Combine alpha transparency values with additive logic

Usage

combine_alphas(x, max_alpha = 1, ...)

Arguments

x: numeric alpha value, typically limited between 0 and 1. The max value can be set using max_alpha.
max_alpha: numeric default 1, the maximum permitted alpha value.
...: additional arguments are ignored.

Value

numeric value after combining alpha values.

Details

Alpha transparency is defined as 0 for fully transparent, and 1 (or max_alpha) for fully opaque (not transparent). The purpose is to permit combining multiple colors, where the alpha transparency builds over time. Each color should contribute some proportional fraction to the overall opacity of the final color.

The basic formula:

new_alpha <- alpha1 + (1 - alpha1) * alpha2

Or when max_alpha is defined:

new_alpha <- alpha1 + (max_alpha - alpha1) * alpha2

Any NA values are considered equivalent to 0 and are therefore not applied.
All input alpha values are restricted to values between 0 and max_alpha.
For more than two values, each value is applied in series, which works out to the same result if applied in any order.

Examples

# it progressively fills 50% of remaining transparency
combine_alphas(c(0.5, 0.5))
#> [1] 0.75
combine_alphas(c(0.5, 0.5, 0.5))
#> [1] 0.875
combine_alphas(c(0.5, 0.5, 0.5, 0.5))
#> [1] 0.9375

base_alpha <- 0.5;
new_alphas <- sapply(1:5, function(i){
   combine_alphas(rep(base_alpha, i))
})
names(new_alphas) <- seq_along(new_alphas);
bp <- barplot(new_alphas, ylim=c(0, 1.1), col="navy",
   xlab=paste0("Number of ",
   base_alpha,
   " alpha values combined"))
abline(h=1, lty=2);
jamba::shadowText(x=bp[, 1], y=new_alphas,
   col="white", cex=1.5,
   pos=1,
   xpd=TRUE,
   label=round(new_alphas, digits=3))