## Overview

At the core of the colorspace package are various utilities for computing with color spaces (Wikipedia 2019d), as the name conveys. Thus, the package helps to map various three-dimensional representations of color to each other (Ihaka 2003). A particularly important mapping is the one from the perceptually-based and device-independent color model HCL (Hue-Chroma-Luminance) to standard Red-Green-Blue (sRGB) which is the basis for color specifications in many systems based on the corresponding hex codes (Wikipedia 2019i), e.g., in HTML but also in R. For completeness further standard color models are included as well in the package. Their connections are illustrated in the following graph:

Color models that are (or try to be) perceptually-based are displayed with circles and models that are not are displayed with rectangles. The corresponding classes and eponymous class constructors in colorspace are:

• RGB() for the classic Red-Green-Blue color model, which mixes three primary colors with different intensities to obtain a spectrum of colors. The advantage of this color model is (or was) that it corresponded to how computer and TV screens generated colors, hence it was widely adopted and still is the basis for color specifications in many systems. For example, hex color codes are employed in HTML but also in R. However, the RGB model also has some important drawbacks: It does not take into account the output device properties, it is not perceptually uniform (a unit step within RGB does not produce a constant perceptual change in color), and it is unintuitive for humans to specify colors (say brown or pink) in this space. (See Wikipedia 2019g.)
• sRGB() addresses the issue of device dependency by adopting a so-called gamma correction. Therefore, the gamma-corrected standard RGB (sRGB), as opposed to the linearized RGB above, is a good model for specifying colors in software and for hardware. But it is still unintuitive for humans to work directly with this color space. Therefore, sRGB is a good place to end up in a color space manipulation but it is not a good place to start. (See Wikipedia 2019h.)
• HSV() is a simple transformation of either the sRGB or the RGB space that tries to capture the perceptual axes: hue (dominant wavelength, the type of color), saturation (colorfulness), and value (brightness, i.e., light vs. dark). Unfortunately, the three axes in the HSV model are confounded so that, e.g., brightness changes dramaticaly with hue. (See Wikipedia 2019f.)
• HLS() (Hue-Lightness-Saturation) is another transformation of either sRGB or RGB that tries to capture the perceptual axes. It does a somewhat better job but the dimensions are still strongly confounded. (See Wikipedia 2019f.)
• XYZ() was established by the CIE (Commission Internationale de l’Eclairage) based on experiments with human subjects. It provides a unique triplet of XYZ values, coding the standard observer’s perception of the color. It is device-independent but it is not perceptually uniform and the XYZ coordinates have no intuitive meaning. (See Wikipedia 2019a.)
• LUV() and LAB() were therefore proposed by the CIE as perceptually uniform color spaces where the former is typically preferred for emissive technologies (such as screens and monitors) whereas the latter is usually preferred when working with dyes and pigments. The L coordinate in both spaces has the same meaning and captures luminace (light-dark contrasts). Both the U and V coordinates as well as the A and B coordinates measure positions on red/green and yellow/blue axes, respectively, albeit in somewhat different ways. While this corresponds to how human color vision likely evolved (see the next section), these two color models still not correspond to perceptual axes that humans use to describe colors. (See also Wikipedia 2019c, 2019b.)
• polarLUV() and polarLAB() therefore take polar coordinates in the UV plane and AB plane, respectively. Specifically, the polar coordinates of the LUV model are known as the HCL (Hue-Chroma-Luminance) model (see Wikipedia 2019e, which points out that the LAB-based polar coordinates are also sometimes referred to as HCL). The HCL model captures the human perceptual axes very well without confounding effects as in the HSV or HLS approaches. (More details follow below.)

All S4 classes for color spaces inherit from a virtual class color which is internally always represented by matrices with three columns (corresponding to the three dimensions).

Note that since the inception of the color space conversion tools in (in , Ihaka 2003) other tools for this purpose became available, notably grDevices::convertColor() (in high-level , R Core Team 2019) and farver::convert_colour() (in , Pedersen, Nicolae, and François 2020). For many basic color conversion purposes the colorspace package and these alternatives are equally suitable. Some details differ, though, and the color conversion tools in colorspace are well-embedded into the remaining functionality of the package and make it self-contained.

## Human color vision and the HCL color model

It has been hypothesized that human color vision has evolved in three distinct stages:

1. Perception of light/dark contrasts (monochrome only).
2. Yellow/blue contrasts (usually associated with our notion of warm/cold colors).
3. Green/red contrasts (helpful for assessing the ripeness of fruit).

See Kaiser and Boynton (1996), Knoblauch (2002), Ihaka (2003), Lumley (2006), Zeileis, Hornik, and Murrell (2009) for more details and references. Thus, colors can be described using a 3-dimensional space:

However, for describing colors in such a space, it is more natural for humans to employ polar coordinates in the color plane (yellow/blue vs. green/red, visualized by the dashed circle above) plus a third light/dark axis. Hence, color models that attempt to capture these perceptual axes are also called perceptually-based color spaces. As already argued above, the HCL model captures these dimensions very well, calling them: hue, chroma, and luminance. The corresponding sRGB gamut, i.e., the HCL colors that can also be represented in sRGB, is visualized in the animation below (by Horvath and Lipka 2017).

The shape of the HCL space is a distorted double cone which is seen best by looking at vertical slices, i.e., chroma-luminance planes for given hues. For example, the left panel below depicts the chroma-luminance plane for a certain blue (hue = 255). Along with luminance the colors change from dark to light. With increasing chroma the colors become more colorful, where the highest chroma is possible for intermediate luminance.

