# 1. When hue is unknown

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).

# 2. Calculation of IM' (Sâˆ¶1, B:1) via Hue

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

# 3. When hue is known - Calculation of M, IM and m

STEP 1: FINDING POINT A (RGB (S1, B1)) VIA HUE

Hue ↔ IM (Sâˆ¶1, B:1)

- Hue is used to calculate the IM (Sâˆ¶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.