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What is red and green together ? ==> (dirty brown).

For color printers add a good black ==> CYMK system

Computer Scientist’s wheel: 2D: Red, Green, Blue. ==> **Additive mixing
**(light beams, CRT).

We are missing some colors: where is brown, olive, pink, dark blue ... ?

Graphics hardware view:

Extension of the additive color wheel to a cone (

Alternative:

Typical spectrum has some broad bumps plus some sharp spectral lines (added or subtracted). Example: Quasar-Spectrum

Sensitivity of these cones differs: green most sensitive, blue least sensitive.

**Metamers**: Colors that look the same (P), but have different spectrum(L1,
L2).

Comparative measurements are done with a color-matching set-up:

3 superposed lights (A,B,C) are compared with test color (T).

You can match almost all colors, as far as human perception
goes with an additive mix of the 3 base colors.

The remainder can be matched when one of the 3 colors is placed on
the test light -- to produce a subtractive effect.

This results in color matching functions with positive and negative
coefficients.

==> Perceptual
space is 3-dimensional. (1st Grassman Law )

**Law #1. Perceptual space is 3-dimensional.**

(see above) A basis of three primary colors is sufficent to generate all colors visble to humans.

**Law #2. Metamer mix (add) to yield metamers:**

L1, L1’ -> P1; L2, L2’ -> P2; then for any a, b :
a*L1 + b*L2 -> P3; then a*L1’ + b*L2’-> P3.

(**This is not true for** paints or pigments with **non-additive behavior**; see example
with filter (dashed) below).

Here filter makes no difference -- but here it reduces intensity dramatically!

**Law #3. As physical color is varied continuously, perceptual color also
varies continuously.**

(Continuity of the perceptual process).

(There are also "rods" that are more sensitive, but are essentially black&white sensors).

This leads to the

However this is not possible with only positive weighting factors; some blue-green components of the spectrum require a negatively weighted red component (Foley Fig.13.20). This means that the desired color sample has to be changed (de-saturated) with some red light, so that it can then be matched by positive blue and green components.

Frequency sensitivity of the eye varies from about 2nm for yellow and blue to about 10nm near the edge of the visible spectrum.

Overall, about 128 fully saturated hues can be distinguished.

A perceptual
color space was formally defined in 1931 by the **Commission International
de l’Eclairage (CIE).**

To avoid the need for negative weights, they defined a new set of basis
vectors (primary colors) X, Y, Z,
that lie completely outside the range of all visible RGB values,
so that the color matching functions x(l),
y(l), z(l) for any
visible hue become entirely positive (Foley Fig.13.22).

In addition, the **y(l)** function is
defined so that it matches the luminosity-efficiency of the human eye (Foley
Fig.13.19);

thus it can be used by itself as an **intensity channel**.

The transformation from the original RGB color matching functions to
the CIE color matching functions is **linear**.

If we intersect the visible portion of the CIE color space with a plane
X+Y+Z=1 (about equal brightness),

then we get the horseshoe-shaped region depicted in the CIE
chromaticity diagram.

The fully saturated, pure, spectral colors all lie on the curved part
of the horseshoe.

Somewhere near the center is a point defined as "white".

Colors lying opposite this "white" point are called **complementary
colors** (Foley Fig.13.26).

A particular tri-stimulus
(3-color) display system has three primaries: I,J,K (Foley Fig.13.27).

It can display only the colors that lie within its convex hull
(=triangle). (Can only use linear combinations of the 3 base colors
with coefficients [0,1]).

Thus we would like to make this triangle as large as possible (-> "ideal
basis"),
but we are limited by what colors of phosphor (or LED's, or gas-discharge)
are available.
The typical CRT display can cover **less than half** of the visible domain
of colors.

Subtractive Mixing

Metamers

Color Mixing/Filtering Combination

and many more ...

and upload an image of a relevant piece of geometry created for your project.

Put this image, as well as the project description from last, week on your website.

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