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diff --git a/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-dv-polar.tex b/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-dv-polar.tex
index 7eb15fde505..5d9f3518052 100644
--- a/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-dv-polar.tex
+++ b/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-dv-polar.tex
@@ -8,27 +8,21 @@
% See the file doc/generic/pgf/licenses/LICENSE for more details.
-
-
\section{Polar Axes}
-
\label{section-dv-polar}
-
\subsection{Overview}
\begin{tikzlibrary}{datavisualization.polar}
- This library contains keys that allow you to create plots in a polar
- axis system is used.
+ This library contains keys that allow you to create plots in a polar axis
+ system is used.
\end{tikzlibrary}
-In a \emph{polar axis system} two attributes are visualized by
-displacing a data point as follows: One attribute is used to compute a
-an angle (a direction) while a second attribute is used as a radius (a
-distance). The angle can be measured in degrees, radians, or can be
-scaled arbitrarily.
-
-
+In a \emph{polar axis system} two attributes are visualized by displacing a
+data point as follows: One attribute is used to compute a an angle (a
+direction) while a second attribute is used as a radius (a distance). The angle
+can be measured in degrees, radians, or can be scaled arbitrarily.
+%
\begin{codeexample}[width=8.5cm]
\tikz \datavisualization [
scientific polar axes={0 to pi, clean},
@@ -50,20 +44,18 @@ scaled arbitrarily.
};
\end{codeexample}
-Most of the time, in order to create a polar axis system, you will
-just use the |scientific polar axes| key, which takes a number of
-options that allow you to configure the axis system in greater
-detail. This key is documented in
-Section~\ref{section-dv-sci-polar-axes}. Internally, this key uses
-more low level keys which are documented in the en suite sections.
-
-It is worthwhile to note that the axes of a polar axis system are,
-still, normal axes of the data visualization system. In particular,
-all the configurations possible for, say, Cartesian axes also apply to
-the ``angle axis'' and the ``radius axis'' of a polar axis system. For
-instance, you can could make both axes logarithmic or style their
-ticks:
-
+Most of the time, in order to create a polar axis system, you will just use the
+|scientific polar axes| key, which takes a number of options that allow you to
+configure the axis system in greater detail. This key is documented in
+Section~\ref{section-dv-sci-polar-axes}. Internally, this key uses more low
+level keys which are documented in the en suite sections.
+
+It is worthwhile to note that the axes of a polar axis system are, still,
+normal axes of the data visualization system. In particular, all the
+configurations possible for, say, Cartesian axes also apply to the ``angle
+axis'' and the ``radius axis'' of a polar axis system. For instance, you can
+could make both axes logarithmic or style their ticks:
+%
\begin{codeexample}[]
\tikz[baseline] \datavisualization [
scientific axes={clean},
@@ -90,7 +82,7 @@ ticks:
var t : interval [-3:3];
func angle = exp(\value t);
func radius = \value{t}*\value{t};
- };
+ };
\end{codeexample}
@@ -98,32 +90,33 @@ ticks:
\label{section-dv-sci-polar-axes}
\begin{key}{/tikz/data visualization/scientific polar axes=\meta{options}}
- This key installs a polar axis system that can be used in a
- ``scientific'' publication. Two axes are created called the
- |angle axis| and the |radius axis|. Unlike ``normal'' Cartesian
- axes, these axes do not point in a specific direction. Rather, the
- |radius axis| is used to map the values of one attribute to a
- distance from the origin while the |angle axis| is used to map the
- values of another attribute to a rotation angle.
-
- The \meta{options} will be executed with the path prefix
+ This key installs a polar axis system that can be used in a ``scientific''
+ publication. Two axes are created called the |angle axis| and the
+ |radius axis|. Unlike ``normal'' Cartesian axes, these axes do not point in
+ a specific direction. Rather, the |radius axis| is used to map the values
+ of one attribute to a distance from the origin while the |angle axis| is
+ used to map the values of another attribute to a rotation angle.
+
+ The \meta{options} will be executed with the path prefix
+ %
\begin{codeexample}[code only]
-/tikz/data visualization/scientific polar axes
+/tikz/data visualization/scientific polar axes
\end{codeexample}
- The permissible keys are documented in the later subsections of this
- section.
