% Copyright 2019 by Till Tantau
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Free Documentation License.
%
% See the file doc/generic/pgf/licenses/LICENSE for more details.


\section{Using Paths}

\subsection{Overview}

Once a path has been constructed, it can be \emph{used} in different ways. For
example, you can draw the path or fill it or use it for clipping.

Numerous graph parameters influence how a path will be rendered. For example,
when you draw a path, the line width is important as well as the dashing
pattern. The options that govern how paths are rendered can all be set with
commands starting with |\pgfset|. \emph{All options that influence how a path
is rendered always influence the complete path.} Thus, it is not possible to
draw part of a path using, say, a red color and drawing another part using a
green color. To achieve such an effect, you must use two paths.

In detail, paths can be used in the following ways:
%
\begin{enumerate}
    \item You can \emph{stroke} (also known as \emph{draw}) a path.
    \item You can add \emph{arrow tips} to a path.
    \item You can \emph{fill} a path with a uniform color.
    \item You can \emph{clip} subsequent renderings against the path.
    \item You can \emph{shade} a path.
    \item You can \emph{use the path as bounding box} for the whole picture.
\end{enumerate}
%
You can also perform any combination of the above, though it makes no sense to
fill and shade a path at the same time.

To perform (a combination of) the first four actions, you can use the following
command:
%
\begin{command}{\pgfusepath\marg{actions}}
    Applies the given \meta{actions} to the current path. Afterwards, the
    current path is (globally) empty. The following actions are possible:
    %
    \begin{itemize}
        \item \declare{|fill|} fills the path. See Section~\ref{section-fill}
            for further details.
            %
\begin{codeexample}[]
\begin{pgfpicture}
  \pgfpathmoveto{\pgfpointorigin}
  \pgfpathlineto{\pgfpoint{1cm}{1cm}}
  \pgfpathlineto{\pgfpoint{1cm}{0cm}}
  \pgfusepath{fill}
\end{pgfpicture}
\end{codeexample}
            %
        \item \declare{|stroke|} strokes the path. See
            Section~\ref{section-stroke} for further details.
            %
\begin{codeexample}[]
\begin{pgfpicture}
  \pgfpathmoveto{\pgfpointorigin}
  \pgfpathlineto{\pgfpoint{1cm}{1cm}}
  \pgfpathlineto{\pgfpoint{1cm}{0cm}}
  \pgfusepath{stroke}
\end{pgfpicture}
\end{codeexample}
            %
        \item \declare{|draw|} has the same effect as |stroke|.
        \item \declare{|clip|} clips all subsequent drawings against the path.
            Always suppresses arrow tips. See Section~\ref{section-clip} for
            further details.
            %
\begin{codeexample}[]
\begin{pgfpicture}
  \pgfpathmoveto{\pgfpointorigin}
  \pgfpathlineto{\pgfpoint{1cm}{1cm}}
  \pgfpathlineto{\pgfpoint{1cm}{0cm}}
  \pgfusepath{stroke,clip}
  \pgfpathcircle{\pgfpoint{1cm}{1cm}}{0.5cm}
  \pgfusepath{fill}
\end{pgfpicture}
\end{codeexample}
            %
        \item \declare{|discard|} discards the path, that is, it is not used at
            all. Giving this option (alone) has the same effect as giving an
            empty options list.
    \end{itemize}
    %
    When more than one of the first three actions are given, they are applied
    in the above ordering, regardless of their ordering in \meta{actions}.
    Thus, |{stroke,fill}| and |{fill,stroke}| have the same effect.
\end{command}

To shade a path, use the |\pgfshadepath| command, which is explained in
Section~\ref{section-shadings}.


\subsection{Stroking a Path}
\label{section-stroke}

When you use |\pgfusepath{stroke}| to stroke a path, several graphic parameters
influence how the path is drawn. The commands for setting these parameters are
explained in the following.

Note that all graphic parameters apply to the path as a whole, never only to a
part of it.

All graphic parameters are local to the current |{pgfscope}|, but they persists
past \TeX\ groups, \emph{except} for the interior rule (even-odd or nonzero)
and the arrow tip kinds. The latter graphic parameters only persist till the
end of the current \TeX\ group, but this may change in the future, so do not
count on this.


