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Ticket information General information. The dimensions of the HSL and HSV geometries—simple transformations of the not-perceptually-based RGB model—are not directly related to the photometric color-making attributes of the same names, as defined by scientists such as the CIE or ASTM.

Nonetheless, it is worth reviewing those definitions before leaping into the derivation of our models. Brightness and colorfulness are absolute measures, which usually describe the spectral distribution of light entering the eye, while lightness and chroma are measured relative to some white point, and are thus often used for descriptions of surface colors, remaining roughly constant even as brightness and colorfulness change with different illumination.

Saturation can be defined as either the ratio of colorfulness to brightness or that of chroma to lightness. HSL, HSV, and related models can be derived via geometric strategies, or can be thought of as specific instances of a "generalized LHS model".

In each of our models, we calculate both hue and what this article will call chroma , after Joblove and Greenberg , in the same way—that is, the hue of a color has the same numerical values in all of these models, as does its chroma.

If we take our tilted RGB cube, and project it onto the "chromaticity plane " perpendicular to the neutral axis, our projection takes the shape of a hexagon, with red, yellow, green, cyan, blue, and magenta at its corners fig.

More precisely, both hue and chroma in this model are defined with respect to the hexagonal shape of the projection. The chroma is the proportion of the distance from the origin to the edge of the hexagon.

This ratio is the difference between the largest and smallest values among R , G , or B in a color. To make our definitions easier to write, we'll define these maximum, minimum, and chroma component values as M , m , and C , respectively.

Thus if we add or subtract the same amount from all three of R , G , and B , we move vertically within our tilted cube, and do not change the projection.

For points which project onto the origin in the chromaticity plane i. Mathematically, this definition of hue is written piecewise : [I].

Sometimes, neutral colors i. After such a transformation, hue is precisely the angle around the origin and chroma the distance from the origin: the angle and magnitude of the vector pointing to a color.

Sometimes for image analysis applications, this hexagon-to-circle transformation is skipped, and hue and chroma we'll denote these H 2 and C 2 are defined by the usual cartesian-to-polar coordinate transformations fig.

The atan2 function, a "two-argument arctangent", computes the angle from a cartesian coordinate pair. Notice that these two definitions of hue H and H 2 nearly coincide, with a maximum difference between them for any color of about 1.

While the definition of hue is relatively uncontroversial—it roughly satisfies the criterion that colors of the same perceived hue should have the same numerical hue—the definition of a lightness or value dimension is less obvious: there are several possibilities depending on the purpose and goals of the representation.

Here are four of the most common fig. All four of these leave the neutral axis alone. The creators of these models considered this a problem for some uses.

For example, in a color selection interface with two of the dimensions in a rectangle and the third on a slider, half of that rectangle is made of unused space.

Now imagine we have a slider for lightness: the user's intent when adjusting this slider is potentially ambiguous: how should the software deal with out-of-gamut colors?

To solve problems such as these, the HSL and HSV models scale the chroma so that it always fits into the range [0, 1] for every combination of hue and lightness or value, calling the new attribute saturation in both cases fig.

To calculate either, simply divide the chroma by the maximum chroma for that value or lightness. The HSI model commonly used for computer vision, which takes H 2 as a hue dimension and the component average I "intensity" as a lightness dimension, does not attempt to "fill" a cylinder by its definition of saturation.

Instead of presenting color choice or modification interfaces to end users, the goal of HSI is to facilitate separation of shapes in an image.

Saturation is therefore defined in line with the psychometric definition: chroma relative to lightness fig.

See the Use in image analysis section of this article. Using the same name for these three different definitions of saturation leads to some confusion, as the three attributes describe substantially different color relationships; in HSV and HSI, the term roughly matches the psychometric definition, of a chroma of a color relative to its own lightness, but in HSL it does not come close.

Even worse, the word saturation is also often used for one of the measurements we call chroma above C or C 2. The original purpose of HSL and HSV and similar models, and their most common current application, is in color selection tools.

At their simplest, some such color pickers provide three sliders, one for each attribute. Most, however, show a two-dimensional slice through the model, along with a slider controlling which particular slice is shown.

Several color choosers from the s are shown to the right, most of which have remained nearly unchanged in the intervening time: today, nearly every computer color chooser uses HSL or HSV, at least as an option.

Some more sophisticated variants are designed for choosing whole sets of colors, basing their suggestions of compatible colors on the HSL or HSV relationships between them.

Most web applications needing color selection also base their tools on HSL or HSV, and pre-packaged open source color choosers exist for most major web front-end frameworks.

The CSS 3 specification allows web authors to specify colors for their pages directly with HSL coordinates. HSL and HSV are sometimes used to define gradients for data visualization , as in maps or medical images.

For example, the popular GIS program ArcGIS historically applied customizable HSV-based gradients to numerical geographical data. Image editing software also commonly includes tools for adjusting colors with reference to HSL or HSV coordinates, or to coordinates in a model based on the "intensity" or luma defined above.

In particular, tools with a pair of "hue" and "saturation" sliders are commonplace, dating to at least the lates, but various more complicated color tools have also been implemented.

For instance, the Unix image viewer and color editor xv allowed six user-definable hue H ranges to be rotated and resized, included a dial -like control for saturation S HSV , and a curves -like interface for controlling value V —see fig.

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