An introduction to qualpalr"
In qualpalr: Automatic Generation of Qualitative Color Palettes

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.

[^1]: Input can also be a predefined set of colors or a subspace of the LCH~ab~ color space.

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.

#| label: basic-usage
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).

#| label: qualpal-list
pal

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

#| fig-show: hold
# 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

#| fig-width: 5
#| fig-height: 5
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).

#| label: details-input
#| message: false
#| echo: false
options(rgl.useNULL = TRUE)
library(rgl)

# Set up color subspace as in qualpal()
h <- c(-200, 120)
s <- c(0.3, 0.8)
l <- c(0.4, 0.9)

# Generate a quasi-random Halton sequence
rnd <- randtoolbox::halton(1000, dim = 3)

# Convert random sequence to specified color space
scale_runif <- function(x, new_min, new_max) {
  (new_max - new_min) * (x - 1) + new_max
}

rnd[, 2] <- sqrt(rnd[, 2])
H <- scale_runif(rnd[, 1], min(h), max(h))
S <- scale_runif(rnd[, 2], min(s), max(s))
L <- scale_runif(rnd[, 3], min(l), max(l))

HSL <- cbind(H, S, L)
HSL[HSL[, 1] < 0, 1] <- HSL[HSL[, 1] < 0, 1] + 360

# Set up variables to produce the HSL cylinder
x <- S * cos(H * pi / 180)
y <- S * sin(H * pi / 180)

# Convert to RGB to enable coloring
RGB <- qualpalr:::convert_colors(HSL, "hsl", "rgb")

plot3d(cbind(x, y, L), col = rgb(RGB), main = "HSL")
rglwidget()

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

#| label: rgb-space
#| echo: false
plot3d(RGB, col = rgb(RGB), main = "RGB")
rglwidget()

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 [@sharma2005], 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_uniform_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.

#| label: din-space
#| echo: false
DIN99d <- qualpalr:::convert_colors(RGB, "rgb", "din99d")

plot3d(DIN99d, col = rgb(RGB), main = "DIN99d")
rglwidget()

When using the DIN99d color space, we also apply a power transformation [@huang_power_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.

#| label: selected-points
#| echo: false
pal <- qualpal(5, list(h = c(-200, 120), s = c(0.3, 0.8), l = c(0.4, 0.9)))
plot3d(DIN99d, col = rgb(RGB), main = "DIN99d", alpha = 0.1)
plot3d(pal$DIN99d, col = pal$hex, main = "DIN99d", add = TRUE, size = 5)
rglwidget()