[Tex/LaTex] tikz draw circle segment

tikz-pgf

How can I use tikz to draw a circle segment if I have the center of the circle and two points on it? Please see the following example

example

Update:
I try to accomplish something like this. This can be done using the method from Tikz: joining points on a circle, but I would prefer a some sort of tikz solution, because this would allow me to use a tikz style.

enter image description here

Best Answer

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

Related Solutions

[Tex/LaTex] Draw the discontinuity symbol with tikz

Here's a solution that uses the decorations library and declares a new discontinuity decoration, which is essentially a single zigzag in the middle of the first segment of a path. The length and amplitude of the discontinuity symbol are controlled using the standard decoration options segment length and amplitude.

Discontinuity symbol

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations}

\begin{document}

\pgfdeclaredecoration{discontinuity}{start}{
  \state{start}[width=0.5\pgfdecoratedinputsegmentremainingdistance-0.5\pgfdecorationsegmentlength,next state=up from center]
  {}
  \state{up from center}[width=+.5\pgfdecorationsegmentlength, next state=big down]
  {
    \pgfpathlineto{\pgfpointorigin}
    \pgfpathlineto{\pgfqpoint{.25\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}}
  }
  \state{big down}[next state=center finish]
  {
    \pgfpathlineto{\pgfqpoint{.25\pgfdecorationsegmentlength}{-\pgfdecorationsegmentamplitude}}
  }
  \state{center finish}[width=0.5\pgfdecoratedinputsegmentremainingdistance, next state=do nothing]{
    \pgfpathlineto{\pgfpointorigin}
    \pgfpathlineto{\pgfpointdecoratedinputsegmentlast}
  }
  \state{do nothing}[width=\pgfdecorationsegmentlength,next state=do nothing]{
    \pgfpathlineto{\pgfpointdecoratedinputsegmentlast}
  }
  \state{final}
  {
    \pgfpathlineto{\pgfpointdecoratedpathlast}
  }
}

\begin{tikzpicture}
\draw [fill=yellow,decoration={discontinuity,amplitude=1ex},decorate](0,0) -- (3,2)  --  (5,1) -- cycle;
\end{tikzpicture}
\end{document}

[Tex/LaTex] Tikz draw an accurate angle in a circle

For compass and protractor constructions, one can actually just use the through library, the calc library and the intersection cs. The turn key can help to find relative polar coordinates.

The through library only provides one key which has to be used with a node: circle through.

It creates a node of the shape circle that has its center at the at part of the node and goes through the point given to the key. I am using the point (right:1) which is the compass-direction version of (0:1) (which is the polar version of (1, 0)).

This allows me to create a circle with dimensions that scales with the scale value without using transform shape or calculating stuff beforehand (which basically is handled by the through library). For different x scale and y scale or other transformations (setting the x and/or y vector for example) will most likely fail anyway, and you will need to use a circle/ellipse path operator. However, the intersection cs can only work with circle nodes and lines (or two lines or two circular nodes). It really is something for compass and protractors.

If the circle’s center (as in our example) does not lie on the origin, you will need to use circle through={([shift={(<center>)}]0:<radius>)}.

The naming of the node ci is needed for

the use with intersection cs as it needs the name of a (circular) node and
the use of its anchor-border where one can use arbitrary angles.

If you don’t use a circular node, instead of (ci.<angle>), you would use (<angle>:<radius>) or ([shift={(<center>)}]<angle>:<radius>).

The points can then be found with:

\usetikzlibrary{through, calc} % preamble

\begin{tikzpicture}[scale=2]
    \coordinate (O) at (0,0);
    \node[draw] (ci) at (O) [circle through=(right:1)] {};
    \coordinate [label=above left:$A$] (A) at (ci.105);
    \coordinate [label=below left:$B$] (B) at (ci.225);
    \path (A) -- (B) -- ([turn]-15:-1) coordinate (B')
          (B) -- (A) -- ([turn]30:-1) coordinate (A');
    \path (intersection cs: first node=ci, second line={(B)--(B')})
      coordinate[label=above:$C$] (C)
          (intersection cs: first node=ci, second line={(A)--(A')})
      coordinate[label=below right:$D$] (D);
    \draw (A) -- (B) -- (C) -- (D) -- cycle [line join=bevel];
\end{tikzpicture}

Unfortunately, this is not very accurate when it comes to circles:

enter image description here

The intersections library can find intersections between arbitrary paths, not only circles and straight lines. However, a little more work is needed, as path need to be named and the used paths actually need to intersect.

\usetikzlibrary{through, intersections} % preamble

\begin{tikzpicture}[scale=2]
    \coordinate (O) at (0,0);
    \node[draw, name path=ci] (ci) at (O) [circle through=(right:1)] {};
    % or \draw [name path=ci] (O) circle[radius=1];
    \coordinate [label=above left:$A$] (A) at (ci.105);
    \coordinate [label=below left:$B$] (B) at (ci.225);
    \path[overlay] (A) -- (B) -- ([turn]-15:-3) coordinate (B');
    \path[overlay] (B) -- (A) -- ([turn]30:-3) coordinate (A');
    \path[overlay, name path=A] (A) -- (A');
    \path[overlay, name path=B] (B) -- (B');
    \path[name intersections=
      {of=A and ci, by={@,[label=below right:$D$]D}}]; % @ is not used (equals A)
    \path[name intersections={of=B and ci, by={[label=above:$C$]C}}];
    \draw (A) -- (B) -- (C) -- (D) -- cycle [line join=bevel];
\end{tikzpicture}

The solution is more correct:

enter image description here

You can also do the calculations beforehand

enter image description here

and just use TikZ for drawing:

\begin{tikzpicture}[scale=2]
    \coordinate (O) at (0,0);
    \node[draw] (ci) at (O) [circle through=(right:1)] {};
    \coordinate [label=above left:$A$]  (A) at (ci.105);
    \coordinate [label=below left:$B$]  (B) at (ci.225);
    \coordinate [label=      above:$C$] (C) at (ci.225-150);
    \coordinate [label=below right:$D$] (D) at (ci.105-180);
    \draw (A) -- (B) -- (C) -- (D) -- cycle [line join=bevel];
\end{tikzpicture}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] Draw the discontinuity symbol with tikz

[Tex/LaTex] Tikz draw an accurate angle in a circle

Related Question