As some colors are relatively dark (e.g., blue and red assume their maximum chroma for relatively low luminances) while others are relatively light (e.g., yellow and green), horizontal slices of hue-chroma planes for given hue have somewhat irregular shapes. The right panel below shows such a hue-chroma plane for moderately light colors (luminance = 70). At that luminance, green and orange can become much more colorful compared to blue or red.

## Utilities

Several utilities are available for working with the S4 classes implementing the color spaces listed above.

• as() method: Convert a color object to the various color spaces, e.g., as(x, "sRGB").
• coords(): Extract the three-dimensional coordinates pertaining to the current color class.
• hex(): Convert a color object to sRGB and code in a hex string that can be used within R plotting functions.
• hex2RGB(): Convert a given hex color string to an sRGB color object which can also be coerced to other color spaces.
• readRGB() and readhex() can read text files into color objects, either from RGB coordinates or hex color strings.
• writehex(): Write hex color strings to a text file.
• whitepoint(): Query and change the so-called white point employed in conversions from CIE XYZ to RGB. Defaults to D65 that has been specified by the CIE to approximate daylight.

## Illustration of basic colorspace functionality

As an example a vector of colors x can be specified in the HCL (or polar LUV) model:

(x <- polarLUV(L = 70, C = 50, H = c(0, 120, 240)))

##       L  C   H
## [1,] 70 50   0
## [2,] 70 50 120
## [3,] 70 50 240

The resulting three colors are pastel red (hue = 0), green (hue = 120), and blue (hue = 240) with moderate chroma and luminance. For display in other systems an sRGB representation might be needed:

(y <- as(x, "sRGB"))

##              R         G         B
## [1,] 0.8931564 0.5853740 0.6465459
## [2,] 0.5266113 0.7224335 0.4590469
## [3,] 0.4907804 0.6911937 0.8673877

The displayed coordinates can also be extracted as numeric matrices by coords(x) or coords(y). We can also, for example, coerce from sRGB to HSV:

as(y, "HSV")

##             H         S         V
## [1,] 348.0750 0.3446008 0.8931564
## [2,] 104.6087 0.3645825 0.7224335
## [3,] 208.0707 0.4341857 0.8673877

For display in many systems (including R itself) hex color codes based on the sRGB coordinates can be created:

hex(x)

## [1] "#E495A5" "#86B875" "#7DB0DD"

## References

Horvath, Michael, and Christoph Lipka. 2017. “sRGB Gamut Within CIELCHuv Color Space Mesh.” https://commons.wikimedia.org/w/index.php?title=File%3ASRGB_gamut_within_CIELCHuv_color_space_mesh.webm.

Ihaka, Ross. 2003. “Colour for Presentation Graphics.” In Proceedings of the 3rd International Workshop on Distributed Statistical Computing, Vienna, Austria, edited by Kurt Hornik, Friedrich Leisch, and Achim Zeileis. http://www.ci.tuwien.ac.at/Conferences/DSC-2003/Proceedings/.

Kaiser, Peter K., and Robert M. Boynton. 1996. Human Color Vision. 2nd ed. Washington, DC: Optical Society of America.

Knoblauch, Kenneth. 2002. “Color Vision.” In Steven’s Handbook of Experimental Psychology – Sensation and Perception, edited by Steven Yantis and Hal Pashler, Third, 1:41–75. New York: John Wiley & Sons.

Lumley, Thomas. 2006. “Color Coding and Color Blindness in Statistical Graphics.” ASA Statistical Computing & Graphics Newsletter 17 (2): 4–7. http://stat-computing.org/newsletter/issues/scgn-17-2.pdf.

Pedersen, Thomas Lin, Berendea Nicolae, and Romain François. 2020. Farver: Vectorised Colour Conversion and Comparison. https://CRAN.R-project.org/package=farver.

R Core Team. 2019. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.

Wikipedia. 2019a. “CIE 1931 Color Space — Wikipedia, the Free Encyclopedia.” URL https://en.wikipedia.org/wiki/CIE_1931_color_space, accessed 2019-01-05.

———. 2019b. “CIELAB Color Space — Wikipedia, the Free Encyclopedia.” URL https://en.wikipedia.org/wiki/CIELAB_color_space, accessed 2019-01-05.

———. 2019c. “CIELUV — Wikipedia, the Free Encyclopedia.” URL https://en.wikipedia.org/wiki/CIELUV, accessed 2019-01-05.

———. 2019d. “Color Space — Wikipedia, the Free Encyclopedia.” URL https://en.wikipedia.org/wiki/Color_space, accessed 2019-03-11.

———. 2019e. “HCL Color Space — Wikipedia, the Free Encyclopedia.” URL https://en.wikipedia.org/wiki/HCL_color_space, accessed 2019-08-23.

———. 2019f. “HSL and HSV — Wikipedia, the Free Encyclopedia.” URL https://en.wikipedia.org/wiki/HSL_and_HSV, accessed 2019-01-05.

———. 2019g. “RGB Color Space — Wikipedia, the Free Encyclopedia.” URL https://en.wikipedia.org/wiki/RGB_color_space, accessed 2019-01-05.

———. 2019h. “sRGB — Wikipedia, the Free Encyclopedia.” URL https://en.wikipedia.org/wiki/sRGB, accessed 2019-01-05.

———. 2019i. “Web Colors — Wikipedia, the Free Encyclopedia.” URL https://en.wikipedia.org/wiki/Web_colors, accessed 2019-03-11.

Zeileis, Achim, Kurt Hornik, and Paul Murrell. 2009. “Escaping RGBland: Selecting Colors for Statistical Graphics.” Computational Statistics & Data Analysis 53: 3259–70. https://doi.org/10.1016/j.csda.2008.11.033.