[Tex/LaTex] Fill a section between two circles with TikZ

tikz-pgf

I am trying to fill a pattern in a section between two circles with TikZ.

In the code below, C0 is a circle with radius=1, center=(0,0).
C1 is a circle through Point z0 with center=z1.

Calculating the coordinates of the two circles' intersections is too complicated task, so I want to specify the arcs between the two intersections' label.

But I found a difficulty in specifying an arc with the start/end points and the center.

Is there any straightforward solution to fill this kind of section?

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,patterns,through,intersections}
\begin{document}
\begin{tikzpicture}
 % x, y axis
 \draw[->] (-1.5,0) -- (3,0) node[right] {$x$};
 \draw[->] (0,-1.5) -- (0,3) node[above] {$y$};
 % Origin
 \coordinate (O) at (0,0);

 % Point z0
 \coordinate (z0) at (1,0);
 \node [below right] at (z0) {$z_0$};
 % Circle C0
 \draw [name path=C0] (O) circle [radius=1];
 \node [above left] at (170:1) {$C_0$};
 % Point z1
 \coordinate (z1) at (30:0.7);
 \fill (z1) circle [radius=1pt];
 \node [below] at (z1) {$z_1$};

 % Circle C1
 \node [draw, circle through=(z0), name path=C1] at (z1) {};
 \node [above right] at ($(30:0.7)+(20:0.5)$) {$C_1$};

 % Intersections
 \path [name intersections={of=C0 and C1}];

\draw [pattern=north west lines, pattern color=gray!60!white] (z0)  arc (?:?:?) --(intersection-2) arc (?:?:1) --(z0);
\end{tikzpicture}
\end{document}

Best Answer

Probably the easiest way is after filling C1 to re-filldraw C0, and finaly to draw the axes. Here is another solution using clipping, that use the "inverse clip" idea from an old Jake's answer and path picture clipping.

\documentclass[tikz,border=7mm]{standalone}
\usetikzlibrary{calc,patterns,through,intersections}
\begin{document}
  \begin{tikzpicture}
    % x, y axis
    \draw[->] (-1.5,0) -- (3,0) node[right] {$x$};
    \draw[->] (0,-1.5) -- (0,3) node[above] {$y$};
    % Origin
    \coordinate (O) at (0,0);
    % Point z0
    \coordinate (z0) at (1,0);
    \node [below right] at (z0) {$z_0$};
    % Circle C0
    \draw [name path=C0] (O) circle [radius=1];
    \node [above left] at (170:1) {$C_0$};
    % Point z1
    \coordinate (z1) at (30:0.7);
    \fill (z1) circle [radius=1pt];
    \node [below] at (z1) {$z_1$};
    % Circle C1
    \node [draw, circle through=(z0), name path=C1,
      path picture={
        \clip (-20,-20) rectangle +(40,40) (O) circle [radius=1 cm +.5\pgflinewidth];
        \fill[pattern=crosshatch, pattern color=green] (-20,-20) rectangle +(40,40);
      }
    ] at (z1) {};
    \node [above right] at ($(30:0.7)+(20:0.5)$) {$C_1$};
  \end{tikzpicture}
\end{document}

Related Solutions

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

A solution which allows to draw intersection segments of any two intersections is available as tikz library fillbetween.

This library works as general purpose tikz library, but it is shipped with pgfplots and you need to load pgfplots in order to make it work:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}];

\end{tikzpicture}

\end{document}

enter image description here

The key intersection segments is described in all detail in the pgfplots reference manual section "5.6.6 Intersection Segment Recombination"; the key idea in this case is to

create a temporary path temp1 which is the first intersection segment of red and blue, more precisely, it is the first intersection segment in the Left argument in red and blue : red. This path is drawn as thin black path. Substitute its \draw statement by \path to make it invisible.
Compute the desired intersection segment by intersecting temp1 and green and use the correct intersection segment. By trial and error I figured that it is the third segment of path temp1 which is written as L3 (L = left argument in temp1 and green and 3 means third segment of that path).

The argument involves some trial and error because fillbetween is unaware of the fact that end and startpoint are connected -- and we as end users do not see start and end point.

Note that you can connect these path segments with other paths. If such an intersection segment should be the continuation of another path, use -- as before the first argument in sequence. This allows to fill paths segments:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,fill=blue,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}]  
    [intersection segments={of=temp1 and green, sequence={--R2}}]
;

\end{tikzpicture}

\end{document}

enter image description here

[Tex/LaTex] Line up nested tikz enviroments or how to get rid of them

As is explained in How do I draw shapes inside a tikz node? pics can be used for defining new objects. My main problem using pics is how to place where you want because they aren't nodes and positioning them is not so easy.

Following code shows how to define EDFA block.

    EDFA/.pic={
        \begin{scope}[scale=.5]
        \draw (-1,0) coordinate (in) --  (-1,1) -- (1,0) coordinate (out) --  (-1,-1) -- cycle;
        \node[anchor=north,inner sep=2pt] at (0,-1) {$1$};
        \end{scope}

In this case, coordinate (-1,0) will act as west anchor and 1,0 as east. Both point will have an special name for further reference. Every pic is placed according its own origin (0,0). You can use Claudio's answer to Anchoring TiKZ pics for better positioning.

As your example was simple, I'd prefer to star with EDFA and place Source and Sink after it.

\documentclass[]{article}

% tikz
\usepackage{tikz}
\usetikzlibrary{positioning} %relative positioning

\begin{document}

\tikzset{%
    EDFA/.pic={
        \begin{scope}[scale=.5]
        \draw (-1,0) coordinate (in) --  (-1,1) -- (1,0) coordinate (out) --  (-1,-1) -- cycle;
        \node[anchor=north,inner sep=2pt] at (0,-1) {$1$};
        \end{scope}
    }
}

\begin{tikzpicture}[
block/.style={draw},
]

\draw pic (edfa) {EDFA};

\node[block, left=of edfain] (source) {Source};

\node[block, right= of edfaout] (sink) {Sink};

\draw[->] (source) -- (edfain);
\draw[->] (edfaout) -- (sink);

\end{tikzpicture}

\end{document}

I understand that your components are more complex than EDFA because for this particular case an isosceles triangle node with a label will do the work and it can be used as a node and not as a pic:

\documentclass[]{article}

% tikz
\usepackage{tikz}
\usetikzlibrary{positioning} %relative positioning
\usetikzlibrary{shapes.geometric}

\begin{document}

\begin{tikzpicture}[
    block/.style={draw},
    edfa/.style={isosceles triangle, minimum width=1cm, 
         draw, anchor=west, isosceles triangle stretches, 
         minimum height=1cm, label=-80:#1}
]

\node[block] (source) {Source};

\node[edfa=1, right=of source] (edfa) {};

\node[block, right= of edfa] (sink) {Sink};

\draw[->] (source) -- (edfa);
\draw[->] (edfa) -- (sink);

\end{tikzpicture}

\end{document}

Best Answer

Related Solutions

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

[Tex/LaTex] Line up nested tikz enviroments or how to get rid of them

Related Question