Filling an area between 2 curves in tikz

Question

I use the following tikz code as a part of a more complicated drawing with other curves using the defined coordinates.

How can I fill the area between the intersection of these compound curves?

I have some codes to fill intersection between 2 circles, but they do not apply for non-closed curves.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{trees, overlay-beamer-styles, arrows, backgrounds, positioning, calc, intersections}
\begin{document}
\begin{center}
\tikzset{lw/.style={line width=.04cm}}
\begin{tikzpicture}[scale=.8, transform shape]
\coordinate (uplt) at (0,0);
\coordinate (strt) at ([shift={(-32.:4.2cm)}]uplt);
\coordinate (strtd) at ([shift={(-120.:.36cm)}]strt);
\coordinate (strtdd) at ([shift={(-148.:1.cm)}]strt);
%
\draw [very thick, blue, looseness=.88] (strtd.center) to [out=140,in=-70] node [pos=.71, circle,black, fill=black, scale=0.8](b){} +(125.:2.6cm) (strtd.center) to [out=-40,in=170] +(-24.:4.cm);
%
\draw [very thick, blue, looseness=.88] (strtdd.center) to [out=140,in=-70] node [pos=1., circle,black, fill=black, scale=0.8](a){} +(125.:2.6cm) (strtdd.center) to [out=-40,in=170] +(-24.:4.4cm);
\begin{scope}[on background layer]
\draw [lw, red, looseness=.8] ([shift={(45:.4cm)}]strt.center) to [out=140,in=-6] +(160.:3.2cm) ([shift={(45:.4cm)}]strt.center) to [out=-40,in=94] +(-65.:4.2cm);
\draw [lw, red, looseness=.8] ([shift={(36:.86cm)}]strt.center) to [out=140,in=-6] +(160.:3.2cm) ([shift={(36:.86cm)}]strt.center) to [out=-40,in=94] +(-65.:4.2cm);
\end{scope}
\end{tikzpicture}
\end{center}
\end{document}

Answer 1

You could use the intersections library to precisely position the nodes and the fillbetween library that comes with PGFPlots to fill the area between the paths. (If the latter is loaded, you don't even need to additionally load the former.)

For this to work, however, it is better to draw the paths in one go, not as two sub-paths as you do, but this can easily be achieved by reordering some values in your code.

By the way, you don't need to add center as anchor to a coordinate since it has no shape.

\documentclass[border=10pt]{standalone}
\usepackage{pgfplots} % loads tikz
\pgfplotsset{compat=newest}
\usetikzlibrary{backgrounds}
\usepgfplotslibrary{fillbetween} % includes intersections library

\tikzset{lw/.style={line width=.04cm}}

\begin{document}
\begin{tikzpicture}[scale=.8, transform shape]

\coordinate (uplt) at (0,0);
\coordinate (strt) at ([shift={(-32:4.2)}]uplt);
\coordinate (strtd) at ([shift={(-120:.36)}]strt);
\coordinate (strtdd) at ([shift={(-148:1)}]strt);

\draw[very thick, blue, looseness=.88, name path=curveA] 
    (strtd) +(125:2.6) to[out=-70, in=140] 
    (strtd) to[out=-40, in=170] +(-24:4);
\draw[very thick, blue, looseness=.88] 
    (strtdd) +(125:2.6) to [out=-70, in=140] 
    (strtdd) to[out=-40, in=170] +(-24:4.4);

\draw[lw, red, looseness=.8, name path=curveB] 
    ([shift={(45:.4)}]strt) +(160:3.2) to[out=-6, in=140] 
    ([shift={(45:.4)}]strt) to[out=-40, in=94] +(-65:4.2);
\draw[lw, red, looseness=.8] 
    ([shift={(36:.86)}]strt) +(160:3.2) to[out=-6, in=140] 
    ([shift={(36:.86)}]strt) to[out=-40, in=94] +(-65:4.2);

\path[name intersections={of=curveA and curveB}]
    (intersection-1) node[circle, black, fill=black, scale=0.8] (a) {}
    (intersection-2) node[circle, black, fill=black, scale=0.8] (b) {};

\begin{scope}[on background layer]
    \fill[green, intersection segments={of=curveA and curveB, sequence={R2 -- L2}}] 
    -- cycle;
\end{scope}

\end{tikzpicture}
\end{document}

---

Filling the area between the other two curves needs a small tweak. Note that they seem not to intersect at the upper left coordinate which is why you cannot place a node using intersections there. Maybe you need to adjust the curves a bit.

If you wonder how to use the intersection segments and sequence options, have a look at the PGFPlots manual. Chapter 5.7. (in version 1.18.1 of the manual) discusses the fillbetween library.

\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usetikzlibrary{backgrounds}
\usepgfplotslibrary{fillbetween}

\tikzset{lw/.style={line width=.04cm}}

\begin{document}
\begin{tikzpicture}[scale=.8, transform shape]
\coordinate (uplt) at (0,0);
\coordinate (strt) at ([shift={(-32:4.2)}]uplt);
\coordinate (strtd) at ([shift={(-120:.36)}]strt);
\coordinate (strtdd) at ([shift={(-148:1)}]strt);

\draw[very thick, blue, looseness=.88, name path=curveA] 
    (strtd) +(125:2.6) to[out=-70, in=140] 
    (strtd) to[out=-40, in=170] +(-24:4);
\draw[very thick, blue, looseness=.88, name path=curveB] 
    (strtdd.center) +(125:2.6) to [out=-70, in=140] 
    (strtdd.center) to[out=-40, in=170] +(-24:4.4);

\draw[lw, red, looseness=.8, name path=curveC] 
    ([shift={(45:.4)}]strt.center) +(160:3.2) to[out=-6, in=140] 
    ([shift={(45:.4)}]strt.center) to[out=-40, in=94] +(-65:4.2);
\draw[lw, red, looseness=.8, name path=curveD] 
    ([shift={(36:.86)}]strt.center) +(160:3.2) to[out=-6, in=140] 
    ([shift={(36:.86)}]strt.center) to[out=-40, in=94] +(-65:4.2);

\path[name intersections={of=curveA and curveC}]
    (intersection-1) node[circle, black, fill=black, scale=0.8] (a) {}
    (intersection-2) node[circle, black, fill=black, scale=0.8] (b) {};

\begin{scope}[on background layer]
    \fill[yellow, intersection segments={of=curveB and curveD, sequence={R1 -- L1[reverse]}}] -- cycle;
    
    \fill[green, intersection segments={of=curveA and curveC, sequence={R2 -- L2}}] -- cycle;
\end{scope}

\end{tikzpicture}
\end{document}