Draw arc in tikz when center of circle is specified

Question

It would be convenient sometimes to be able to draw an arc in tikz by specifying

• the center of the corresponding circle
• its radius
• the initial/final angle

i.e., the "natural" way an arc is defined, instead of the "first point of the arc".

Is there a way to do it?

Answer 1

You can use the parametrization

x(t)=a+r*cos(t)
y(t)=b+r*sin(t)

where r is the radius of the circle and (a,b) are the coordinates of its center. In Tikz this can be implemented as follows:

\documentclass[border=5mm]{standalone}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
   \draw [red,thick,domain=0:90] plot ({cos(\x)}, {sin(\x)});
   \draw [blue,thick,domain=180:270] plot ({cos(\x)}, {sin(\x)});
\end{tikzpicture}

\end{document}

which produces

Depending on your application, you might like to do this using the pgfplots package.

Also, in case this is used frequently, consider defining a custom command \centerarc as suggested in a comment by Tom Bombadil (this requires \usetikzlibrary{calc}):

\def\centerarc[#1](#2)(#3:#4:#5)% Syntax: [draw options] (center) (initial angle:final angle:radius)
    { \draw[#1] ($(#2)+({#5*cos(#3)},{#5*sin(#3)})$) arc (#3:#4:#5); }

Then use it by invoking

\centerarc[red,thick](0,0)(5:85:1)

Answer 2

You should use a coordinate transformation for this, to get a proper starting point of the arc. Say, ([shift=(t:r)] x, y) is the proper starting point, where (x,y) is the center and (t:r) is the polar coordinate of starting point.

Full example:

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
\draw[help lines] (0,0) grid (4,3);
\draw (2,1) -- ++(30:2cm)
      (2,1) -- ++(60:2cm);
% Draw the arc which center is (2,1)
\draw[thick,red] ([shift=(30:1cm)]2,1) arc (30:60:1cm);
\end{tikzpicture}

\end{document}

Answer 3

Notation: each arc is defined by <center>, <radius>, <init angle> and <final angle>.

If you want to be able to link several arcs in a single path, you can use shift with following syntax:

• initial point:([shift={(<init angle>:<radius>)}]<center>)

• to draw your arc: arc (<init angle>:<final angle>:<radius>)

Example (orange path uses proposed syntax and cyan path uses a style):

\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
  \draw[fill=orange]
  ([shift={(-40:1cm)}]-1.1,0) arc (-40:40:1cm)
  --
  ([shift={(-40+180:1cm)}]1.1,0) arc (-40+180:40+180:1cm)
  -- cycle;
\end{tikzpicture}
\begin{tikzpicture}
  \tikzset{translate/.style={shift={(#1)}}}
  \draw[fill=cyan]
  ([translate=-40:1cm]-1.1,0) arc (-40:40:1cm)
  --
  ([translate=-40+180:1cm]1.1,0) arc (-40+180:40+180:1cm)
  -- cycle;
\end{tikzpicture}
\end{document}

Edit: a simpler notation!

Using calc TikZ library, you can use a simpler notation:

• initial point: ($(<center>) + (<init angle>:<radius>)$).

Example:

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
  % center c1
  \coordinate (c1) at (0,0);

  \draw[fill=green]
  % radius=3mm, initial=0, final=90
  %([shift={(0:3mm)}]c1) arc (0:90:3mm)
  ($(c1) + (0:3mm)$) arc (0:90:3mm)
  --
  % radius=4mm, reversed
  ($(c1) + (90:4mm)$) arc (90:0:4mm)
  -- cycle;

  \draw[fill=yellow]
  % radius=4mm, initial=22.5, final=180
  ($(c1) + (22.5:4mm)$) arc (22.5:180:4mm)
  --
  % radius=5mm, reversed
  ($(c1) + (180:5mm)$) arc (180:22.5:5mm)
  -- cycle;

  % center c2
  \coordinate (c2) at (0,12mm);

  \draw[fill=red]
  % radius=5mm, initial=45, final=270
  ($(c2) + (45:5mm)$) arc (45:270:5mm)
  --
  % radius=6mm, reversed
  ($(c2) + (270:6mm)$) arc (270:45:6mm)
  -- cycle;

  \draw[fill=gray]
  % radius=6mm, initial=67.5, final=360
  ($(c2) + (67.5:6mm)$) arc (67.5:360:6mm)
  --
  % radius=7mm, reversed
  ($(c2) + (360:7mm)$) arc (360:67.5:7mm)
  -- cycle;
\end{tikzpicture}
\end{document}

Answer 4

Possible is to use tkz-euclide. I f you want something independent of tkz-euclide you can take the code inside the file tkz-obj-arcs.tex. In each cases, I use the center

1) \tkzDrawArc and towards

towards is the option by defaut so it's not necessary to indicate this option. In the the example, the arc starts from A towards the axe OB.

 \begin{tikzpicture}[scale=1.5]
  \tkzDefPoint(0,0){O}
  \tkzDefPoint(2,-1){A}
  \tkzDefPoint(1,1){B}
  \tkzDrawArc[color=blue](O,A)(B)
  \tkzDrawArc[color=Maroon](O,B)(A)
  \tkzDrawArc(O,B)(A)
  \tkzDrawLines[add = 0 and .5](O,A O,B)
  \tkzDrawPoints(O,A,B)
  \tkzLabelPoints[below](O,A,B)
 \end{tikzpicture}

2) \tkzDrawArc and rotate

Here the center is O, the arc starts from A and the measure of the angle is 180 degrees.

\begin{tikzpicture}
  \tkzDefPoint(0,0){O}
  \tkzDefPoint(2,-2){A}
  \tkzDefPoint(60:2){B}
  \tkzDrawLines[add = 0 and .5](O,A O,B)
  \tkzDrawArc[rotate,color=red](O,A)(180)
  \tkzDrawPoints(O,A,B)
  \tkzLabelPoints[below](O,A,B)
\end{tikzpicture}

3) \tkzDrawArc and R

In this case the center is O and you need to give the radius R and two angles

\begin{tikzpicture}
  \tkzDefPoints{0/0/O}
  \tikzset{compass style/.append style={<->}}
  \tkzDrawArc[R, color=orange,double](O,3cm)(270,360)
  \tkzDrawArc[R, color=blue,double](O,2cm)(0,270)
  \tkzDrawPoint(O)
  \tkzLabelPoint[below](O){$O$}
\end{tikzpicture}

4) \tkzDrawArc and R with nodes In this case, we need to know the center, the radius and the arc starts from the line BA towards the line BO

\begin{tikzpicture}
  \tkzDefPoint(0,0){O}
  \tkzDefPoint(2,-1){A}
  \tkzDefPoint(1,1){B}
  \tkzCalcLength(B,A)\tkzGetLength{radius}
  \tkzDrawArc[R with nodes](B,\radius pt)(A,O)
\end{tikzpicture}

5) \tkzDrawArc and delta

Useful to add an arc like with a compass.

\begin{tikzpicture}
\tkzInit
\tkzDefPoint(0,0){A} \tkzDefPoint(5,0){B} \tkzDefPointBy[rotation= center A%
                angle 60](B) \tkzGetPoint{C}
 \tkzSetUpLine[color=gray]
 \tkzDefPointBy[symmetry= center C](A)
    \tkzGetPoint{D}
 \tkzDrawSegments(A,B A,D)
 \tkzDrawLine(B,D)
 \tkzSetUpCompass[color=orange]
 \tkzDrawArc[delta=10](A,B)(C)
 \tkzDrawArc[delta=10](B,C)(A)
 \tkzDrawArc[delta=10](C,D)(D)
 \tkzDrawPoints(A,B,C,D)
 \tkzLabelPoints(A,B,C,D)
 \tkzMarkRightAngle(D,B,A)
\end{tikzpicture}

Answer 5

You can create a new command, like this one

\documentclass[12pt]{standalone}
\usepackage{tikz}


\newcommand{\cercle}[4]{
\node[circle,inner sep=0,minimum size={2*#2}](a) at (#1) {};
\draw[red,thick] (a.#3) arc (#3:{#3+#4}:#2);
}
\begin{document}
\begin{tikzpicture}

\coordinate (center) at (3,2);

\cercle{center}{2cm}{25}{-90}
![\cercle{4,5}{1cm}{15}{130}][1]

\end{tikzpicture}
\end{document}

Answer 6

Just repeat the first coordinate

%\draw (center) +(th0:rad) arc +(th0:th1:rad)
\draw (1,2) +(-20:3) arc (-20:40:3) ;

which will draw an arc with the center at (1,2), a radius of 3, covering an angle from -20 to 40 degrees. To use units (e.g. cm) one can replace the 3 with 3cm.

• The \draw (1,2) command starts the path at the coordinate of the arc center;
• Then +(-20:3) moves to the starting point of the arc (in the polar direction theta=20deg at a distance rad=3 from the center). The + notation means that the reference position for the path is unchanged by this move;
• Finally, the last command draws the arc, but keeps the original center position (1,2).

(corrected as commented by Ignasi)

Answer 7

A combination of Leo Liu's and cmhughes' solutions (ie, without the calc library):

\documentclass{standalone} 
\usepackage{tikz}

\def\centerarc[#1](#2)(#3:#4:#5);%
%Syntax: [draw options] (center) (initial angle:final angle:radius)
    {
    %\draw[#1] ($(#2)+({#5*cos(#3)},{#5*sin(#3)})$) arc (#3:#4:#5);
    \draw[#1]([shift=(#3:#5)]#2) arc (#3:#4:#5);
    }

\begin{document}
\begin{tikzpicture}[>=stealth]
\draw[help lines] (-2,-2) grid (2,2);
\centerarc[thick,<->,blue](1,1)(70:195:1cm);
\centerarc[thick,blue](1,1)(-90:25:1cm);
\draw[thin,dashed,blue] (1,1) circle (1cm);
\centerarc[thick,<->,red](0,0)(165:285:2cm);
\centerarc[thick,red](0,0)(-45:45:2cm);
\draw[thin,dashed,red] (0,0) circle (2cm);
\end{tikzpicture}
\end{document}

Remark: As seen below, the <-> option in the \centerarc examples seems to distort the arcs themselves. I believe this is an unwanted effect, or even a bug.

Answer 8

I added line width and color to your command @rpapa, I find it pretty useful and very handy! Coupled with some very simple polar coordinates, it can handle a lot.

\documentclass{standalone}
\usepackage{tikz}

\newcommand{\cercle}[6]{
\node[circle,inner sep=0,minimum size={2*#2}](a) at (#1) {};
\draw[#6,line width=#5] (a.#3) arc (#3:{#3+#4}:#2);
}
% USAGE: \cercle {center} {radius in cm} {begin degrees} {value of the arc} {line width} {color}
% \coordinate (OO) at (2.8,2.2);
% \cercle{OO}{0.5cm}{-20}{60}{1.0pt}{blue};

\begin{document}

\begin{tikzpicture}
  \coordinate (OR) at (0.00, 0.00);
  \filldraw [orange] (OR) circle(2pt);
  \node[above left, orange] at (OR) {\textbf{\textit{0}}};
  \draw[step = 0.1cm, gray, ultra thin] (-1.5,-2) grid (1.5,2);
  \draw[black, thin] (-1.5,0)--(1.5,0) (0,-2)--(0,2);
  % 30 degree arc, starting at +15 degrees
  \cercle {OR} {0.5cm} {15} {30} {1.00} {red};
  \draw[red,thin] (OR) -- (pi/12 r:0.5);
  \draw[red,thin] (OR) -- (pi/4 r:0.5);
  % 75 degree arc, starting at -15 degrees
  \cercle {OR} {1.0cm} {-15} {75} {1.50} {blue};
  \draw[blue,thin] (OR) -- (-pi/12 r:1.0);
  \draw[blue,thin] (OR) -- (pi/3 r:1.0);
  % 90 degree arc, starting at -135 degrees
  \cercle {OR} {1.5cm} {-135} {90} {2.00} {teal};
  \draw[teal,thin] (OR) -- (-pi/4 r:1.5);
  \draw[teal,thin] (OR) -- (-3*pi/4 r:1.5);
\end{tikzpicture}

\end{document}