-
- Let us start with the configuration of the radius axis since it is
- easier. Firstly, you should specify which attribute is linked to the
- radius. The default is |radius|, but you will typically wish to
- change this. As with any other axis, the |attribute| key is used to
- configure the axis, see Section~\ref{section-dv-axis-attribute} for
- details. You can also apply all other configurations to the radius
- axis like, say, |unit length| or |length| or |style|. Note, however,
- that the |logarithmic| key will not work with the radius axis for a
- |scientific polar axes| system since the attribute value zero is
- always placed at the center -- and for a logarithmic plot the value
- |0| cannot be mapped.
+ %
+ The permissible keys are documented in the later subsections of this
+ section.
+
+ Let us start with the configuration of the radius axis since it is easier.
+ Firstly, you should specify which attribute is linked to the radius. The
+ default is |radius|, but you will typically wish to change this. As with
+ any other axis, the |attribute| key is used to configure the axis, see
+ Section~\ref{section-dv-axis-attribute} for details. You can also apply all
+ other configurations to the radius axis like, say, |unit length| or
+ |length| or |style|. Note, however, that the |logarithmic| key will not
+ work with the radius axis for a |scientific polar axes| system since the
+ attribute value zero is always placed at the center -- and for a
+ logarithmic plot the value |0| cannot be mapped.
+ %
\begin{codeexample}[width=8.8cm]
\tikz \datavisualization [
scientific polar axes,
@@ -141,24 +134,23 @@ data [format=function] {
};
\end{codeexample}
- For the |angle axis|, you can also specify an attribute using the
- |attribute| key. However, for this axis the mapping of a value to an
- actual angle is a complicated process involving many considerations
- of how the polar axis system should be visualized. For this reason,
- there are a large number of predefined such mappings documented in
- Section~\ref{section-dv-angle-ranges}.
-
- Finally, as for a |scientific plot|, you can configure where the
- ticks should be shown using the keys |inner ticks|, |outer ticks|,
- and |clean|, documented below.
+ For the |angle axis|, you can also specify an attribute using the
+ |attribute| key. However, for this axis the mapping of a value to an actual
+ angle is a complicated process involving many considerations of how the
+ polar axis system should be visualized. For this reason, there are a large
+ number of predefined such mappings documented in
+ Section~\ref{section-dv-angle-ranges}. Finally, as for a |scientific plot|,
+ you can configure where the ticks should be shown using the keys
+ |inner ticks|, |outer ticks|, and |clean|, documented below.
\end{key}
\subsubsection{Tick Placements}
\begin{key}{/tikz/data visualization/scientific polar axes/outer ticks}
- This key, which is the default, causes ticks to be drawn
- ``outside'' the outer ``ring'' of the polar axes:
+ This key, which is the default, causes ticks to be drawn ``outside'' the
+ outer ``ring'' of the polar axes:
+ %
\begin{codeexample}[width=8.8cm]
\tikz \datavisualization [
scientific polar axes={outer ticks, 0 to 180},
@@ -168,11 +160,13 @@ data [format=function] {
func radius = \value{angle};
};
\end{codeexample}
+ %
\end{key}
\begin{key}{/tikz/data visualization/scientific polar axes/inner ticks}
- This key causes the ticks to be ``turned to the inside.'' I do not
- recommend using this key.
+ This key causes the ticks to be ``turned to the inside''. I do not
+ recommend using this key.
+ %
\begin{codeexample}[width=8.8cm]
\tikz \datavisualization [
scientific polar axes={inner ticks, 0 to 180},
@@ -182,13 +176,14 @@ data [format=function] {
func radius = \value{angle};
};
\end{codeexample}
+ %
\end{key}
\begin{key}{/tikz/data visualization/scientific polar axes/clean}
- This key separates the area where the data is shown from the area
- where the ticks are shown. Usually, this is the best choice for the
- tick placement since it avoids a collision of data and
- explanations.
+ This key separates the area where the data is shown from the area where the
+ ticks are shown. Usually, this is the best choice for the tick placement
+ since it avoids a collision of data and explanations.
