Converting HSV (Hue, Saturation, Value) to RGB (Red, Green, Blue) involves a series of steps. The HSV color model represents color in terms of Hue (the color type), Saturation (the vibrancy of the color), and Value (brightness). The RGB model is based on the additive combination of Red, Green, and Blue light.
Here's the process for converting HSV to RGB:
Steps to Convert HSV to RGB:
Normalize the HSV values:
Hue (H): Must be in the range of 0° to 360°.
Saturation (S): Should be a percentage, so it must be in the range of 0 to 100. If it's between 0 and 1, convert it to a percentage.
Value (V): Should be a percentage, so it must be in the range of 0 to 100. If it's between 0 and 1, convert it to a percentage.
Make sure that Saturation (S) and Value (V) are in the range of 0 to 1 (i.e., divide by 100 if they are percentages).
Calculate intermediate values:
C = V × S (Chroma)
X = C × (1 - |((H / 60) % 2) - 1|) (This helps adjust the intermediate RGB values based on the hue)
m = V - C (This is used to adjust the final RGB values)
Determine the RGB values: Based on the Hue (H) value, you need to figure out where the color falls on the color wheel (6 sectors). Based on that, you use the following formulas:
If 0° ≤ H < 60°:
R' = C, G' = X, B' = 0
If 60° ≤ H < 120°:
R' = X, G' = C, B' = 0
If 120° ≤ H < 180°:
R' = 0, G' = C, B' = X
If 180° ≤ H < 240°:
R' = 0, G' = X, B' = C
If 240° ≤ H < 300°:
R' = X, G' = 0, B' = C
If 300° ≤ H < 360°:
R' = C, G' = 0, B' = X
Adjust the RGB values: After calculating R', G', and B', you adjust them by adding m to each channel:
R = (R' + m) × 255
G = (G' + m) × 255
B = (B' + m) × 255
Round the values to integers if needed, since RGB values are generally integers.
Example 1: HSV(0°, 100%, 100%)
HSV: (0°, 100%, 100%)
H = 0°, S = 100% = 1.0, V = 100% = 1.0
Step 1: Calculate intermediate values:
C = 1.0 × 1.0 = 1.0
X = 1.0 × (1 - |(0° / 60) % 2 - 1|) = 1.0 × 1 = 1.0
m = 1.0 - 1.0 = 0.0
Step 2: Determine RGB values: Since H = 0° (the red sector), use the formula for 0° ≤ H < 60°:
R' = C = 1.0, G' = X = 1.0, B' = 0
Step 3: Adjust RGB values:
R = (1.0 + 0.0) × 255 = 255
G = (1.0 + 0.0) × 255 = 255
B = (0 + 0.0) × 255 = 0
RGB = (255, 0, 0) — Pure red.
Example 2: HSV(120°, 100%, 100%)
HSV: (120°, 100%, 100%)
H = 120°, S = 100% = 1.0, V = 100% = 1.0
Step 1: Calculate intermediate values:
C = 1.0 × 1.0 = 1.0
X = 1.0 × (1 - |(120° / 60) % 2 - 1|) = 1.0 × (1 - |2 - 1|) = 1.0
m = 1.0 - 1.0 = 0.0
Step 2: Determine RGB values: Since 120° ≤ H < 180° (the green sector), use the formula for 120° ≤ H < 180°:
R' = 0, G' = C = 1.0, B' = X = 1.0
Step 3: Adjust RGB values:
R = (0 + 0.0) × 255 = 0
G = (1.0 + 0.0) × 255 = 255
B = (1.0 + 0.0) × 255 = 255
RGB = (0, 255, 0) — Pure green.
Example 3: HSV(240°, 100%, 50%)
HSV: (240°, 100%, 50%)
H = 240°, S = 100% = 1.0, V = 50% = 0.5
Step 1: Calculate intermediate values:
C = 0.5 × 1.0 = 0.5
X = 0.5 × (1 - |(240° / 60) % 2 - 1|) = 0.5 × (1 - |4 % 2 - 1|) = 0.5
m = 0.5 - 0.5 = 0.0
Step 2: Determine RGB values: Since 240° ≤ H < 300° (the blue sector), use the formula for 240° ≤ H < 300°:
R' = X = 0.5, G' = 0, B' = C = 0.5
Step 3: Adjust RGB values:
R = (0.5 + 0.0) × 255 = 127.5 ≈ 128
G = (0 + 0.0) × 255 = 0
B = (0.5 + 0.0) × 255 = 127.5 ≈ 128
RGB = (128, 0, 128) — Purple.
Example 4: HSV(60°, 50%, 100%)
HSV: (60°, 50%, 100%)
H = 60°, S = 50% = 0.5, V = 100% = 1.0
Step 1: Calculate intermediate values:
C = 1.0 × 0.5 = 0.5
X = 0.5 × (1 - |(60° / 60) % 2 - 1|) = 0.5 × (1 - |1 - 1|) = 0.5
m = 1.0 - 0.5 = 0.5
Step 2: Determine RGB values: Since 60° ≤ H < 120° (the yellow sector), use the formula for 60° ≤ H < 120°:
R' = C = 0.5, G' = X = 0.5, B' = 0
Step 3: Adjust RGB values:
R = (0.5 + 0.5) × 255 = 255
G = (0.5 + 0.5) × 255 = 255
B = (0 + 0.5) × 255 = 127.5 ≈ 128
RGB = (255, 255, 128) — Yellow.