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-\subsection{Polar Axes}
-{
-\tikzset{external/figure name/.add={}{polar_}}%
-
-\begin{pgfplotslibrary}{polar}
- A library to draw polar axes and plot types relying on polar coordinates, represented by angle (in degrees or, optionally, in radians) and radius.
-\end{pgfplotslibrary}
-
-\subsubsection{Polar Axes}
-\begin{environment}{{polaraxis}}
- The |polar| library provides the |polaraxis| environment.
- Inside of such an environment, all coordinates are expected to be given in polar representation of the form $(\meta{angle},\meta{radius})$, i.e.\ the $x$ coordinate is always the angle and the $y$ coordinate the radius:
-\end{environment}
-\begin{codeexample}[]
-\begin{tikzpicture}
- \begin{polaraxis}
- \addplot coordinates {(0,1) (90,1)
- (180,1) (270,1)};
- \end{polaraxis}
-\end{tikzpicture}
-\end{codeexample}
-
-\begin{codeexample}[]
-\begin{tikzpicture}
- \begin{polaraxis}
- \addplot+[domain=0:3] (360*x,x); % (angle,radius)
- \end{polaraxis}
-\end{tikzpicture}
-\end{codeexample}
-
-\begin{codeexample}[]
-\begin{tikzpicture}
- \begin{polaraxis}
- \addplot+[mark=none,domain=0:720,samples=600]
- {sin(2*x)*cos(2*x)};
- % equivalent to (x,{sin(..)cos(..)}), i.e.
- % the expression is the RADIUS
- \end{polaraxis}
-\end{tikzpicture}
-\end{codeexample}
-
-Polar axes support most of the \PGFPlots\ user interface, i.e.\ |legend entries|, any axis descriptions, |xtick|/|ytick| and so on:
-\begin{codeexample}[]
-\begin{tikzpicture}
- \begin{polaraxis}[
- xtick={0,90,180,270},
- title=A polar axis]
-
- \addplot coordinates {(0,1) (45,1)};
- \addlegendentry{First}
-
- \addplot coordinates {(180,0.5) (0,0)};
- \addlegendentry{Second}
- \end{polaraxis}
-\end{tikzpicture}
-\end{codeexample}
-\noindent Furthermore, you can use all of the supported input coordinate methods (like \verbpdfref{\addplot coordinates}, \verbpdfref{\addplot table}, \verbpdfref{\addplot expression}). The only difference is that polar axes interpret the (first two) input coordinates as polar coordinates of the form $(\meta{angle in degrees},\meta{radius})$.
-
-It is also possible to provide \verbpdfref{\addplot3}; in this case, the third coordinate will be ignored (although it can be used as color data using |point meta=z|). An example can be found below in Section~\ref{sec:polar:cart}.
-
-
-\subsubsection{Using Radians instead of Degrees}
-The initial configuration uses degrees for the angle ($x$ component of every input coordinate). \PGFPlots\ also supports to provide the angle in radians using the |data cs=polarrad| switch:
-\begin{codeexample}[]
-\begin{tikzpicture}
- \begin{polaraxis}[title={Degrees and/or Radians}]
- \addplot
- coordinates {(0,1) (90,1) (180,1) (270,1)};
- \addlegendentry{Deg}
-
- \addplot+[data cs=polarrad]
- coordinates {(0,1.5) (pi/2,1.5)
- (pi,1.5) (pi*3/2,1.5)};
- \addlegendentry{Rad}
- \end{polaraxis}
-\end{tikzpicture}
-\end{codeexample}
-The |data cs| key is described in all detail on page~\pageref{key:data:cs}; it tells \PGFPlots\ the coordinate system of input data. \PGFPlots\ will then take steps to automatically transform each coordinate into the required coordinate system (in our case, this is |data cs=polar|).
-
-\subsubsection{Mixing With Cartesian Coordinates}
-\label{sec:polar:cart}
-Similarly to the procedure described above, you can also provide Cartesian coordinates inside of a polar axis: simply tell \PGFPlots\ that it should automatically transform them to polar representation by means of |data cs=cart|:
-\begin{codeexample}[]
-\begin{tikzpicture}
- \begin{polaraxis}[title=Cartesian Input]
- \addplot+[data cs=cart]
- coordinates {(1,0) (0,1) (-1,0) (0,-1)};
- \end{polaraxis}
-\end{tikzpicture}
-\end{codeexample}
-\noindent More details about the |data cs| key can be found on page~\pageref{key:data:cs}.
