Filling region bounded by multiple paths

Question

I would like to fill the portion which is bounded by two ellipses and two lines. The portion is indicated with "Here" in the figure. I tried multiclip with no success. Is there any simpler way?

\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{shapes, calc, fit, arrows.meta, arrows, patterns, 
positioning, intersections, 3d, matrix}
\usetikzlibrary{decorations.pathmorphing, decorations.shapes}

\begin{document}

\begin{tikzpicture}

    \draw (0,0) ellipse (2 and 1);
    \draw (0,0) ellipse (3 and 2);
    \draw (0,0) ellipse (4 and 3);
    \draw (0,1) -- (0,3);
    \draw (0,-1) -- (0,-3);
    \draw (2,0) -- (4,0);
    \draw (-2,0) -- (-4,0);
    \draw (1.36,0.75) -- (3.0,2);
    \draw (-1.36,0.75) -- (-3.0,2);
    \draw (1.36,-0.75) -- (3.0,-2);
    \draw (-1.36,-0.75) -- (-3.0,-2);        
    \node at (1,1.4){Here};

\end{tikzpicture}

\end{document}

John Kormylo · Answer 1 · 2019-05-30T13:42:40.613

Here are two solutions. In the first I combined a polygonal clip with an elliptical fill. In the second I computed the arc angles corresponding to the given points (actually, the intersection between them and the middle ellipse).

\documentclass[multi=tikzpicture]{standalone}% or just [tikz]

\usepackage{tikz}
\usetikzlibrary{shapes, calc, fit, arrows.meta, arrows, patterns, 
positioning, intersections, 3d, matrix}
\usetikzlibrary{decorations.pathmorphing, decorations.shapes}

\begin{document}

\begin{tikzpicture}
    \begin{scope}
      \clip (0,1) -- (0,3) -- (3,2) -- (1.36,0.75) -- cycle;
      \fill[pink, even odd rule] (0,0) ellipse (3 and 2) ellipse (2 and 1);
    \end{scope}
    \draw (0,0) ellipse (2 and 1);
    \draw (0,0) ellipse (3 and 2);
    \draw (0,0) ellipse (4 and 3);
    \draw (0,1) -- (0,3);
    \draw (0,-1) -- (0,-3);
    \draw (2,0) -- (4,0);
    \draw (-2,0) -- (-4,0);
    \draw (1.36,0.75) -- (3.0,2);
    \draw (-1.36,0.75) -- (-3.0,2);
    \draw (1.36,-0.75) -- (3.0,-2);
    \draw (-1.36,-0.75) -- (-3.0,-2);      
    \node at (1,1.4){Here};
\end{tikzpicture}

\begin{tikzpicture}
    \pgfmathsetmacro{\inner}{atan2(0.75,1.36/2)}%
    \path[name path=A] (0,0) ellipse (3 and 2);
    \path[name path=B] (1.36,0.75) -- (3.0,2);
    \path[name intersections={of=A and B, by=C}] (C);
    \pgfgetlastxy{\Cx}{\Cy}
    \pgfmathsetmacro{\outer}{atan2(\Cy/2,\Cx/3)}%

    \fill[pink] (0,1) -- (0,2) arc[x radius=3, y radius=2, start angle=90, end angle={\outer}]
                -- (1.36,0.75) arc[x radius=2, y radius=1, start angle={\inner}, end angle=90] -- cycle;

    \draw (0,0) ellipse (2 and 1);
    \draw (0,0) ellipse (3 and 2);
    \draw (0,0) ellipse (4 and 3);
    \draw (0,1) -- (0,3);
    \draw (0,-1) -- (0,-3);
    \draw (2,0) -- (4,0);
    \draw (-2,0) -- (-4,0);
    \draw (1.36,0.75) -- (3.0,2);
    \draw (-1.36,0.75) -- (-3.0,2);
    \draw (1.36,-0.75) -- (3.0,-2);
    \draw (-1.36,-0.75) -- (-3.0,-2);      
    \node at (1,1.4){Here};
\end{tikzpicture}

\end{document}

frougon · Answer 2 · 2019-05-30T18:46:53.967

Here is a solution essentially based on a parametric representation of the two inner ellipses (though I used the ellipse node shape from shapes.geometric to draw the complete ellipses, which is the easiest part):

