Draw circle covering of a triangle with Tikz

graphicstikz-pgftikz-styles

I want to modify the answer to this post in two ways:

Pack a triangle
Put a point at the center of each circle with label y_1,y_2,…

How can this be done? Thanks in advance 🙂

Best Answer

An approach could be replacing the drawn circles by nodes. Here is an example of how to do this, but I'll leave some of the kinks of the solution for you to work out, including the optimal orientation of the triangles and sizes and such, which highly depend on your use case.

\documentclass[tikz]{standalone}
\usetikzlibrary{shapes.geometric,fit}
\pgfdeclarelayer{background}
\pgfsetlayers{background,main}
\begin{document}

\begin{tikzpicture}[x=3cm,y=3cm]
    \pgfmathsetmacro\rad{1.1}
    \begin{scope}[every node/.style={regular polygon,regular polygon sides=3,inner sep=0cm,minimum width=1.3cm}]
        \node[fill=blue!40!red,inner sep=.12cm] at (0,0) {};
        \foreach \i in {0,...,6}
            \node[fill=blue!30!red] at (60*\i:.30*\rad) {y$_\i$};
        \foreach \n [count=\i] in {7,...,18}
            \node[fill=blue!20!red] at  ({15+30*\i}:0.57*\rad) {y$_{\n}$};
        \foreach \n [count=\i] in {19,...,36}
            \node[fill=blue!10!red] (outer\i) at ({10+20*\i}:0.86*\rad) {y$_{\n}$};
    \end{scope}

    \begin{pgfonlayer}{background}
        \node[fit=(outer1) (outer10),circle,fill=red!40,minimum width=\rad,inner sep=0cm]{};    
    \end{pgfonlayer}
\end{tikzpicture}
\end{document}

Related Solutions

[Tex/LaTex] tikz draw circle segment

Result

Using calc library and the operators let and in you can compute the radius, initial angle and final angle for the arc from the three points you have (center and two circle points), and use then the computed numbers as part of the path. The following MWE shows how:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\thispagestyle{empty}
\usetikzlibrary{calc}

\begin{tikzpicture}
\coordinate (center) at (3,3);
\coordinate (1) at (0,0);
\coordinate (2) at (5, .5);
\coordinate (3) at ($(center) +(30:2)$);
\coordinate (4) at ($(center) +(70:2)$);
\coordinate (5) at (0,6);

\draw[blue, dotted]
      let \p1 =  ($(3)-(center)$),
          \n0 = {veclen(\x1,\y1)}
      in (center) circle(\n0);


\filldraw[draw=black, fill=green, fill opacity=0.3]
   let \p1 = ($(3) - (center)$),
       \p2 = ($(4) - (center)$),
       \n0 = {veclen(\x1,\y1)},            % Radius
       \n1 = {atan(\y1/\x1)+180*(\x1<0)},  % initial angle
       \n2 = {atan(\y2/\x2)+180*(\x2<0)}   % Final angle
    in
    (1) -- (2) --  (3) arc(\n1:\n2:\n0)  -- (5)  -- cycle;

\foreach \dot in {1,2,3,4,5,center} {
  \fill (\dot) circle(2pt);
  \node[above] at (\dot) {\dot};
}

\end{tikzpicture}
\end{document}

If you have v2.10 of pgf/tikz, you can calculate the initial and final angles using atan2(x,y) instead of the above expression, (thanks to qrrbrbirlbel for suggesting it), i.e:

       \n1 = {atan2(\x1,\y1)},  % initial angle
       \n2 = {atan2(\x2,\y2)}   % Final angle

[Tex/LaTex] Automatically draw and labels angles of a triangle in TikZ

I'd use tkz-euclide for this task. It provides a nice macro \tkzMarkAngle which is really of help in this case.

The code:

\documentclass[tikz,border=2pt,png]{standalone}
\usepackage{tkz-euclide}
\usetkzobj{all}

\begin{document}
\begin{tikzpicture}[thick]
\coordinate (O) at (0,0);
\coordinate (A) at (4,0);
\coordinate (B) at (0,2);
\draw (O)--(A)--(B)--cycle;

\tkzLabelSegment[below=2pt](O,A){\textit{adjacent leg}}
\tkzLabelSegment[left=2pt](O,B){\textit{opposite leg}}
\tkzLabelSegment[above right=2pt](A,B){\textit{hypotenuse}}

\tkzMarkAngle[fill= orange,size=0.65cm,%
opacity=.4](A,O,B)
\tkzLabelAngle[pos = 0.35](A,O,B){$\gamma$}

\tkzMarkAngle[fill= orange,size=0.8cm,%
opacity=.4](B,A,O)
\tkzLabelAngle[pos = 0.6](B,A,O){$\alpha$}

\tkzMarkAngle[fill= orange,size=0.7cm,%
opacity=.4](O,B,A)
\tkzLabelAngle[pos = 0.5](O,B,A){$\beta$}


\end{tikzpicture}
\end{document}

The result:

enter image description here

Disclaimer

Hoping that the labels are right.

As Torbjørn T. was suggesting in its comment, it is even possible to create square angles thanks to the macro \tkzMarkRightAngle. The previous example becomes:

\documentclass[tikz,border=2pt,png]{standalone}
\usepackage{tkz-euclide}
\usetkzobj{all}

\begin{document}
\begin{tikzpicture}[thick]
\coordinate (O) at (0,0);
\coordinate (A) at (4,0);
\coordinate (B) at (0,2);
\draw (O)--(A)--(B)--cycle;

\tkzLabelSegment[below=2pt](O,A){\textit{adjacent leg}}
\tkzLabelSegment[left=2pt](O,B){\textit{opposite leg}}
\tkzLabelSegment[above right=2pt](A,B){\textit{hypotenuse}}

\tkzMarkRightAngle[fill=orange,size=0.5,opacity=.4](A,O,B)% square angle here
\tkzLabelAngle[pos = 0.35](A,O,B){$\gamma$}

\tkzMarkAngle[fill= orange,size=0.8cm,%
opacity=.4](B,A,O)
\tkzLabelAngle[pos = 0.6](B,A,O){$\alpha$}

\tkzMarkAngle[fill= orange,size=0.7cm,%
opacity=.4](O,B,A)
\tkzLabelAngle[pos = 0.5](O,B,A){$\beta$}

\end{tikzpicture}
\end{document}