Tikz: convert an object to a filled path?

Question

Let's say I have such a simple tikz "contour" object defined with \draw:

\documentclass{standalone}

\usepackage{tikz}
    \tikzset{x=1pt, y=1pt, z=1pt}

\begin{document}

\def\object{
    \draw[blue, thick, -stealth] (0,  0)
                     .. controls (5, -5)
                             and (10, 5)
                              .. (15, 0);
}

\begin{tikzpicture}
    \object
\end{tikzpicture}

\end{document}

Is there a way I could convert it to an actual \filled path? Drawing it is easy with \draw, but transforming it (in particular, fading it) would be more easy if it were drawn with \fill.. but what a pain would it be to design it with \fill!

I am aware that the problem is that, since it is declared as a path, it has no width in theory. The thing is that it does have a width orelse we could not see it. The question is: how to take this actual width into account and turn it into an explicit path?

Put it another way: how would you draw a black outline around this object?

(Yes, I am thinking about Inkscape's object to path or convert to path feature.)

---

[EDIT] If my understanding of this related question is correct, I would need to highjack the code from stealth in a heavy \makeatletter .. \makeatother section so that I could retrieve the actual contour of the whole arrow.

However, I am actually using Stealth from arrows.meta, and I would not like the code to be rewritten if I fancy change Stealth to Latex. What I am looking for is a more generic solution to retrieve the actual path primitive built when I type: \draw[blue, thick, -stealth] (0, 0) .. controls (5, -5) and (10, 5) .. (15, 0); It must be computed at some point internally otherwise the compilation would be meaningless. How can I get this intermediate result?

---

In an ideal world, I would type:

\getActualPath{\object}{\result}

and \result would then be magically expanded as:

\path[cm={{0.8,0.0,0.0,-0.8,(-0.398,5.38)}}]
    (17.3457,1.2305) -- (16.9707,3.8555) .. controls (16.4721,3.4476) and
    (15.9195,3.2113) .. (15.3516,3.1621) .. controls (14.6806,3.1040) and
    (14.0125,3.2715) .. (13.3496,3.5488) .. controls (12.0238,4.1035) and
    (10.6766,5.1107) .. (9.2793,6.0215) .. controls (7.8820,6.9323) and
    (6.4476,7.7369) .. (5.0586,7.9473) .. controls (3.6696,8.1576) and
    (2.3182,7.8417) .. (0.8496,6.3730) -- (0.1465,7.0762) .. controls
    (1.7912,8.7209) and (3.5542,9.1820) .. (5.2070,8.9316) .. controls
    (6.8598,8.6813) and (8.3943,7.7895) .. (9.8242,6.8574) .. controls
    (11.2541,5.9253) and (12.5908,4.9452) .. (13.7344,4.4668) .. controls
    (14.3062,4.2276) and (14.8182,4.1155) .. (15.2656,4.1543) .. controls
    (15.6068,4.1839) and (15.9194,4.2931) .. (16.2363,4.5293) --
    (13.6836,4.8926) -- (19.1777,6.7246) -- (17.3457,1.2305) -- cycle

so that

\begin{tikzpicture}
    \result[draw, fill=blue, line width=.1pt];
\end{tikzpicture}

would draw

and, with \usetikzlibrary{fadings},

\begin{tikzpicture}
    \result[path fading=west, fill=blue];
\end{tikzpicture}

would draw

and

\begin{tikzpicture}
    \result[clip];
    \node () at (8, 5) {\includegraphics[width=50pt]{example-image-a}};
\end{tikzpicture}

would draw

.. would this not be neat?

Answer 1

For fading, there really isn't a problem as we can fade a path or use a scope fading to apply whatever fading effects we wish to any path, even if the path is merely drawn rather than filled. We can apply this equally to paths specified and drawn within the scope and to predefined paths such as \object. For example

\begin{scope}[opacity=1,transparency group] \path [scope fading=west] (0,-2) rectangle (3,1); \object \draw [green, ultra thick, -{Stealth[bend]}] (0,1) .. controls (1,-1) and (2,1) .. (3,1); \end{scope}

There is one caveat to this which is that the method works fine when the arrows are heading in the direction of opacity, but less well when the arrows head for transparency. That is, if we add

    \draw [magenta, ultra thick, {Stealth[bend]}-] (0,-1) .. controls (1,-1) and (2,1) .. (3,-1);

to our scope, the results will be less satisfactory. How much of an issue this is depends on the amount of transparency, type of arrow tip and size of arrow tip.

For greater flexibility, you can define \object to take an optional argument allowing you to write, for example,

\object[path fading=east]

or whatever.

This also permits a rather fiddly and not entirely satisfactory workaround for the outlining issue because we can say, for example

    \object[double=blue, draw=black, line width=.4pt, double distance=1.2pt, -{Stealth[sep=-9.5pt,fill=blue,width=1.7ex,length=2.1ex,bend]}]

to approximate an outlined version of our arrow. This can be additionally faded if placed within the scope we defined above. However, the solution is fiddly and the outline of the arrow tip is drawn completely which we would prefer not to happen.

The results look as follows:

\documentclass[tikz,multi,border=10pt]{standalone}
\usetikzlibrary{bending,arrows.meta,fadings}
\begin{document}
\newcommand*\object[1][]{%
  \draw [blue, ultra thick, -{Stealth[bend]}, #1] (0,0) .. controls (1,-1) and (2,1) .. (3,0);
}
\begin{tikzpicture}
  \begin{scope}[opacity=1,transparency group]
    \path [scope fading=west] (0,-2) rectangle (3,1);
    \scoped[yshift=-15mm]{\object[double=blue, draw=black, line width=.4pt, double distance=1.2pt, -{Stealth[sep=-9.5pt,fill=blue,width=1.7ex,length=2.1ex,bend]}]}
    \object
    \draw [green, ultra thick, -{Stealth[bend]}] (0,1) .. controls (1,-1) and (2,1) .. (3,1);
    \draw [magenta, ultra thick, {Stealth[bend]}-] (0,-1) .. controls (1,-1) and (2,1) .. (3,-1);
  \end{scope}
\end{tikzpicture}
\end{document}