How to draw arrows as those appear on military maps?

I wish to draw a curved arrow whose thickness changes from end to head. Such arrows are commonly used in military maps to denote the moves of forces. Below is an example. Is it possible to do it in tikz? Thanks!

• Although typically questions like this will get a lot of comments about "showing what you've tried", in this case, the problem is truly quite difficult with TikZ. Related: Stroke with variable thickness and possibly Is it possible to increase the line's width from its start to its end? Oct 24 '17 at 4:02
• OTOH, if you don't think of it as an arrow, but as two curved lines with a straight line at one end and a triangle at the other... Oct 24 '17 at 4:11
• @JohnKormylo Yes, that's probably the simplest way to draw them, but still not totally straightforward. Oct 24 '17 at 4:15
• @AlanMunn - The question is how to parameterize the arrow. End points aren't enough, you need the starting width, ending width and curvature. Oct 24 '17 at 4:19

Not amazing, and will quite happily produce horrendous results with extreme curves or parameter values. Currently for single curveto operations only (i.e., paths consisting of a single Bézier curve).

\documentclass[tikz,margin=5]{standalone}
\usetikzlibrary{calc,decorations.pathreplacing,decorations.markings}
\tikzset{big arrow/.style={
/tikz/big arrow/.cd, #1, /tikz/.cd,
decoration={show path construction,
curveto code={%
%
mark=at position -\bigarrowlength with {\coordinate (@); }}, decorate]
(\tikzinputsegmentfirst) .. controls (\tikzinputsegmentsupporta)
and (\tikzinputsegmentsupportb) .. (\tikzinputsegmentlast);
\path[big arrow/.cd,#1]
let \p1=(\tikzinputsegmentfirst), \p2=(\tikzinputsegmentsupporta),
\p3=(\tikzinputsegmentsupportb), \p4=(@), \p5=(\tikzinputsegmentlast),
\n1={atan2(\y2-\y1,\x2-\x1)}, \n2={atan2(\y4-\y3,\x4-\x3)} in
(\p1) -- ++(\n1+90:\bigarrowstartwidth/2)
.. controls ++(\x2-\x1, \y2-\y1) and ++(\x3-\x4, \y3-\y4) ..
($(\p4)+(\n2+90:\bigarrowendwidth/2)$) --
($(\p4)+(\n2+90:\bigarrowwidth/2)$) -- (\p5) --
($(\p4)+(\n2-90:\bigarrowwidth/2)$) --
($(\p4)+(\n2-90:\bigarrowendwidth/2)$)
.. controls ++(\x3-\x4, \y3-\y4) and ++(\x2-\x1, \y2-\y1) ..
($(\p1)+(\n1-90:\bigarrowstartwidth/2)$) -- cycle;
%
}}, decorate
},
big arrow/.cd,
start width/.store in=\bigarrowstartwidth,
end width/.store in=\bigarrowendwidth,
length/.store in=\bigarrowlength,
width/.store in=\bigarrowwidth,
start width=1cm,
end width=0.5cm,
length=0.25cm,
width=1cm,
.unknown/.code=%
{\let\searchname=\pgfkeyscurrentname\pgfkeysalso{/tikz/\searchname=#1}}%
}
\begin{document}
\begin{tikzpicture}
\draw [big arrow={fill=red}] (0,0) to [bend left] (5,5);
\draw [big arrow={fill=green, length=0.5cm}] (0,0) to [bend right] (-3,3);
\draw [big arrow={fill=blue, start width=1.5cm, end width=1cm,
width=1.5cm, length=0.75cm}] (0,0) to [bend right] (4,0);
\end{tikzpicture}
\end{document} 