RGB och HSB (HSV) - Härledning av ekvationer
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1. Proportionalitet mellan RGB-färger.
Step 1 & 2. Determination of point C by using point A as a starting point.
To predict point C from point A, a combination of equations 3 and 7 is required.
STEP 3. CALCULATION OF HUE
Alternative 1. To calculate Hue with RGB:
Alternative 2. To calculate how to predict point C via point A in RGB format:
This formula refers to the Preucil hue error and grayness system (I960).
1. Proportionalitet mellan RGB-färger.
If moving circularly - Two-dimensional plane:
(A) M – m, (B) M – IM, (C) IM - m remains constant over the entire distance.
How to Draw: linearizing the curve (color placement)
By using photoshop: Opacity and Fill considered equal.
(Opacity = Fill) < 100%
CONVERSION FROM RGB TO HSB
CALCULATION OF RGB IM (S:1, B:1):
The range (M – m) of point A predicts saturation at point B and brightness at point C.
Alternative.1 (B pathway): To predict point D via point A
Alternative.2 (C pathway): To predict point D via point A
1. Proportionalitet mellan RGB-färger.
STEP 1: FINDING POINT A (RGB (S1, B1)) VIA HUE
Hue ↔ IM (S∶1, B:1)
- Hue is used to calculate the IM (S∶1, B:1) and vice versa:
- The designation S1, B1 means that the saturation and brightness of this color are 100%.
Eq. 17 & 18:
- RGB min (S1, B1) and RGB max (S1, B1) are always 0 and 1, while RGB intermediate varies. Eqs. 17 and 18 use hue to calculate IM (S1, B1).
STEP 2 & 3: MOVING FROM POINT A TO POINT C
Combination of eq: 3 and 7.
A similar formula has been mentioned by George H. Joblove and Donald Greenberg (1978) [link].
CALCULATION OF RGB MAX
CALCULATION OF RGB INTERMEDIATE – SLOPE UP
Alternative.1
Alternative.2
When moving vertically, the saturation is unchanged:
S (Initial) = S (Final)
When moving horizontally, the brightness is unchanged:
B (Initial) = B (Final)
CALCULATION OF RGB INTERMEDIATE – SLOPE DOWN
Alternative.1
Alternative.2
When moving vertically, the saturation is unchanged:
S (Initial) = S (Final)
When moving horizontally, the brightness is unchanged:
B (Initial) = B (Final)
CALCULATION OF RGB MIN
When moving vertically, the saturation is unchanged:
When moving horizontally, the brightness is unchanged:
References:
[1] George H. J & Green, Donald.,1978. Color spaces for computer graphics. Program of Computer Graphics. 12, pp. 23
[2] Preucii, F. (i960), "Color Diagram," TAGA Proc., 12, pp. 151 – 155.