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}

% Define the start and end angles of the sector to be filled
\def\sectorStartAngle{45}
\def\sectorEndAngle{90}

% Allows scaling the ellipses
\def\myUnit{8em}

% Dimensions of the inner ellipse
\def\innerXDiameter{2}         % in \myUnit
\def\innerYDiameter{1}         % in \myUnit

% Dimensions of the middle ellipse
\def\middleXDiameter{3}        % in \myUnit
\def\middleYDiameter{2}        % in \myUnit

% Dimensions of the outer ellipse
\def\outerXDiameter{4}         % in \myUnit
\def\outerYDiameter{3}         % in \myUnit

\begin{document}
\begin{tikzpicture}[
  my ellipse/.style args={#1and #2}{%
    draw, color=blue, shape=ellipse, inner sep=0pt,
    minimum width={(#1)*\myUnit},minimum height={(#2)*\myUnit}}]
\node[my ellipse={\innerXDiameter and \innerYDiameter}] (inner) at (0,0) {};
\node[my ellipse={\middleXDiameter and \middleYDiameter}] (middle) at (0,0) {};
\node[my ellipse={\outerXDiameter and \outerYDiameter}] (outer) at (0,0) {};

% Parameter transformations for the two inner ellipses. These transformations
% allow one to specify the plot parameter in degrees as if we had a circle
% parametrization. Thanks to this, the start and end angles can be given in
% degrees below, instead of in some skewed approximation.
\def\innerParam{atan2(\innerXDiameter*sin(\theta), \innerYDiameter*cos(\theta))}
\def\middleParam{atan2(\middleXDiameter*sin(\theta), \middleYDiameter*cos(\theta))}

\fill[red!20, smooth, variable=\theta]
  plot[domain=\sectorStartAngle:\sectorEndAngle]
    ({0.5*\innerXDiameter*\myUnit*cos(\innerParam)},
     {0.5*\innerYDiameter*\myUnit*sin(\innerParam)})
  --
  plot[domain=\sectorEndAngle:\sectorStartAngle]
    ({0.5*\middleXDiameter*\myUnit*cos(\middleParam)},
     {0.5*\middleYDiameter*\myUnit*sin(\middleParam)})
  -- cycle;

\foreach \i in {0, ..., 7} {
  \draw[help lines] (node cs:name=inner, angle=45*\i) --
                    (node cs:name=outer, angle=45*\i);
}
\end{tikzpicture}
\end{document}

Note: there may be a way to simplify a little bit the definition of the path to be filled using the arc operation, however the following:

(node cs:name=inner, angle=\sectorStartAngle)
  arc[start angle=\sectorStartAngle, end angle=\sectorEndAngle,
      x radius=0.5*\innerXDiameter*\myUnit,
      y radius=0.5*\innerYDiameter*\myUnit]

does not give the first arc from my filled path above. Anyway, working with parametric plots as done above can be very helpful for other problems (it is “empowering“).

score 4 · Answer 3 · answered May 30 '19 at 15:05

Here is an alternative to John Kormylo's answer. In this very case, this is not needed, but in general clip even odd rule can be very useful.

\documentclass{standalone}
\usepackage{tikz}
% see https://tex.stackexchange.com/a/359661/121799
\tikzset{clip even odd rule/.code={\pgfseteorule}}
\begin{document}
\begin{tikzpicture}
    \begin{scope}
     \clip[clip even odd rule] (0,0) ellipse (2 and 1) (0,0) ellipse (3 and 2);
     \fill[blue!20] (0,0) -- (0,3) -- (3,2) -- (1.36,0.75);
    \end{scope}

    \draw (0,0) ellipse (2 and 1);
    \draw (0,0) ellipse (3 and 2);
    \draw (0,0) ellipse (4 and 3);
    \draw (0,1) -- (0,3);
    \draw (0,-1) -- (0,-3);
    \draw (2,0) -- (4,0);
    \draw (-2,0) -- (-4,0);
    \draw (1.36,0.75) -- (3.0,2);
    \draw (-1.36,0.75) -- (-3.0,2);
    \draw (1.36,-0.75) -- (3.0,-2);
    \draw (-1.36,-0.75) -- (-3.0,-2);        
    \node at (1,1.4){Here};
\end{tikzpicture}
\end{document}

Filling region bounded by multiple paths

3 Answers3