give them all a simple dielectric setup and using resultant renders to match the color values for each sphere.

The setup is simple spheres ranging in size from 0.1m, 0.25m, 0.5m, 0.75m, 1.0m, 1.25m, 1.5m, 1.5m, 2m. I then setup a floor plane and reflectors to act as the light source. The spheres surfaces are a simple dielectric setup with a blue color of (100, 100, 255), an glass IOR of 1.517, a surface roughness of 2.
The floor is a pure white with 50% diffuse. The reflectors have a luminosity or 500% with no other lights or ambient intensity in the scene. Interpolated Monte Carlo radiosity is used to allow the reflectors to light the scene. A simple solid gray backdrop is used to provide a consistent color through the spheres with the camera set to see them almost floor level on.
Its not 100% perfect but pretty dang close.


Heres the resultant image.
http://www.auroragrafx.com/images/Posting/PresetStandard/9.2/AbsorptionScale.jpg

Heres a quick excel table and graph showing the absorption values versus the sphere radius.
http://www.auroragrafx.com/images/Posting/PresetStandard/9.2/AbsorptionGraph.jpg

cagey5
05-10-2007, 03:46 PM
A straight equation of 1 divided by diameter gives the following table of figures.

0.1 ...... 10.00
0.25 ....... 4.00
0.5 ....... 2.00
0.75 ....... 1.33
1.0 ....... 1.0
1.25 ........ 0.8
1.5 ....... 0.67
1.75 ...... 0.57
2.0 ........ 0.5




so yeah.. pretty dang close. Nice test :thumbsup:

jameswillmott
05-10-2007, 05:03 PM
http://upload.wikimedia.org/math/b/0/5/b051dba6f3fcf90a14d661e2a83ddebe.png

http://en.wikipedia.org/wiki/Beers_law

Beer's Law of absorption I'm guessing.

Matt
05-10-2007, 05:57 PM
A straight equation of 1 divided by diameter gives the following table of figures.

0.1 ...... 10.00
0.25 ....... 4.00
0.5 ....... 2.00
0.75 ....... 1.33
1.0 ....... 1.0
1.25 ........ 0.8
1.5 ....... 0.67
1.75 ...... 0.57
2.0 ........ 0.5

so yeah.. pretty dang close. Nice test :thumbsup:

That is worth knowing, coolness!

warrenwc
05-10-2007, 11:08 PM
A summary of this thread belongs in the new docs with the chart & render.
Excellent!:thumbsup:

aurora
05-11-2007, 09:25 AM
Ah you beat me, I had posted the same thing on SQ yesterday but never got back here. Thanks Cagey:thumbsup:
Just to show how close I was heres a side by side
Try this 1/radius


Radius Abs 1/radius

0.10 9.00 10
0.25 3.80 4
0.50 2.00 2
0.75 1.33 1.333333333
1.00 1.00 1
1.25 0.80 0.8
1.50 0.68 0.666666667
1.75 0.58 0.571428571
2.00 0.50 0.5

mattclary
05-11-2007, 01:26 PM
Color me lost. I guess I need to start reading up on this stuff.

So the big sphere is more absorbtive than the small sphere? I can't see much of a difference in color, if anything, the big sphere looks lighter... :confused:

The setup for the test render is not what my intuition tells me would have been a good test. If the light were on the opposite side of the sphere from the viewer, it would be more apparent that more or less light were absorbed. The reflections on the sphere cause visual confusion I think.

p.s. forgive my ignorance

Mr_Bester
05-11-2007, 01:32 PM
That was the point. It was to show the correct absorption to get the same color throughout on different sized pieces of dielectric....

aurora
05-11-2007, 01:33 PM
Just out of curiosity I changed the Absorption values to work on the 1/radius premise and this is what you get.

http://www.auroragrafx.com/images/Posting/PresetStandard/9.2/AbsorptionScale2.jpg

cagey5
05-11-2007, 01:43 PM
As Mr Bester says the test was to demonstrate how you can calculate the absorption figure required to give the same appearance over varying sphere sizes.
You're right the bigger the sphere the more it absorbs and the darker it appears, which is the case in real life. SO to use a typical value from the table if you had one sphere measuring 1 meter with an absorption of 4 and you had another sphere 1.25 meters that you want to have the same appearance, then you need to multiply the original absorption figure [4] by the absorption value alongside 1.25. i.e 0.8

4 x 0.8 = 3.2.

Which is the absorption required for the larger sphere.

mattclary
05-14-2007, 12:05 PM
OK, I think I see. The spheres are SUPPOSED to be the same, as the absorption was changed. I misunderstood and thought the spheres had a constant surface, tus, the larger ones should have been... darker?

cagey5
05-14-2007, 03:14 PM
Yep... darker with the same absorption level as it will have absorbed more light due to the addtional thickness.

EXOSOUL
05-14-2007, 04:45 PM
very cool info, thanks