+ %
\begin{codeexample}[width=8.8cm]
\tikz \datavisualization [
scientific polar axes={clean, 0 to 180},
@@ -197,63 +192,60 @@ data [format=function] {
var angle : interval [0:100];
func radius = \value{angle};
};
-\end{codeexample}
+\end{codeexample}
+ %
\end{key}
\subsubsection{Angle Ranges}
\label{section-dv-angle-ranges}
-Suppose you create a polar plot in which the radius values vary
-between, say, $567$ and $1234$. Then the normal axis scaling mechanisms
-can be used to compute a good scaling for the ``radius axis'': Place
-the value $1234$ at a distance of , say, $5\,\mathrm{cm}$ from the
-origin and place the value $0$ at the origin. Now, by comparison,
-suppose that the values of the angle axis's attribute ranged between,
-say, $10$ and $75.7$. In this case, we may wish the angles to be
-scaled so that the minimum value is horizontal and the maximum value is
-vertical. But we may also wish the a value of $0$ is horizontal and a
-value of $90$ is vertical.
-
-Since it is unclear which interpretation is the right one, you have to
-use an option to select which should happen. The applicable options
-fall into three categories:
-
+Suppose you create a polar plot in which the radius values vary between, say,
+$567$ and $1234$. Then the normal axis scaling mechanisms can be used to
+compute a good scaling for the ``radius axis'': Place the value $1234$ at a
+distance of , say, $5\,\mathrm{cm}$ from the origin and place the value $0$ at
+the origin. Now, by comparison, suppose that the values of the angle axis's
+attribute ranged between, say, $10$ and $75.7$. In this case, we may wish the
+angles to be scaled so that the minimum value is horizontal and the maximum
+value is vertical. But we may also wish the a value of $0$ is horizontal and a
+value of $90$ is vertical.
+
+Since it is unclear which interpretation is the right one, you have to use an
+option to select which should happen. The applicable options fall into three
+categories:
+%
\begin{itemize}
-\item Options that request the scaling to be done in such a way that
- the attribute is interpreted as a value in degrees and such that the
- minimum and maximum of the depicted range is a multiple of
- $90^\circ$. For instance, the option |0 to 180| causes the angle
- axis to range from $0^\circ$ to $180^\circ$, independently of the
- actual range of the values.
-\item Options that work as above, but use radians rather than
- degrees. An example is the option |0 to pi|.
-\item Options that map the minimum value in the data to a horizontal
- or vertical line and the maximum value to another such line. This is
- useful when the values neither directly correspond to degrees or
- radians. In this case, the angle axis may also be a logarithmic
- axis.
+ \item Options that request the scaling to be done in such a way that the
+ attribute is interpreted as a value in degrees and such that the
+ minimum and maximum of the depicted range is a multiple of $90^\circ$.
+ For instance, the option |0 to 180| causes the angle axis to range from
+ $0^\circ$ to $180^\circ$, independently of the actual range of the
+ values.
+ \item Options that work as above, but use radians rather than degrees. An
+ example is the option |0 to pi|.
+ \item Options that map the minimum value in the data to a horizontal or
+ vertical line and the maximum value to another such line. This is
+ useful when the values neither directly correspond to degrees or
+ radians. In this case, the angle axis may also be a logarithmic axis.
\end{itemize}
-In addition to the above categories, all of the option documented in
-the following implicitly also select quadrants that are used to depict
-the data. For instance, the |0 to 90| key and also the |0 to pi half|
-key setup the polar axis system in such a way that only first (upper
-right) quadrant is used. No check is done whether the data fill
-actually lie in this quadrant -- if it does not, the data will ``bleed
-outside'' the range. Naturally, with a key like |0 to 360| or
-|0 to 2pi| this cannot happen.
-
-In order to save some space in this manual, in the following the
-different possible keys are only given in a table together with a
-small example for each key. The examples were created using the
-following code:
-
+In addition to the above categories, all of the option documented in the
+following implicitly also select quadrants that are used to depict the data.
+For instance, the |0 to 90| key and also the |0 to pi half| key setup the polar
+axis system in such a way that only first (upper right) quadrant is used. No
+check is done whether the data fill actually lie in this quadrant -- if it does
+not, the data will ``bleed outside'' the range. Naturally, with a key like
+|0 to 360| or |0 to 2pi| this cannot happen.
