# An introduction to qualpalr

#### Johan Larsson

#### 2025-10-17

## Overview

`qualpalr` generates qualitative color palettes optimized for maximally distinct colors. Given `n` (the number of colors to generate), along with a subset in the hsl color space 1 (a cylindrical representation of the RGB color space) `qualpalr` attempts to find the `n` colors in the provided color subspace that maximize the smallest pairwise color difference. This is done by computing the pairwise color differences between all the input colors, and then selecting the `n` colors that maximize the minimum pairwise color difference.

## Examples

`qualpalr` main workhorse is `qualpal()`, which takes as its input `n` (the number of colors to generate) and `colorspace`, which can be either

- a list of numeric vectors `h` (hue from -360 to 360), `s` (saturation from 0 to 1), and `l` (lightness from 0 to 1), all of length 2, specifying a min and max,
- a list of numeric vectors `h` (hue from -360 to 360), `c` (chroma from 0 to 100), and `l` (lightness from 0 to 100), all of length 2, specifying a min and max, or
- a character vector specifying a predefined color palette.

    library(qualpalr)
    pal <- qualpal(5, list(h = c(-200, 120), s = c(0.3, 0.8), l = c(0.4, 0.9)))

    # Adapt the color space to deuteranopia of severity 0.7
    pal <- qualpal(5, cvd = c(deutan = 0.7))

The resulting object, `pal`, is a list with several color tables and a distance matrix based based on the color difference metric used, by default CIEDE2000 (`metric = ciede2000`).

    pal

    ## ----------------------------------------
    ## Colors in the HSL color space
    ##
    ##           Hue Saturation Lightness
    ## #6e6cca 240.8       0.47      0.61
    ## #c8e8df 162.8       0.40      0.85
    ## #c984a9 327.7       0.39      0.65
    ## #cb7469   6.7       0.49      0.60
    ## #c9cb70  61.5       0.47      0.62
    ##
    ##  ----------------------------------------
    ## DIN99d color difference distance matrix
    ##
    ##         #6e6cca #c8e8df #c984a9 #cb7469
    ## #c8e8df      24
    ## #c984a9      17      22
    ## #cb7469      23      24      12
    ## #c9cb70      29      16      23      20

Methods for `pairs` and `plot` have been written for `qualpal` objects to help visualize the results.

    # Multidimensional scaling plot
    plot(pal)

    # Pairs plot in the DIN99d color space
    pairs(pal, colorspace = "DIN99d")

The colors are most easily used in R by accessing `pal$hex`

    library(maps)
    map("france", fill = TRUE, col = pal$hex, mar = c(0, 0, 0, 0))

## Details

`qualpal` begins by generating a point cloud out of the HSL color subspace provided by the user, using a quasi-random Halton sequence. Here is the color subspace in HSL with settings `h = c(-200, 120), s = c(0.3, 0.8), l = c(0.4, 0.9)`.

The program then proceeds by projecting these colors into the sRGB space.

It then continues projecting the colors into the XYZ space. After this, behavior depends on the metric used. By default, qualpal uses the CIEDE2000 color difference formula (Sharma, Wu, and Dalal 2005), which is the current state of the art in color difference metrics and standard as defined by the International Commission on Illumination (CIE). For illustrative purposes, however, we will show the procedure when the DIN99d color space (Cui et al. 2002) is used instead, which is a perceptually uniform color space that uses the Euclidean distance as a color difference metric. This makes for a computationally simpler and faster algorithm, but it is not as accurate as CIEDE2000.

When using the DIN99d color space, we also apply a power transformation (Huang et al. 2015) to fine tune these differences.

To select the `n` colors that the user wanted, we proceed greedily: first, we find the two most distant points, then we find the third point that maximizes the minimum distance to the previously selected points. This is repeated until `n` points are selected. These points are then returned to the user; below is an example using `n = 5`.

## Thanks

Bruce Lindbloom’s webpage has been instrumental in making qualpalr. Thanks also to i want hue, which inspired me to make qualpalr.

## References

Cui, G., M. R. Luo, B. Rigg, G. Roesler, and K. Witt. 2002. “Uniform Colour Spaces Based on the DIN99 Colour-Difference Formula.” Color Research & Application 27 (4): 282–90. https://doi.org/10.1002/col.10066.
Huang, Min, Guihua Cui, Manuel Melgosa, Manuel Sánchez-Marañón, Changjun Li, M. Ronnier Luo, and Haoxue Liu. 2015. “Power Functions Improving the Performance of Color-Difference Formulas.” Optics Express 23 (1): 597. https://doi.org/10.1364/OE.23.000597.
Sharma, Gaurav, Wencheng Wu, and Edul N. Dalal. 2005. “The CIEDE2000 Color-Difference Formula: Implementation Notes, Supplementary Test Data, and Mathematical Observations.” Color Research & Application 30 (1): 21–30. https://doi.org/10.1002/col.20070.

1. Input can also be a predefined set of colors or a subspace of the LCHab color space.↩︎