\subsubsection{Graphic Parameter: Line Width}

\begin{command}{\pgfsetlinewidth\marg{line width}}
    This command sets the line width for subsequent strokes (in the current
    |pgfscope|). The line width is given as a normal \TeX\ dimension like
    |0.4pt| or |1mm|.
    %
\begin{codeexample}[]
\begin{pgfpicture}
  \pgfsetlinewidth{1mm}
  \pgfpathmoveto{\pgfpoint{0mm}{0mm}}
  \pgfpathlineto{\pgfpoint{2cm}{0mm}}
  \pgfusepath{stroke}
  \pgfsetlinewidth{2\pgflinewidth} % double in size
  \pgfpathmoveto{\pgfpoint{0mm}{5mm}}
  \pgfpathlineto{\pgfpoint{2cm}{5mm}}
  \pgfusepath{stroke}
\end{pgfpicture}
\end{codeexample}
    %
\end{command}

\begin{textoken}{\pgflinewidth}
    You can access the current line width via the \TeX\ dimension
    |\pgflinewidth|. It will be set to the correct line width, that is, even
    when a \TeX\ group closed, the value will be correct since it is set
    globally, but when a |{pgfscope}| closes, the value is set to the correct
    value it had before the scope.
\end{textoken}


\subsubsection{Graphic Parameter: Caps and Joins}

\begin{command}{\pgfsetbuttcap}
    Sets the line cap to a butt cap. See Section~\ref{section-cap-joins} for an
    explanation of what this is.
\end{command}
%
\begin{command}{\pgfsetroundcap}
    Sets the line cap to a round cap. See again Section~\ref{section-cap-joins}.
\end{command}
\begin{command}{\pgfsetrectcap}
    Sets the line cap to a square cap. See again Section~\ref{section-cap-joins}.
\end{command}
%
\begin{command}{\pgfsetroundjoin}
    Sets the line join to a round join. See again Section~\ref{section-cap-joins}.
\end{command}
%
\begin{command}{\pgfsetbeveljoin}
    Sets the line join to a bevel join. See again Section~\ref{section-cap-joins}.
\end{command}
%
\begin{command}{\pgfsetmiterjoin}
    Sets the line join to a miter join. See again Section~\ref{section-cap-joins}.
\end{command}
%
\begin{command}{\pgfsetmiterlimit\marg{miter limit factor}}
    Sets the miter limit to  \meta{miter limit factor}. See again
    Section~\ref{section-cap-joins}.
\end{command}


\subsubsection{Graphic Parameter: Dashing}

\begin{command}{\pgfsetdash\marg{list of even length of dimensions}\marg{phase}}
    Sets the dashing of a line. The first entry in the list specifies the
    length of the first solid part of the list. The second entry specifies the
    length of the following gap. Then comes the length of the second solid
    part, following by the length of the second gap, and so on. The
    \meta{phase} specifies where the first solid part starts relative to the
    beginning of the line.
    %
\begin{codeexample}[]
\begin{pgfpicture}
  \pgfsetdash{{0.5cm}{0.5cm}{0.1cm}{0.2cm}}{0cm}
  \pgfpathmoveto{\pgfpoint{0mm}{0mm}}
  \pgfpathlineto{\pgfpoint{2cm}{0mm}}
  \pgfusepath{stroke}
  \pgfsetdash{{0.5cm}{0.5cm}{0.1cm}{0.2cm}}{0.1cm}
  \pgfpathmoveto{\pgfpoint{0mm}{1mm}}
  \pgfpathlineto{\pgfpoint{2cm}{1mm}}
  \pgfusepath{stroke}
  \pgfsetdash{{0.5cm}{0.5cm}{0.1cm}{0.2cm}}{0.2cm}
  \pgfpathmoveto{\pgfpoint{0mm}{2mm}}
  \pgfpathlineto{\pgfpoint{2cm}{2mm}}
  \pgfusepath{stroke}
\end{pgfpicture}
\end{codeexample}

    Use |\pgfsetdash{}{0pt}| to get a solid dashing.
\end{command}


\subsubsection{Graphic Parameter: Stroke Color}

\begin{command}{\pgfsetstrokecolor\marg{color}}
    Sets the color used for stroking lines to \meta{color}, where \meta{color}
    is a \LaTeX\ color like |red| or |black!20!red|. Unlike the |\color|
    command, the effect of this command lasts till the end of the current
    |{pgfscope}| and not till the end of the current \TeX\ group.

    The color used for stroking may be different from the color used for
    filling. However, a |\color| command will always ``immediately override''
    any special settings for the stroke and fill colors.