+
+In order to save some space in this manual, in the following the different
+possible keys are only given in a table together with a small example for each
+key. The examples were created using the following code:
+%
\begin{codeexample}[]
\tikz \datavisualization [
scientific polar axes={
clean,
- 0 to 90 % the option
+ 0 to 90 % the option
},
angle axis={ticks={step=30}},
radius axis={length=1cm, ticks={step=1}},
@@ -263,13 +255,13 @@ data point [angle=30, radius=1]
data point [angle=40, radius=1.5];
\end{codeexample}
-For the options on radians, the angle values have been replaced by
-|0.2|, |0.3|, and |0.4| and the stepping has been changed by setting
-|step=(pi/6)|. For the quadrant options, no stepping is set at all (it
-is computed automatically).
+For the options on radians, the angle values have been replaced by |0.2|,
+|0.3|, and |0.4| and the stepping has been changed by setting |step=(pi/6)|.
+For the quadrant options, no stepping is set at all (it is computed
+automatically).
\def\polarexample#1#2#3#4#5{%
- \texttt{#1}%
+ \texttt{#1}%
\indexkey{/tikz/data visualization/scientific polar axes/#1}&
\tikz [baseline]{\path(-2.25cm,0)(2.25cm,0); \datavisualization [
scientific polar axes={clean, #1},
@@ -297,62 +289,60 @@ is computed automatically).
}
\begin{tabular}{lcc}
- \emph{Option} & \emph{With clean ticks} & \emph{With outer ticks} \\
- \polarexample{0 to 90}{step=30}{20}{30}{40}
- \polarexample{-90 to 0}{step=30}{20}{30}{40}
- \polarexample{0 to 180}{step=30}{20}{30}{40}
- \polarexample{-90 to 90}{step=30}{20}{30}{40}
- \polarexample{0 to 360}{step=30}{20}{30}{40}
- \polarexample{-180 to 180}{step=30}{20}{30}{40}
+ \emph{Option} & \emph{With clean ticks} & \emph{With outer ticks} \\
+ \polarexample{0 to 90}{step=30}{20}{30}{40}
+ \polarexample{-90 to 0}{step=30}{20}{30}{40}
+ \polarexample{0 to 180}{step=30}{20}{30}{40}
+ \polarexample{-90 to 90}{step=30}{20}{30}{40}
+ \polarexample{0 to 360}{step=30}{20}{30}{40}
+ \polarexample{-180 to 180}{step=30}{20}{30}{40}
\end{tabular}
\begin{tabular}{lcc}
- \emph{Option} & \emph{With clean ticks} & \emph{With outer ticks} \\
- \polarexample{0 to pi half}{step=(pi/6)}{0.2}{0.3}{0.4}
- \polarexample{-pi half to 0}{step=(pi/6)}{0.2}{0.3}{0.4}
- \polarexample{0 to pi}{step=(pi/6)}{0.2}{0.3}{0.4}
- \polarexample{-pi half to pi half}{step=(pi/6)}{0.2}{0.3}{0.4}
- \polarexample{0 to 2pi}{step=(pi/6)}{0.2}{0.3}{0.4}
- \polarexample{-pi to pi}{step=(pi/6)}{0.2}{0.3}{0.4}
+ \emph{Option} & \emph{With clean ticks} & \emph{With outer ticks} \\
+ \polarexample{0 to pi half}{step=(pi/6)}{0.2}{0.3}{0.4}
+ \polarexample{-pi half to 0}{step=(pi/6)}{0.2}{0.3}{0.4}
+ \polarexample{0 to pi}{step=(pi/6)}{0.2}{0.3}{0.4}
+ \polarexample{-pi half to pi half}{step=(pi/6)}{0.2}{0.3}{0.4}
+ \polarexample{0 to 2pi}{step=(pi/6)}{0.2}{0.3}{0.4}
+ \polarexample{-pi to pi}{step=(pi/6)}{0.2}{0.3}{0.4}
\end{tabular}
\begin{tabular}{lcc}
- \emph{Option} & \emph{With clean ticks} & \emph{With outer ticks} \\
- \polarexample{quadrant}{}{20}{30}{40}
- \polarexample{quadrant clockwise}{}{20}{30}{40}
- \polarexample{fourth quadrant}{}{20}{30}{40}
