How to plot variable arrowheads AND variable colors?

Question

Is there any way to have variable arrowheads AND variable colors?

I know that I can define different arrowstyle with different heads. However, if I am using variable arrowstyle I cannot set a variable color. I will get an error:

duplicated or contradicting arguments in plot options

Apparently, e.g. an additional lc rgb 0x123456 can't overwrite the selected arrowstyle properties? Too bad. So, would this mean I have to define arrowstyles for all combinations of possible arrowheads and all possible colors in advance? Alternatively, if I use only 4 different arrowheads, I could split the arrowheads into 4 separate plot elements (with many different colors). Are there better solutions which I don't see? I tried with gnuplot 5.5.

Script:

### how to plot variable arrowheads AND variable colors?
reset session

$Data <<EOD
 1   -1    0x000000
 2    0    0xff0000
 3    1    0x00ff00
 4    2    0x0000ff
 5    1    0xff00ff
 6    2    0xffff00
 6    2    0x00ffff
EOD

set style arrow 1 backhead lw 3   # -1
set style arrow 2 nohead   lw 3   #  0
set style arrow 3 head     lw 3   #  1
set style arrow 4 heads    lw 3   #  2

set key noautotitle
set offset 0.5,0.5,0.5,0.5

set multiplot layout 1,3

    set title "variable arrowstyle"
    plot $Data u (0):1:(2):(0):($2+2) w vectors as var

    set title "variable color"
    plot $Data u (0):1:(2):(0):3 w vectors lc rgb var lw 3
    
    set title "variable arrowhead and color???"
    plot $Data u (0):1:(2):(0):3 w vectors nohead lc "black" lw 1 dt 3
    
unset multiplot
### end of script

Result:

Answer 1

You come up with such great corner cases! I love it. The intended way to do this is to set lc rgb variable or lc variable in the arrow style itself.

set style arrow 1 backhead lw 3 lc rgb variable
set style arrow 2 nohead   lw 3 lc rgb variable
set style arrow 3 head     lw 3 lc rgb variable
set style arrow 4 heads    lw 3 lc rgb variable

set title "variable arrowhead and color"
plot $Data u (0):1:(2):(0):($0+1):3 w vectors as variable

I say "the intended way" because it turns out this doesn't quite work in practice. It requires 6 columns in the using specifier: x y dx dy arrowstyle rgbcolor but the program thinks that the maximum possible for this plot style is 5 and gives an error message Too many using specs for this style.

That should be an easy fix, so look for an update to the development version soonish.

Update (21 May 2022)

Now fixed upstream. This code will work in release 5.4.4.

Answer 2

This is one solution which I mentioned in the question. Basically, it plots the data four times for 4 different arrowheads and each time blanking the data for the other arrowheads by using the ternary operator and NaN.

Maybe there are better solutions?

Script:

### plotting variable arrowheads AND variable colors
reset session

$Data <<EOD
 1   -1    0x000000
 2    0    0xff0000
 3    1    0x00ff00
 4    2    0x0000ff
 5    1    0xff00ff
 6    2    0xffff00
 6    2    0x00ffff
EOD

set style arrow 1 backhead lw 3   # -1
set style arrow 2 nohead   lw 3   #  0
set style arrow 3 head     lw 3   #  1
set style arrow 4 heads    lw 3   #  2
set key noautotitle
set offset 0.5,0.5,0.5,0.5

set multiplot layout 1,3
    set title "variable arrowstyle"
    plot $Data u (0):1:(2):(0):($2+2) w vectors as var

    set title "variable color"
    plot $Data u (0):1:(2):(0):3 w vectors lc rgb var lw 3
    
    set title "variable arrowhead and color"
    plot $Data u (0):1:(2):($2==-1?0:NaN):3 w vectors lc rgb var lw 2 backhead, \
            '' u (0):1:(2):($2== 0?0:NaN):3 w vectors lc rgb var lw 2 nohead, \
            '' u (0):1:(2):($2== 1?0:NaN):3 w vectors lc rgb var lw 2 head, \
            '' u (0):1:(2):($2== 2?0:NaN):3 w vectors lc rgb var lw 2 heads
unset multiplot
### end of script

Result: