Well, I really hope this problem is as easy as overlay two pieces of paper. Unfortunately there are a few extra miles to go. The steps are clear though:

- get the rgb number on the corresponding position for paint and background heatmap, regardless of the values in the dataset
- merge two rgbs cell by cell
- plot the result rgb color matrix.

heatmap_col <- function(val_array, col_list) {

minv = min(val_array)

maxv = max(val_array)

out = val_array

for( i in 1:nrow(val_array))

for( j in 1:ncol(val_array))

# take max of 1 or the other value in case 0 is the ceiling result

out[i,j] = col_list[max(1, ceiling((val_array[i,j] - minv) / (maxv - minv) * length(col_list)))]

out

}

With this then, I can easily get the rgb used on each cell of the heatmap. However, the returns are simply rgb code, like '#FF000045'(red,green,blue,alpha). We need to know the exact numbers of red, green, blue and even alpha, which are critical for the blending. After some serious googling, I found this colorful presentation very helpful. It contains a hex constant table, which could be used to break down rgb color into 4 numbers between 0 and 1, corresponding to red, green, blue and alpha. R code is here

hex_constant = data.frame(hex=c(seq(from=0, to=9, by=1), toupper(letters[1:6])), decimal=seq(from=0, to=15, by=1), stringsAsFactors=F)

rgb2hex_number <- function(x, hex_constant){

num_collector = hex_constant$decimal[hex_constant$hex == toupper(substr(x, start=2, stop=2))]

for(i in 3:nchar(x))

num_collector = c(num_collector, hex_constant$decimal[hex_constant$hex == toupper(substr(x, start=i, stop=i)]))

R = (num_collector[1]*16+num_collector[2])/255

G = (num_collector[3]*16+num_collector[4])/255

B = (num_collector[5]*16+num_collector[6])/255

with_alpha = ifelse(nchar(x) > 7, TRUE, FALSE)

if(with_alpha) {

A = (num_collector[7]*16+num_collector[8])/255

return(c(R, G, B, A))

} else { # fill in alpha of 0

return(c(R, G, B, 0))

}

}

The next step is to merge two rgb numbers on the same position. Two stackoverflow posts (here and there) talked about how to do it in python. If one happens to look up in wikipedia, one has to be skeptical with it.

Wiki is wrong about the operation could be associative. It's actually not, meaning switching background and paint colors while blending can yield different color. A quick algebra is enough. The R code for this step is trivial.

mix_2rgb <- function(x, y){

# x is the paint color, y is the background color

# NOTICE: this operation is not associative. Switching x and y may yield different result.

# lookup table of hex and decimal

hex_constant=data.frame(hex=c(seq(from=0, to=9, by=1), toupper(letters[1:6])), decimal=seq(from=0, to=15, by=1), stringsAsFactors=F)

# belending two rgb colors evenly

x_out = rgb2hex_number(x, hex_constant)

y_out = rgb2hex_number(y, hex_constant)

# with alpha channel considered

ax = 1- (1 - x_out[4]) * (1 - y_out[4])

if( ax > 0 ) {

rx = x_out[1] * x_out[4] / ax + y_out[1] * y_out[4] * (1 - x_out[4]) / ax

gx = x_out[2] * x_out[4] / ax + y_out[2] * y_out[4] * (1 - x_out[4]) / ax

bx = x_out[3] * x_out[4] / ax + y_out[3] * y_out[4] * (1 - x_out[4]) / ax

return(rgb(rx, gx, bx, ax))

} else {

rx = (x_out[1] + y_out[1]) / 2

gx = (x_out[2] + y_out[2]) / 2

bx = (x_out[3] + y_out[3]) / 2

return(rgb(rx, gx, bx))

}

}

The last step is a little bit tricky. Since all I have for now is the colors I want to plot at each cell, but I don't have a data matrix to pass to "heatmap" function. So I have to do a hack using "rect" function. Anyway, This is the end result. Not bad, huh?