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RGB and HSB (HSV) - ​Derivation of equations.

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1. Saturation

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The saturation has a value between 0 and 1 and changes horizontally.
 

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S = 

1 - S = 

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Saturation remains constant vertically:

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2. Saturation - When brightness is 1 (100%)

Step 1. Moving from a pure color (S: 1, B:1) to white (S: 0, B:1)

The distance between the RGB at saturation (S): 0 and saturation (S): 1 can be calculated as follows:

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To predict the RGB code when the saturation (S) changes:

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Step 2. MOVING FROM ALMOST WHITE (0 < S) TO PURE COLOR   

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Calculation of R', G', B' (S:1,   B:1) by using eq.5:

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Step 3. EQUATION COMBINATION   

Plugging Eq.6 into the original equation (Eq.5)

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3. Saturation: When brightness is ≤ 1

Displacement of saturation when brightness is equal or less than 100%.

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Step 1 & 2. Determination of point C by using point A as a starting point:

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Step 3. Determination of point D by using point C as a starting point  

- Moving from C to D can be obtained by combining equations 3 and 8.
- The answers tells which equation is needed to predict D from A.

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The expression:
(A) Is valid when the colors are within the same 
hue range.

(B) Predicts the RGB code for horizontal 
changes.

(C) B Initial = B Final

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4. Saturation and brightness:
Horizontal and vertical changes

HOW TO PREDICT THE RGB FINAL REGARDLESS OF LOCATION 

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The expression:
(A) Is valid when the colors are within the same
hue range.
(B) Predicts the RGB code for horizontal and 
vertical changes.

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5. RGB prediction

CALCULATION OF RGB MAX, INTERMEDIATE AND MIN 

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The expression:
(A)  Is valid when the colors are within the same hue range.
(B)  Predicts the RGB code for horizontal and vertical changes. 

RGB and HSB (HSV) - ​Derivation of equations.

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