- \polarexample{fourth quadrant clockwise}{}{20}{30}{40}
- \polarexample{upper half}{}{20}{30}{40}
- \polarexample{upper half clockwise}{}{20}{30}{40}
- \polarexample{lower half}{}{20}{30}{40}
- \polarexample{lower half clockwise}{}{20}{30}{40}
+ \emph{Option} & \emph{With clean ticks} & \emph{With outer ticks} \\
+ \polarexample{quadrant}{}{20}{30}{40}
+ \polarexample{quadrant clockwise}{}{20}{30}{40}
+ \polarexample{fourth quadrant}{}{20}{30}{40}
+ \polarexample{fourth quadrant clockwise}{}{20}{30}{40}
+ \polarexample{upper half}{}{20}{30}{40}
+ \polarexample{upper half clockwise}{}{20}{30}{40}
+ \polarexample{lower half}{}{20}{30}{40}
+ \polarexample{lower half clockwise}{}{20}{30}{40}
\end{tabular}
\begin{tabular}{lcc}
- \emph{Option} & \emph{With clean ticks} & \emph{With outer ticks} \\
- \polarexample{left half}{}{20}{30}{40}
- \polarexample{left half clockwise}{}{20}{30}{40}
- \polarexample{right half}{}{20}{30}{40}
- \polarexample{right half clockwise}{}{20}{30}{40}
+ \emph{Option} & \emph{With clean ticks} & \emph{With outer ticks} \\
+ \polarexample{left half}{}{20}{30}{40}
+ \polarexample{left half clockwise}{}{20}{30}{40}
+ \polarexample{right half}{}{20}{30}{40}
+ \polarexample{right half clockwise}{}{20}{30}{40}
\end{tabular}
-
\subsection{Advanced: Creating a New Polar Axis System}
-\begin{key}{/tikz/data visualization/new polar axes=|\char`\{|\meta{angle axis
- name}|\char`\}||\char`\{|\meta{radius axis name}|\char`\}|}
- This key actually creates two axes, whose names are give as
- parameters: An \emph{angle axis} and a \emph{radius axis}. These two
- axes work in concert in the following way: Suppose a data point has two
- attributes called |angle| and |radius| (these attribute names can be
- changed by changing the |attribute| of the \meta{angle axis name} or
- the \meta{radius axis name}, respectively). These two attributes are
- then scaled as usual, resulting in two ``reasonable'' values $a$
- (for the angle) and $r$ (for the radius). Then, the data point gets
- visualized (in principle, details will follow) at a position on the
- page that is at a distance of $r$ from the origin and at an angle
- of~$a$.
+\begin{key}{/tikz/data visualization/new polar axes=|\char`\{|\meta{angle axis name}|\char`\}||\char`\{|\meta{radius axis name}|\char`\}|}
+ This key actually creates two axes, whose names are give as parameters: An
+ \emph{angle axis} and a \emph{radius axis}. These two axes work in concert
+ in the following way: Suppose a data point has two attributes called
+ |angle| and |radius| (these attribute names can be changed by changing the
+ |attribute| of the \meta{angle axis name} or the \meta{radius axis name},
+ respectively). These two attributes are then scaled as usual, resulting in
+ two ``reasonable'' values $a$ (for the angle) and $r$ (for the radius).
+ Then, the data point gets visualized (in principle, details will follow) at
+ a position on the page that is at a distance of $r$ from the origin and at
+ an angle of~$a$.
+ %
\begin{codeexample}[]
\tikz \datavisualization
[new polar axes={angle axis}{radius axis},
@@ -362,26 +352,27 @@ is computed automatically).
