Drawing a smooth, tapered path ending in an arrow

Question

I'm looking for a convenient way to draw a smooth, tapered path (i.e. a path of variable line width) ending in an arrowhead using TikZ — something like this (drawn in Inkscape):

One approach would be to use a custom decoration as described in this answer (from March 2011), but perhaps there are more straightforward approaches nowadays.

An idea that comes to mind is to draw a smooth path of constant line width and clip it with another path starting at the tail, going up to the start of the arrowhead. However, I just noticed that adding an arrowhead to a path actually changes the path itself (see code snippet and output below), which probably makes this approach a bit more complicated than I originally thought.

\usetikzlibrary{arrows.meta}
\begin{tikzpicture}
\draw[line width=1mm, black!40, -{Stealth[length=10mm, width=6mm]}] (0,0) .. controls (2,-1) and (4,-1) .. (6,0);
\draw[line width=.2mm] (0,0) .. controls (2,-1) and (4,-1) .. (6,0);
\end{tikzpicture}

[Edit] Thanks to @Markus G.'s comment, the changed path issue is resolved (see below). How to proceed?

\usetikzlibrary{bending, arrows.meta}

Answer 1

I propose a solution (or at least the beginning of a solution) based on @Alain Matthes's answer. Looking at the image above, we see, on the left, a case when the solution works (a simple to[] operation) and a case when it doesn't (an arc operation). The lower-right curve is the original curve from Alain's answer with width factor = 1 (for reference).

I introduce a decoration that puts together Alain's and a show path construction that introduces the arrow tip. There are three arguments: the width factor and the colors, start color and end color (already present in the previous answer).

Note that the resulting curve is slightly longer; the yellow curve drawn over the lower-left curve in the image shows the original path.

Remark 1. You can modify the relationship between the widths of the curve and arrow at their meeting point by modifying the constants in the definitions of \w and \d.

Remark 2. I think Alain's decoration could be modified in a more intelligent way to produce the result you are looking for, but I don't know how (I don't know how to use pgf commands).

The code

\documentclass[11pt, border=.5cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{math, arrows.meta}
\usetikzlibrary{decorations.pathreplacing}
%%% Alain Matthes's decoration
\pgfkeys{/pgf/decoration/.cd,
  width factor/.store in =\wfactor,
  start color/.store in =\startcolor,
  end color/.store in =\endcolor
}
\makeatletter
\pgfdeclaredecoration{width and color change}{initial}{
  \state{initial}[width=0pt, next state=line, persistent precomputation={%
    \pgfmathdivide{50}{\pgfdecoratedpathlength}%
    \let\increment=\pgfmathresult%
    \def\x{0}%
  }]{}
  \state{line}[width=.5pt, persistent postcomputation={%
    \pgfmathadd@{\x}{\increment}%
    \let\x=\pgfmathresult%
  }]{%
    \pgfsetlinewidth{\wfactor\x/500.075pt+\pgflinewidth}%
    \pgfsetarrows{-}%
    \pgfpathmoveto{\pgfpointorigin}%
    \pgfpathlineto{\pgfqpoint{.75pt}{0pt}}%
    \pgfsetstrokecolor{\endcolor!\x!\startcolor}%
    \pgfusepath{stroke}%
  }
  \state{final}{%
    \pgfsetlinewidth{\pgflinewidth}%
    \pgfpathmoveto{\pgfpointorigin}%
    \color{\endcolor!\x!\startcolor}%
    \pgfusepath{stroke}% 
  }
}
\makeatother
\begin{document}
\tikzset{
  tmp/.style n args={3}{
    postaction={
      decoration={
        width and color change,
        width factor=#1,
        start color=#2,
        end color=#3
      }, decorate
    },
    preaction={
      decoration={
        show path construction,
        curveto code={
          \tikzmath{
            real \w, \d;
            \w = {#160};
            \d = {#190};
          }
          \draw[#3,
          arrows={-Stealth[width=\w pt, length=\d pt]}]
          (\tikzinputsegmentfirst) .. controls
          (\tikzinputsegmentsupporta) and (\tikzinputsegmentsupportb)
          ..(\tikzinputsegmentlast) -- ([turn]0: \w pt);
        }
      }, decorate
    }
  }
}
\begin{tikzpicture}
  \draw[tmp={.4}{blue}{gray}] (0, 0) to[out=0, in=150] ++(6, 2);
  \draw[tmp={.4}{blue}{gray}] (0, -1) to[out=0, in=150] ++(6, 2);
  \draw[yellow, thin] (0, -1) to[out=0, in=150] ++(6, 2);
\path[tmp={.4}{yellow}{red}] (14, -1) arc (0: 120: 4);
  \draw[line width=.4pt, decoration={width and color change,

    width factor=1, start color=yellow, end color=red},
  decorate] (14, -3) arc (0:120:4cm);
\end{tikzpicture}
\end{document}