RGB to HSV Conversion

Given a single RGB pixel with values in [0, 255], convert it to HSV color space.

Algorithm:

Normalize R, G, B to [0, 1] by dividing by 255
Compute $C_{max} = \max(R', G', B')$ , $C_{min} = \min(R', G', B')$ , $\Delta = C_{max} - C_{min}$
Hue (0-360 degrees):
- If $\Delta = 0$ : $H = 0$
- If $C_{max} = R'$ : $H = 60 \times (((G' - B') / \Delta) \mod 6)$
- If $C_{max} = G'$ : $H = 60 \times (((B' - R') / \Delta) + 2)$
- If $C_{max} = B'$ : $H = 60 \times (((R' - G') / \Delta) + 4)$
Saturation (0-1): $S = 0$ if $C_{max} = 0$ , else $\Delta / C_{max}$
Value (0-1): $V = C_{max}$

Return $[H, S, V]$ with H rounded to 2 decimal places, S and V rounded to 4 decimal places.

Example

Input

pixel = [255, 0, 0]

Output

[0.0, 1.0, 1.0]

Reasoning

Input: pixel holds one colour as three integer intensities in $[0, 255]$ : red $255$ (full), green $0$ , blue $0$ . That is pure, fully bright red.
Normalise: dividing each by $255$ gives $R' = 1$ , $G' = 0$ , $B' = 0$ . So $C_{max} = 1$ (from red), $C_{min} = 0$ and $\Delta = 1 - 0 = 1$ .
Hue: red is the largest channel, so the red formula applies: $H = 60 \times \left(\frac{0 - 0}{1} \bmod 6\right) = 60 \times 0 = 0^\circ$ . Hue is an angle on the colour wheel, and red sits at $0^\circ$ (green at $120^\circ$ , blue at $240^\circ$ ).
Saturation: $S = \Delta / C_{max} = 1/1 = 1$ , meaning no grey mixed in. Value: $V = C_{max} = 1$ , maximum brightness.
Output: [0.0, 1.0, 1.0], as floats after rounding (H to 2 places, S and V to 4).
Notice that a darker red such as $[128, 0, 0]$ keeps $H = 0$ and $S = 1$ ; only $V$ drops, to $128/255 \approx 0.502$ . Brightness lives entirely in $V$ .

Constraints

Pixel is [R, G, B] with integer values in [0, 255]
H in [0, 360), S in [0, 1], V in [0, 1]
If max = 0, then H = 0 and S = 0
Return list [H, S, V]

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Concept primer

Background Knowledge

The RGB (Red, Green, Blue) color model is an additive color model in which red, green, and blue lights are combined in various ways to reproduce a broad array of colors. However, this model is not intuitive for humans when it comes to understanding the color's properties such as hue, saturation, and value. The HSV (Hue, Saturation, Value) color model, on the other hand, is more intuitive as it separates the color into its core attributes: hue (the actual color), saturation (the purity of the color), and value (the brightness of the color).

The conversion from RGB to HSV involves a series of calculations that transform the RGB values into their HSV equivalents. This process includes normalizing the RGB values, determining the maximum and minimum values among them, and then using these to calculate the hue, saturation, and value. Understanding the mathematical relationships between these color models is crucial for performing such conversions accurately.

The key to converting RGB to HSV lies in understanding how the hue is calculated based on the maximum and minimum RGB values and their differences. The hue is calculated in degrees (0-360 degrees), with different ranges corresponding to different colors (e.g., red, yellow, green, etc.). Saturation and value are calculated as ratios, with saturation representing how vibrant the color is and value representing the color's brightness.

Algorithm/Approach

The general approach to solving this type of problem involves:

Normalizing the input RGB values to a standard range (in this case, [0, 1]) to simplify calculations.
Identifying the maximum and minimum values among the RGB components, which are crucial for determining the hue, saturation, and value.
Applying the specific formulas for calculating hue, saturation, and value based on the maximum and minimum RGB values and their differences.

Step-by-Step Strategy

To implement the solution:

Normalize RGB Values: Divide each RGB value by 255 to normalize them to the range [0, 1].
Find Maximum and Minimum: Determine $C_{max}$ and $C_{min}$ from the normalized RGB values.
Calculate Delta: Compute $\Delta = C_{max} - C_{min}$ .
Determine Hue: Apply the given formulas to calculate the hue based on $C_{max}$ and $\Delta$ .
Calculate Saturation and Value: Use the formulas $S = \Delta / C_{max}$ (if $C_{max} \neq 0$ ) and $V = C_{max}$ to find the saturation and value.
Round Values: Round the hue to 2 decimal places and saturation and value to 4 decimal places.

Common Pitfalls

Forgetting to normalize the RGB values before calculation.
Incorrectly applying the formulas for hue, especially considering the different cases based on $C_{max}$ .
Not handling the case where $\Delta = 0$ or $C_{max} = 0$ correctly.

Time & Space Complexity

The time complexity of this algorithm is $O(1)$ because it involves a constant number of operations regardless of the input size. The space complexity is also $O(1)$ as it only uses a constant amount of space to store the input and output values.

solution.py

Python 3.13

Test results