Grassmann's Laws of Additive Colors

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Grassman's laws Laws governing the results of additive color matching experiments (see additive mixture). Grassman's laws assert the existence of exactly three dimensions of variation in perceived color, e.g. hue, brightness, and saturation. They also imply the linear additivity of color matches, a fact of importance to colorimetry. Thus if stimulus a matches stimulus b, and stimulus c matches stimulus d, then the additive mixture of a and c will match the mixture of b and d irrespective of the stimuli's spectral composition.

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Check Wikipedia

Hermann Grassmann

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Grassmann's law

One might ask "why is it possible that Wright and Guild's results can be summarized using different primaries and different intensities from those actually used"? One might also ask "what about the case when the test colors being matched are not monochromatic"? The answer to both of these questions lies in the (near) linearity of human color perception. This linearity is expressed in Grassmann's law: If the test color is the combination of two monochromatic colors, then the observer's matching value of each primary will be the sum of the matching values for each of the monochromatic colors when viewed separately. In other words, if beam 1 and 2 are monochromatic, and the observer chooses R1 G1 B1 as the strengths of the primaries that match beam 1 and R2 G2 B2 as the strengths of the primaries that match beam 2, then, if the two beams were combined, the matching values will be R, G, B where:

R= R_1+R_2\,

G= G_1+G_2\,

B= B_1+B_2\,

Grassmann's law can be expressed in general form by stating that for a given color with a spectral power distribution I(λ) the RGB coordinates are given by:

R= \int_0^\infty I(\lambda)\,\overline{r}(\lambda)\,d\lambda

G= \int_0^\infty I(\lambda)\,\overline{g}(\lambda)\,d\lambda

B= \int_0^\infty I(\lambda)\,\overline{b}(\lambda)\,d\lambda

The CIE RGB space can be used to define chromaticity in the usual way: The chromaticity coordinates are r and g where:

r= \frac{R}{R+G+B},

g= \frac{G}{R+G+B}.

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Law 1: A Color can be matched by a combination of three other primary colors.

This law actually is associated with the word: "Tristimuli."

This basically says that we can create any color by combining at most three monochromatic primary color sources. A primary color source is a color that cannot be made by any mixture of the other two primary colors.

This law only operates within the color gamut triangle defined by the primary colors selected. [link to page about rgb color gamut triangle]

Law 2: A mixture colors is equvalent to the linear combination of the components

This law says that combining any number of additive colors is the same as combining the primary color components.

For example:

Combining a Color that's 40% Red, 40% Green and 20% Blue with a color that's 20% Red, 60% Green and 20% Blue will result in a color that matches the color: 80% Red, 100% Green and 40% Blue.

Law 3: Laws 1 and 2 are effective at any light level.

These Color Matching functions are remain true for any level of brightness. It doesn't matter if we take the double the percentages in our example in Law 2, or halve them... The combined color matches the combination.

It turns out that this third law isn't completely true with very dark colors, which is due our eye's inability to see colors correctly in the dark.

For example

[ref]

Section [3] Grassman's Laws of additive colour mixture.

Any colour (source C) can be matched by a linear combination of three other
colours (primaries eg. RGB), provided that none of those three can be matched
by a combination of the other two. This is fundamental to colorimetry and is
Grassman's first law of colour mixture. So a colour C can be matched by Rc
units of red, Gc units of green and Bc units of blue. The units are can be
measured in any form that quantifies light power.

C = Rc(R) + Gc(G) + Bc(B)

A mixture of any two colours (sources C1 and C2) can be matched by linearly
adding together the mixtures of any three other colours that individually
match the two source colours. This is Grassman's second law of colour
mixture. It can be extended to any number of source colours.

C3(C3) = C1(C1) + C2(C2) = [R1+R2](R) + [G1+G2](G) + [B1+B2](B)

Colour matching persists at all luminances. This is Grassman's third law. It
fails at very low light levels where rod cell vision (scoptopic) takes over
from cone cell vision (photopic).

kC3(C3) = kC1(C1) + kC2(C2).

The symbols in square brackets are the names of the colours, and not numerical
values. The equality sign should not be used to signify an identity, in
colorimetry it means a colour matching, the colour on one side of the equality
looks the same as the colour on the other side.

These laws govern all aspects of additive colour work, but they apply only
signals in the "linear-light" domain. They can be extended into subtractive
colour work.

TODO TODO TODO TODO - delete this stuff

  "toaff" Code for affiliate links. Put this in for all affiliate links in case we need to find them.

YellowHighlighting    (Must put an "x" in yellowhighlighting of cssoptions in IncColors to enable.)

Underline    Strong    em    xxlg    xlg    lg    sm    xs

Text  Link. 

Alternative - Open New Window - link that is a different way to have it open a new window

Simple - These are smaller/simpler

Simple - These are smaller/simpler

Random - These are smaller/simpler

Random - These are smaller/simpler. They are controlled by just the align="center/left or right"

Specific - Caption.

TODO

Specific - Caption.

Specific, Caption and Link

TODO

Specific, Caption and Link

Random, Caption

TODO

Random, Caption

Random, LINK , Caption

TODO

Random, LINK , Caption

Random, RANDOM LINK , Caption

TODO

Random, RANDOM LINK , Caption

Cells are sized by the largest cell in a column. To make the cells larger, put nbsp in them. But make every other one a regular space (use a space in the text) becuase it takes less code and allows a carriage return to be inserted if someone's screen is small. Otherwise, they will have to scroll back and forth.

If no table border (tb1, ex.) is defined, the default is tb0, or no border around the cells.

Text Centered Table

Text Left Justified Table

l

Left

To have a different background color, go to cssoptions in IncColors and put an X in colorsbg to enable this feature. Define the class for the bg color.

To have no borders:

• Do not define a border (ex., tb1). The default is no border.
• Define style="background:#xxxxxx" where xxxxxx = the color code of the bg color.

HIDDEN COMMENT IN TEXT:

HIDDEN UNIQUE TEXT MARKER:

The first essential to the application of the Munsell Color System is a clear understanding of the three dimensions of color. Once the simple logic of these dimensions is grasped, the practical advantages of the Munsell System will be apparent.

Example of linking to a Named Anchor:

www.SiteName/PageName/index.php#ManMadeDiamonds

To Redirect a File:

Open an existing php file using NoteTab. Delete everything and replace it with the following code. Save with NoteTab, making sure it is still a php file.

function redirect($to)
{
$pc = $_SERVER['SERVER_PORT'] == '443' ? 'https' : 'http';
// $host = strlen($_SERVER['HTTP_HOST'])?$_SERVER['HTTP_HOST']:$_SERVER['SERVER_NAME'];
if (headers_sent()) return false;
else
{
// header("HTTP/1.1 302 Found"); HIGHLY SUGGESSTED YOU DONT USE THIS !!!!!!!!
// header("HTTP/1.1 303 See Other");
header("HTTP/1.1 301 Moved Permanently");
header("Location: $pc://$to");
exit();
}
}
?>

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