angle={0,20,...,160}, radius={0,...,5}
};
\end{codeexample}
- In detail, the \meta{angle axis} keeps track of two vectors $v_0$
- and $v_{90}$, each of which will usually have unit length (length
- |1pt|) and which point in two different directions. Given a radius
- $r$ (measured in \TeX\ |pt|s, so if the
- radius attribute |10pt|, then $r$ would be $10$) and an angle $a$,
- let $s$ be the sine of $a$ and let $c$ be the cosine
- of $a$, where $a$ is a number is degrees (so $s$
- would be $1$ for $a = 90$). Then, the current page position is
- shifted by $c \cdot r$ times $v_0$ and, additionally, by $s \cdot r$
- times $v_{90}$. This means that in the
- ``polar coordinate system'' $v_0$ is the unit vector along the
- ``$0^\circ$-axis'' and $v_{90}$ is the unit vector along
- ``$90^\circ$-axis''. The values of $v_0$ and $v_{90}$ can be changed
- using the following key on the \meta{angle axis}:
- \begin{key}{/tikz/data visualization/axis options/unit
- vectors=|\char`\{|\meta{unit vector 0
- degrees}|\char`\}\char`\{|\meta{unit vector 90
- degrees}|\char`\}| (initially {\char`\{(1pt,0pt)\char`\}\char`\{(0pt,1pt)\char`\}})}
- Both the \meta{unit vector 0 degrees} and the \meta{unit vector 90
- degrees} are \tikzname\ coordinates:
+ %
+ In detail, the \meta{angle axis} keeps track of two vectors $v_0$ and
+ $v_{90}$, each of which will usually have unit length (length |1pt|) and
+ which point in two different directions. Given a radius $r$ (measured in
+ \TeX\ |pt|s, so if the radius attribute |10pt|, then $r$ would be $10$) and
+ an angle $a$, let $s$ be the sine of $a$ and let $c$ be the cosine of $a$,
+ where $a$ is a number is degrees (so $s$ would be $1$ for $a = 90$). Then,
+ the current page position is shifted by $c \cdot r$ times $v_0$ and,
+ additionally, by $s \cdot r$ times $v_{90}$. This means that in the ``polar
+ coordinate system'' $v_0$ is the unit vector along the ``$0^\circ$-axis''
+ and $v_{90}$ is the unit vector along ``$90^\circ$-axis''. The values of
+ $v_0$ and $v_{90}$ can be changed using the following key on the
+ \meta{angle axis}:
+ %
+ \begin{key}{/tikz/data visualization/axis options/unit vectors=%
+ |\char`\{|\meta{unit vector 0 degrees}|\char`\}\char`\{|\meta{unit vector 90 degrees}|\char`\}|
+ (initially {\char`\{(1pt,0pt)\char`\}\char`\{(0pt,1pt)\char`\}})%
+ }
+ Both the \meta{unit vector 0 degrees} and the \meta{unit vector 90 degrees}
+ are \tikzname\ coordinates:
+ %
\begin{codeexample}[]
\tikz \datavisualization
[new polar axes={angle axis}{radius axis},
@@ -391,17 +382,18 @@ is computed automatically).
data [format=named] {
angle={0,90}, radius={0.25,0.5,...,2}
};
-\end{codeexample}
- \end{key}
+\end{codeexample}
+ \end{key}
\end{key}
-Once created, the |angle axis| can be scaled conveniently using the
-following keys:
+Once created, the |angle axis| can be scaled conveniently using the following
+keys:
\begin{key}{/tikz/data visualization/axis options/degrees}
- When this key is passed to the angle axis of a polar axis system, it
- sets up the scaling so that a value of |360| on this axis
- corresponds to a complete circle.
+ When this key is passed to the angle axis of a polar axis system, it sets
+ up the scaling so that a value of |360| on this axis corresponds to a
+ complete circle.
+ %
\begin{codeexample}[]
\tikz \datavisualization
[new polar axes={angle axis}{radius axis},
@@ -411,12 +403,14 @@ following keys:
data [format=named] {
angle={10,90}, radius={0.25,0.5,...,2}
};
-\end{codeexample}
+\end{codeexample}
+ %
\end{key}
\begin{key}{/tikz/data visualization/axis options/radians}
- In contrast to |degrees|, this option sets up things so that a value
- of |2*pi| on this axis corresponds to a complete circle.
+ In contrast to |degrees|, this option sets up things so that a value of
+ |2*pi| on this axis corresponds to a complete circle.
+ %
\begin{codeexample}[]
\tikz \datavisualization
[new polar axes={angle axis}{radius axis},
@@ -427,7 +421,5 @@ following keys:
angle={0,1.5}, radius={0.25,0.5,...,2}
};
\end{codeexample}
+ %
\end{key}
-
-
-
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-10 19:10:41 +0000