How can one mix 2 or more color palettes to show a combined color value

Question

I'm trying to create a plot where color represents the combination of several values. In the example below, I am applying increasing values for red associated with the x-coordinate and increasing values for blue in associated with the y-coordinate.

#required function 'val2col' from: http://www.menugget.blogspot.de/2011/09/converting-values-to-color-levels.html

val2col<-function(z, zlim, col = heat.colors(12), breaks){
 if(!missing(breaks)){
  if(length(breaks) != (length(col)+1)){stop("must have one more break than colour")}
 }
 if(missing(breaks) & !missing(zlim)){
  zlim[2] <- zlim[2]+c(zlim[2]-zlim[1])*(1E-3)#adds a bit to the range in both directions
  zlim[1] <- zlim[1]-c(zlim[2]-zlim[1])*(1E-3)
  breaks <- seq(zlim[1], zlim[2], length.out=(length(col)+1)) 
 }
 if(missing(breaks) & missing(zlim)){
  zlim <- range(z, na.rm=TRUE)
  zlim[2] <- zlim[2]+c(zlim[2]-zlim[1])*(1E-3)#adds a bit to the range in both directions
  zlim[1] <- zlim[1]-c(zlim[2]-zlim[1])*(1E-3)
  breaks <- seq(zlim[1], zlim[2], length.out=(length(col)+1))
 }
 colorlevels <- col[((as.vector(z)-breaks[1])/(range(breaks)[2]-range(breaks)[1]))*(length(breaks)-1)+1] # assign colors to heights for each point
 colorlevels
}


#data
x <- seq(100)
y <- seq(100)
grd <- expand.grid(x=x,y=y)

#assign colors to grd levels
pal1 <- colorRampPalette(c("white", rgb(1,0,0)), space = "rgb")
col1 <- val2col(x, col=pal1(10))
pal2 <- colorRampPalette(c("white", rgb(0,0,1)), space = "rgb")
col2 <- val2col(y, col=pal2(10))
col3 <- NA*seq(nrow(grd))
for(i in seq(nrow(grd))){
    xpos <- grd$x[i]
    ypos <- grd$y[i]
    coltmp <- (col2rgb(col1[xpos])/2) + (col2rgb(col2[ypos])/2)
    col3[i] <- rgb(coltmp[1], coltmp[2], coltmp[3], maxColorValue = 255)
}

    #plot
png("2_color_scales.png", width=6, height=4, units="in", res=200)
layout(matrix(c(1,2,3), nrow=1, ncol=3), widths=c(4,1,1), heights=4, respect=T)
par(mar=c(4,4,2,2))
plot(grd,col=col3, pch=19)
par(mar=c(4,0,2,5))
image(x=1, y=x, z=t(as.matrix(x)), col=pal1(10), xaxt="n", yaxt="n", xlab="", ylab="")
box()
axis(4)
mtext("x", side=4, line=3, cex=0.7)
par(mar=c(4,0,2,5))
image(x=1, y=y, z=t(as.matrix(y)), col=pal2(10), xaxt="n", yaxt="n", xlab="", ylab="")
box()
axis(4)
mtext("y", side=4, line=3, cex=0.7)
dev.off()

The result is technically correct in that when x = 1 and y = 10, the mixing of colors "white" and "blue", respectively, returns the lighter shade of blue. However, I would rather like this position to look as "blue" as the darkest blue of the y color bar. I imagine this would require one to use transparency for lower values rather than the color white. Does anyone have suggestions on how this might be accomplished? Adding two colors, including their transparency, is beyond me... I thought one might be able to use the transparency value as a weighting in the mixing step?

Thanks for your help.

Crenelation

Answer 1

Since I'm more familiar with ggplot, I'll show a solution using ggplot. This has the side benefit that, since the ggplot code is very simple, we can focus the discussion on the topic of colour management, rather than R code.

1. Start by using expand.grid to create a data frame dat containing the grid of red and blue input values.
2. Use the function rgb() to create the colour mix, and assign it to dat$mix
3. Plot.

The code:

dat <- expand.grid(blue=seq(0, 100, by=10), red=seq(0, 100, by=10))
dat <- within(dat, mix <- rgb(green=0, red=red, blue=blue, maxColorValue=100))

library(ggplot2)
ggplot(dat, aes(x=red, y=blue)) + 
  geom_tile(aes(fill=mix), color="white") + 
  scale_fill_identity()

---

You will notice that the colour scale is different from what you suggested, but possibly more intuitive.

When mixing light, absence of any colour yields black, and presence of all colours yields white.

This is clearly indicated by the plot, which I find rather intuitive to interpret.

Beyond

+1 Thanks Andre - it is quite intuitive. Very compact code too. Would it be easy for you to add the corresponding color scales to such a plot? I guess I thought that a subtractive Cyan-Magenta-Yellow type color model (i.e. equaling white when no colors are applied) might be better for printing than an additive RGB color model. – Crenelation

@Marcinthebox My suspicion is that any attempt at mixing two elements into a single colour scale is going to be rather tricky to interpret. What are you trying to plot? Can you use some other aesthetic instead, e.g. size or shape to indicate a second element? – Beyond

I was thinking of using such a plot in the presentation of three nutrient concentrations in surface waters (i.e. spatially). I was hoping that such a map might be an intuitive way to see these spatial patterns. I envisioned the corresponding color key to be a tri-plot showing the color gradient for the 3 nutrient concentrations. – Crenelation

I would suggest you use facets instead. I find the tri-plots utterly confusing and non-intuitive. If you then add a potentially confusing colour mix on top of that, it gets even worse. Three maps, side by side, each demonstrating the levels of a specific nutrient should be much easier to interpret. – Beyond