Hue Angle Calculator Math

Hue Angle Formula:

\[ Hue = \arctan2(b, a) \times \frac{180}{\pi} \]

Hue Angle:

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1. What is Hue Angle?

The hue angle is a measurement used in color science to represent the dominant wavelength of a color in degrees. It's calculated from chroma components a and b, providing a numerical representation of color hue in various color spaces.

2. How Does the Calculator Work?

The calculator uses the hue angle formula:

\[ Hue = \arctan2(b, a) \times \frac{180}{\pi} \]

Where:

\( a \) — Chroma component representing green-red axis
\( b \) — Chroma component representing blue-yellow axis
\( \arctan2 \) — Two-argument arctangent function
\( \frac{180}{\pi} \) — Conversion factor from radians to degrees

Explanation: The arctan2 function calculates the angle between the positive x-axis and the point (a, b), providing the hue angle in degrees.

3. Importance of Hue Angle Calculation

Details: Hue angle calculation is crucial in colorimetry, image processing, and color management systems. It helps in color classification, color matching, and ensuring color consistency across different devices and applications.

4. Using the Calculator

Tips: Enter both chroma components (a and b) values. The calculator will compute the hue angle in degrees (0-360° range). Both values can be positive or negative.

5. Frequently Asked Questions (FAQ)

Q1: What color spaces use hue angle?
A: Hue angle is commonly used in CIELAB, CIELCh, and HSL color spaces for color representation and analysis.

Q2: What is the range of hue angle values?
A: Hue angle typically ranges from 0° to 360°, representing the full color circle from red through green, blue, and back to red.

Q3: How does atan2 differ from regular atan?
A: atan2 takes two arguments and considers the signs of both inputs to determine the correct quadrant of the result, providing angles in the full 360° range.

Q4: What do negative hue values mean?
A: Negative values are normalized to the 0-360° range by adding 360, ensuring all results are positive angles.

Q5: Can hue angle be used for color comparison?
A: Yes, hue angle is excellent for comparing color similarity and identifying color differences in various applications including quality control and digital imaging.