Dan Connelly wrote in message <35DAA5EB.BD9BA1FE@flash.net>...
>> It helps me for one. I have a (much more difficult to answer) question:
how
>> about Fourier analysis of a rgb coded color?
>
>I think there is a problem with this statement, or in my
>interpretation of it.
>


Must be my fault, I'm not a math person

>Fourier analysis is based on the principle that for linear
>systems, functions continuous to all derivatives can be expressed
>as a superposition of sinusoids.

Well, there's discrete FFT... maybe another means of finding out what
wavelengths *might* be responsible for a rgb colors

However, for functions
>of unconstrained periodicity, it takes a superposition over all
>possible wavelengths to do so optimally.
>


Well, some degree of accuracy can be a threshold, right?

>The fourier representation of a color of frequency f1 is a
>color of frequency f1 -- this means that one cannot express
>all colors in terms of RGB components : if sinusoids are
>chosen as a basis function, you still need all of them to
>do the job correctly.
>

You are right. I think the problem is that the physical representation of a
rgb color (almost certainly) is not unique. Foe example, rgb <0,1,0> is
550nm, but can also be a sum of several wavelengths, wide bands and thin
lines in the spectrum etc. This is due to the imperfections of the eye

>However, the human eye happens to be sensitive to R, G, and B
>due to its limited capacity to perceive color.  If, like some
>species, we had 4 color receptors, RGB displays would appear
>as distorted as an RG display does to us.

Agreed on that.

>So Physics can't be represented as a superposition of red, green,
>and blue -- it requires a much finer sampling across the optical
>spectrum to yield credible results in many cases.  Otherwise
>rainbows would be red, green, and blue bands instead of a continuous
>spread.

Yes, but still a nice approximation may be possible. POV approximated
inter-diffuse reflection in two ways, one cheap 'n' cheesy, the other slow
but more realistic, both being imperfect, but satisfying as a final result.
My question arose several years ago (back on POV 2.2) when I saw the books
behind my aquarium and how light was dispersed, nd how hard it was to model
in pov. Now, this problem solved, the problem with nice coloured refractive
custics remains. I've been willing to model a spectrograph for years now,
but that will have to wait. Maybe some day...

>
>Dan
>--
>http://www.flash.net/~djconnel/

Thanks for your input.

--Peter

pet### [at] usanet

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