Outline boundary of a union of two curvilinear areas in TikZ

Question

Found several questions here obviously related to what I want, TikZ outline stroke of a compound shape, How to outline the union of an annulus and a rectangle in TikZ?, TikZ: Drawing an arc from an intersection to an intersection and some others, but still could not figure out how to adapt them for my needs.

I have this:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,intersections}
\begin{document}
\begin{tikzpicture}
\clip (-4,-1) rectangle (4,3);
\coordinate (a) at (-4,-3);
\coordinate (va) at (3,7.5);
\shadedraw[name path=higher,opacity=.3] (a) .. controls ($(a)+(va)$) .. ($(a)+(6,0)$);
\coordinate (b) at (4,-5);
\coordinate (vb) at (-3,7.5);
\shadedraw[name path=lower,opacity=.3] ($(b)-(6,0)$) .. controls ($(b)+(vb)$) .. (b);
\path [name intersections={of=higher and lower,by=x}];
\coordinate (xa) at (-1.65,3.45);
\coordinate (xb) at (1,.75);
\draw[thick] (a) .. controls ($(a)+.89(va)$) and ($(x)+(xa)$) .. (x)
                 .. controls ($(x)+(xb)$) and ($(b)+.6(vb)$) .. (b);
\end{tikzpicture}
\end{document} 

and the result is

but it took me quite some effort to find, by blind trial-and-error, the six decimals in the code, and, if you look attentively, the picture is still not entirely accurate.

Is there a better way to draw that thick line?

Answer 1

This can be achieved by use of the spath3 library (this ought to work with the current version on CTAN but if not the latest version is available from github - it's just waiting for me to upload it to CTAN).

After drawing and shading the original paths, it splits then at the point where they intersect. Individual components can then be rendered separately, and also welded together to form a nice joint at the intersection point.

\documentclass{article}
%\url{https://tex.stackexchange.com/q/598243/86}
\usepackage{tikz}
\usetikzlibrary{
  calc,
  intersections,
  spath3
}
\begin{document}
\begin{tikzpicture}
\clip (-4,-1) rectangle (4,3);
\coordinate (a) at (-4,-3);
\coordinate (va) at (3,7.5);
\shadedraw[spath/save=higher,opacity=.3] (a) .. controls ($(a)+(va)$) .. ($(a)+(6,0)$);
\coordinate (b) at (4,-5);
\coordinate (vb) at (-3,7.5);
\shadedraw[spath/save=lower,opacity=.3] ($(b)-(6,0)$) .. controls ($(b)+(vb)$) .. (b);
\tikzset{
  spath/split at intersections={higher}{lower},
  spath/get components of={higher}\higherPath,
  spath/get components of={lower}\lowerPath,
}
\draw[
  thick,
  spath/use=\getComponentOf\higherPath{1},
  spath/use={\getComponentOf\lowerPath{2},weld},
];
\end{tikzpicture}
\end{document} 

End result:

Detail of the intersection:

Answer 2

One simple way of doing this is to clip out the portion below node (x). Store your two curves to be able to use them twice, one for the shading, and one for the line drawing.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,intersections}
\begin{document}
\begin{tikzpicture}
    \clip (-4,-1) rectangle (4,3);
    \coordinate (a) at (-4,-3);
    \coordinate (va) at (3,7.5);
    \coordinate (b) at (4,-5);
    \coordinate (vb) at (-3,7.5);

    \def\higherpath{(a) .. controls ($(a)+(va)$) .. ($(a)+(6,0)$)}
    \def\lowerpath{($(b)-(6,0)$) .. controls ($(b)+(vb)$) .. (b)}

    \shadedraw[name path=higher,opacity=.3] \higherpath;
    \shadedraw[name path=lower,opacity=.3] \lowerpath;

    \path [name intersections={of=higher and lower,by=x}];

    \clip (-4,-1) -- (-2,-1) -- (x) -- (2,-1) -- (3,-1) -- (3,3) -| cycle;
    \draw \higherpath \lowerpath;
\end{tikzpicture}


\end{document}