    In plain \TeX, this command will also work, but the problem of
    \emph{defining} a color arises. After all, plain \TeX\ does not provide
    \LaTeX\ colors. For this reason, \pgfname\ implements a minimalistic
    ``emulation'' of the |\definecolor|, |\colorlet|, and |\color| commands.
    Only gray-scale and rgb colors are supported. For most cases this turns out
    to be enough.
    %
\begin{codeexample}[]
\begin{pgfpicture}
  \pgfsetlinewidth{1pt}
  \color{red}
  \pgfpathcircle{\pgfpoint{0cm}{0cm}}{3mm} \pgfusepath{fill,stroke}
  \pgfsetstrokecolor{black}
  \pgfpathcircle{\pgfpoint{1cm}{0cm}}{3mm} \pgfusepath{fill,stroke}
  \color{red}
  \pgfpathcircle{\pgfpoint{2cm}{0cm}}{3mm} \pgfusepath{fill,stroke}
\end{pgfpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfsetcolor\marg{color}}
    Sets both the stroke and fill color. The difference to the normal |\color|
    command is that the effect lasts till the end of the current |{pgfscope}|,
    not only till the end of the current \TeX\ group.
\end{command}


\subsubsection{Graphic Parameter: Stroke Opacity}

You can set the stroke opacity using |\pgfsetstrokeopacity|. This command is
described in Section~\ref{section-transparency}.


\subsubsection{Inner Lines}

When a path is stroked, it is possible to request that it is stroked twice, the
second time with a different line width and a different color. This is a useful
effect for creating ``double'' lines, for instance by setting the line width to
2pt and stroking a black line and then setting the inner line width to 1pt and
stroking a white line on the same path as the original path. This results in
what looks like two lines, each of thickness 0.5pt, spaced 1pt apart.

You may wonder why there is direct support for this ``double stroking'' in the
basic layer. After all, this effect is easy to achieve ``by hand''. The main
reason is that arrow tips must be treated in a special manner when such
``double lines'' are present. First, the order of actions is important: First,
the (thick) main line should be stroked, then the (thin) inner line, and only
then should the arrow tip be drawn. Second, the way an arrow tip looks
typically depends strongly on the width of the inner line, so the arrow tip
code, which is part of the basic layer, needs access to the inner line
thickness.

Two commands are used to set the inner line width and color.

\begin{command}{\pgfsetinnerlinewidth\marg{dimension}}
    This command sets the width of the inner line. Whenever a path is stroked
    (and only then), it will be stroked normally and, afterward, it is stroked
    once more with the color set to the inner line color and the line width set
    to \meta{dimension}.

    In case arrow tips are added to a path, the path is first stroked normally,
    then the inner line is stroked, and then the arrow tip is added. In case
    the main path is shortened because of the added arrow tip, this shortened
    path is double stroked, not the original path (which is exactly what you
    want).

    When the inner line width is set to 0pt, which is the default, no inner
    line is stroked at all (not even a line of width 0pt). So, in order to
    ``switch off'' double stroking, set \meta{dimension} to~|0pt|.

    The setting of the inner line width is local to the current \TeX\ group and
    \emph{not} to the current \pgfname\ scope.

    Note that inner lines will \emph{not} be drawn for paths that are also used
    for clipping. However, this may change in the future, so you should not
    depend on this.
    %
\begin{codeexample}[]
\begin{pgfpicture}
  \pgfpathmoveto{\pgfpointorigin}
  \pgfpathlineto{\pgfpoint{1cm}{1cm}}
  \pgfpathlineto{\pgfpoint{1cm}{0cm}}
  \pgfsetlinewidth{2pt}
  \pgfsetinnerlinewidth{1pt}
  \pgfusepath{stroke}
\end{pgfpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfsetinnerstrokecolor\marg{color}}
    This command sets the \meta{color} that is to be used when the inner line
    is stroked. The effect of this command is also local to the current \TeX\
    group.
    %
\begin{codeexample}[]
\begin{pgfpicture}
  \pgfpathmoveto{\pgfpointorigin}
  \pgfpathlineto{\pgfpoint{1cm}{1cm}}
  \pgfpathlineto{\pgfpoint{1cm}{0cm}}
  \pgfsetlinewidth{2pt}
  \pgfsetinnerlinewidth{1pt}
  \pgfsetinnerstrokecolor{red!50}
  \pgfusepath{stroke}
\end{pgfpicture}
\end{codeexample}
    %
\end{command}


\subsection{Arrow Tips on a Path}
\label{section-tips}

After a path has been drawn, \pgfname\ can add arrow tips at the ends,
depending on how the |tips| key is set, on whether |stroke| or |clip| are used
and on whether the path contains closed subpaths. The exact rules when arrow
tips are added are explained in Section~\ref{section-arrow-tips-where}.

\begin{command}{\pgfsetarrowsstart\marg{start arrow tip specification}}
    Sets the arrow tip kind used at the start of a (possibly curved) path. The
    syntax of the \meta{start arrow specification} is detailed in
    Section~\ref{section-arrow-spec}.

