Point-mark discrimination probability for a pair of colors

The point-mark analogue of line_discrim_prob(): predicts the proportion of viewers who would detect the color difference between two circular scatterplot-style point marks, as a function of point diameter, using the model fit by Szafir (2018) for scatterplots (Experiment One; see Details).

Usage

point_discrim_prob(hex1, hex2, size = seq(0.25, 2, by = 0.05))

Arguments

hex1, hex2: two hex color strings, e.g. "#3B4CC0" and "#B40426"
size: numeric vector of point diameters in degrees of visual angle. Szafir's tested range was 0.25 to 2.0 degrees; see the validated-range caveat above for values outside that range.

Value

data.frame with columns size_deg and p_discriminable

Details

Model: p = m_x(s) * dx, m_x(s) = c_x + k_x / s, per CIELAB axis (L*, a*, b*), combined across axes as sqrt(sum((dx * m_x(s))^2)) and clipped to [0, 1] – identical form to line_discrim_prob(), but with its own coefficients fit on point marks, and s is point diameter rather than line thickness.

Caveats (see line_discrim_prob() for the shared ones – white background only, cross-axis combination untested):

Validated range. Fit using six diameter steps from 0.25 to 2.0 degrees. This is a much higher floor than the line model's 0.05-0.35 degrees – do not feed sizes below roughly 0.25 degrees into this function. Below about 0.1-0.2 degrees (depending on axis), c_x + k_x/s goes negative, which is not a meaningful extrapolation, just a sign flip from being far outside the fitted domain.
Points are less discriminable than lines of the same size. Szafir's own comparison found colors generally more discriminable on elongated marks (lines, bars) than on points – don't expect a point and a line of the same visual-angle size to give similar probabilities for the same color pair.

References

Szafir, D.A. (2018). Modeling Color Difference for Visualization Design. IEEE Transactions on Visualization and Computer Graphics, 24(1), Experiment One.