-
-This does also allow more involved visualization techniques which may operate on Cartesian coordinates. The following example uses \verbpdfref{\addplot3} to sample a function $f\colon \R^2 \to \R$, computes |contour| lines (with the help of |gnuplot|) and displays the result in a |polaraxis|:
-\pgfplotsexpensiveexample
-\begin{codeexample}[]
-\begin{tikzpicture}
- \begin{polaraxis}
- \addplot3[contour gnuplot,domain=-3:3,
- data cs=cart]
- {exp(-x^2-y^2)};
- \end{polaraxis}
-\end{tikzpicture}
-\end{codeexample}
-\noindent What happens is that $z=\exp(-x^2-y^2)$ is sampled for $x,y \in [-3,3]$, then contour lines are computed on $(x,y,z)$, then the resulting triples $(x,y,z)$ are transformed to polar coordinates $(\alpha,r,z)$ (leaving $z$ intact). Finally, the $z$ coordinate is used as |point meta| to determine the color.
-
-Note that \verbpdfref{\addplot3} allows to process three--dimensional input types, but the result will always be two--dimensional (the $z$ coordinate is ignored for point placement in |polaraxis|). However, the $z$ coordinate can be used to determine point colors (using |point meta=z|).
-
-\subsubsection{Special Polar Plot Types}
-\begin{plottype}{polar comb}
- The |polar comb| plot handler is provided by \Tikz; it draws paths from the origin to the designated position and places |mark|s at the positions (similar to the |comb| plot handler). Since the paths always start at the origin, it is particularly suited for |polaraxis|:
-\begin{codeexample}[]
-\begin{tikzpicture}
- \begin{polaraxis}
- \addplot+[polar comb]
- coordinates {(300,1) (20,0.3) (40,0.5)
- (120,1) (200,0.4)};
- \end{polaraxis}
-\end{tikzpicture}
-\end{codeexample}
-\end{plottype}
-
-\subsubsection{Partial Polar Axes}
-The |polar| library also supports partial axes. If you provide |xmin|/|xmax|, you can restrict the angles used for the axis:
-\begin{codeexample}[]
-\begin{tikzpicture}
- \begin{polaraxis}[xmin=45,xmax=360]
- \addplot coordinates {(0,1) (90,1) (180,1) (270,1)};
- \end{polaraxis}
-\end{tikzpicture}
-\end{codeexample}
-
-Currently, the first angle must be lower than the second one. But you can employ the periodicity to get pies as follows:
-\message{Overfull hbox is OK}%
-\begin{codeexample}[]
-\begin{tikzpicture}
- \begin{polaraxis}[xmin=90,xmax=270]
- \addplot coordinates {(0,1) (90,1) (180,1) (270,1)};
- \end{polaraxis}
-\end{tikzpicture}~%
-\begin{tikzpicture}
- \begin{polaraxis}[xmin=270,xmax=420]
- \addplot coordinates {(0,1) (90,1) (180,1) (270,1)};
- \end{polaraxis}
-\end{tikzpicture}
-\end{codeexample}
-\noindent Similarly, an explicitly provided value for |ymin| allows to reduce the displayed range away from $0$:
-\begin{codeexample}[]
-\begin{tikzpicture}
- \begin{polaraxis}[ymin=0.3]
- \addplot coordinates {(0,1) (90,1)
- (180,1) (270,1)};
- \end{polaraxis}
-\end{tikzpicture}
-\end{codeexample}
-
-\noindent Modifying |xmin| and |xmax| manually can also be used to move the $y$ axis line (the line with |ytick| and |yticklabels|):
-\begin{codeexample}[]
-\begin{tikzpicture}
- \begin{polaraxis}[xmin=45,xmax=405]
- \addplot coordinates {(0,1) (90,1) (180,1) (270,1)};
- \end{polaraxis}
-\end{tikzpicture}
-\end{codeexample}
-}