coloring left region of a path in a string diagram

Question

I would like to draw figures like these, where some part is colored between 2 paths, which are defined independantly.

So in code the question is the following.

Given curves :

\documentclass{article}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}    
\draw (1.5, 5) .. controls (1.5,4)  and (1, 3.5) .. (0,3.5) .. controls (-1,3.5) and (-1.5,3) .. (-1.5,2) .. controls (-1.5541,1.2387) and (-1.4786,0.9369) .. (-1.5,0) ;
\draw (-1,0) .. controls (-1,1) and (-1,2.5) .. (-0.5,2.5) .. controls (0,2.5) and (0,1.5) .. (0.5,1.5) .. controls (1,1.5) and (0.5,3) .. (1.5,3);
\end{tikzpicture}
\end{document}

How to fill the region to the right of the left curve and to the right of the left curve with the color red ?

--

Previous code

So far, I can describe manually the region by adding points and explicitely filling them. But It would be nicer to draw just the boundaries of such regions and ask to color them in one go.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning, intersections}

\begin{document}
\begin{tikzpicture}[scale=1, transform shape]
\coordinate (v1) at (0,3) {};
\coordinate(v2) at (0,0) {};
\coordinate (v3) at (-3,3) {};
\coordinate (v4) at (-3,0) {};
\coordinate (v5) at (3,3) {};
\coordinate (v6) at (3,0) {};
\fill[fill=blue!20]
(v4.center) -- (v3.center) -- (v1.center) -- (v2.center) -- cycle;
\fill[fill=yellow!10]
(v1.center) -- (v5.center) -- (v6.center) -- (v2.center);
\draw  (v1) edge (v2);
\draw (v1) node[below right,scale=2] {$x$};
\draw (v2) node[above right,scale=2] {$x$};
\draw (-1.5,0) node[above left,scale=2]{$p$};
\draw (0,1.5) .. controls (-1,1.5) and (-1.5,1) .. (-1.5,0);
\draw (0,1.5) circle [radius=0.5] node[scale=2]{$a$};
\end{tikzpicture}
\end{document}

Can I clip the right/left part of a path ? That is, give the x-x line and ask to have the left part be blue, the right part be yellow, without having to compute the boundaries.

Is there a smarter way to do things ?

---

Answer 1

To clip something you need an area to clip; intersections library could help to define it, see my second tikzpicture.

However, in your MWE, no clipping is needed. Instead, I suggest to you to:

1. use rectangle option, if you have to draw a rectangle
2. use arc option, if you have to draw an arc.

Moreover, coordinates have no dimensions, so you don't need .center after their name.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning, intersections}

\begin{document}
No clipping is needed for your MWE:

\begin{tikzpicture}
    \path[fill=blue!20] (-3,0) coordinate (v4) rectangle (0,3) coordinate (v1);%coordinates have no dimension, you don't need .center
    \path[fill=yellow!10] (0,0) coordinate[label={[label distance=4pt]30:{\huge $x$}}] (v2) rectangle (3,3);%if you have to draw a rectangle, use rectangle
    \node[below right=4pt and 4pt of v1] {\huge $x$};
    \draw (v1) edge (v2);
    \node[draw,circle,inner sep=5pt] (a) at (0,1.5) {\huge $a$};
    \coordinate[label={[label distance=4pt]120:{\huge $p$}}] (p) at (-1.5,0);
    \draw (a) arc (-90:0:-1.5);% if you have to draw an arc, use arc
\end{tikzpicture}

An example with clipping:

\begin{tikzpicture}
    \path[fill=blue!20] (-3,0) coordinate (v4) rectangle (0,3) coordinate (v1);
    \path[fill=yellow!10] (0,0) coordinate[label={[label distance=4pt]30:{\huge $x$}}] (v2) rectangle (3,3);
    \node[below right=4pt and 4pt of v1] {\huge $x$};
    \draw (v1) edge (v2);
    \node (a) at (0,1.5) {\huge $a$};
    \draw[name path=cerchio] (a) circle (.5);
    \coordinate[label={[label distance=4pt]120:{\huge $p$}}] (p) at (-1.5,0);
    \path[name path=arco] (a) arc (-90:0:-1.5);
    \path (a) arc (-90:0:-1.5);
    \path[name intersections={of=arco and cerchio,by=inter}];
    \begin{scope}
        \clip(inter) rectangle (v4);
        \draw (a) arc (-90:0:-1.5);
    \end{scope}
\end{tikzpicture}

\end{document}

EDIT:

Filling between curves:

\documentclass{article}
\usepackage{tikz}
\newcommand{\leftpath}{(1.5, 5) .. controls (1.5,4)  and (1, 3.5) .. (0,3.5) .. controls (-1,3.5) and (-1.5,3) .. (-1.5,2) .. controls (-1.5541,1.2387) and (-1.4786,0.9369) .. (-1.5,0)}
\newcommand{\rightpath}{(-1,0) .. controls (-1,1) and (-1,2.5) .. (-0.5,2.5) .. controls (0,2.5) and (0,1.5) .. (0.5,1.5) .. controls (1,1.5) and (0.5,3) .. (1.5,3)}

\begin{document}
    \begin{tikzpicture}    
        \filldraw[pink] \leftpath -- \rightpath -- cycle;
        \draw[red, thick] \leftpath \rightpath;
    \end{tikzpicture}
\end{document}