    To ``clear'' the start arrow, say |\pgfsetarrowsstart{}|.
    %
\begin{codeexample}[preamble={\usepgflibrary{arrows.meta}}]
\begin{pgfpicture}
  \pgfsetarrowsstart{Latex[length=10pt]}
  \pgfpathmoveto{\pgfpointorigin}
  \pgfpathlineto{\pgfpoint{1cm}{0cm}}
  \pgfusepath{stroke}
  \pgfsetarrowsstart{Computer Modern Rightarrow}
  \pgfpathmoveto{\pgfpoint{0cm}{2mm}}
  \pgfpathlineto{\pgfpoint{1cm}{2mm}}
  \pgfusepath{stroke}
\end{pgfpicture}
\end{codeexample}

    The effect of this command persists only till the end of the current \TeX\
    scope.
\end{command}

\begin{command}{\pgfsetarrowsend\marg{end arrow tip specification}}
    Sets the arrow tip kind used at the end of a path.
    %
\begin{codeexample}[preamble={\usepgflibrary{arrows.meta}}]
\begin{pgfpicture}
  \pgfsetarrowsstart{Latex[length=10pt]}
  \pgfsetarrowsend{Computer Modern Rightarrow}
  \pgfpathmoveto{\pgfpointorigin}
  \pgfpathlineto{\pgfpoint{1cm}{0cm}}
  \pgfusepath{stroke}
\end{pgfpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfsetarrows\marg{argument}}
    The \meta{argument} can be of the form \meta{start arrow tip
    specification}|-|\meta{end arrow tip specification}. In this case, both the
    start and the end arrow specification are set:
    %
\begin{codeexample}[preamble={\usepgflibrary{arrows.meta}}]
\begin{pgfpicture}
  \pgfsetarrows{Latex[length=10pt]->>}
  \pgfpathmoveto{\pgfpointorigin}
  \pgfpathlineto{\pgfpoint{1cm}{0cm}}
  \pgfusepath{stroke}
\end{pgfpicture}
\end{codeexample}
    %
    Alternatively, \meta{argument} can be of the form |[|\meta{arrow keys}|]|.
    In this case, the \meta{arrow keys} will be set for all arrow tips in the
    current scope, see Section~\ref{section-arrow-scopes}.
\end{command}

\begin{command}{\pgfsetshortenstart\marg{dimension}}
    This command will shortened the start of every stroked path by the given
    dimension. This shortening is done in addition to automatic shortening done
    by a start arrow, but it can be used even if no start arrow is given.

    It is usually better to use the |sep| key with arrow tips.

    This command is useful if you wish arrows or lines to ``stop shortly
    before'' a given point.
    %
\begin{codeexample}[preamble={\usepgflibrary{arrows.meta}}]
\begin{pgfpicture}
  \pgfpathcircle{\pgfpointorigin}{5mm}
  \pgfusepath{stroke}
  \pgfsetarrows{Latex-}
  \pgfsetshortenstart{4pt}
  \pgfpathmoveto{\pgfpoint{5mm}{0cm}} % would be on the circle
  \pgfpathlineto{\pgfpoint{2cm}{0cm}}
  \pgfusepath{stroke}
\end{pgfpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfsetshortenend\marg{dimension}}
    Works like |\pgfsetshortenstart|.
\end{command}


\subsection{Filling a Path}
\label{section-fill}

Filling a path means coloring every interior point of the path with the current
fill color. It is not always obvious whether a point is ``inside'' a  path when
the path is self-intersecting and/or consists or multiple parts. In this case
either the nonzero winding number rule or the even-odd crossing number rule is
used to decide which points lie ``inside''. These rules are explained in
Section~\ref{section-rules}.


\subsubsection{Graphic Parameter: Interior Rule}

You can set which rule is used using the following commands:

\begin{command}{\pgfseteorule}
    Dictates that the even-odd rule is used in subsequent fillings in the
    current \emph{\TeX\ scope}. Thus, for once, the effect of this command does
    not persist past the current \TeX\ scope.
    %
\begin{codeexample}[]
\begin{pgfpicture}
  \pgfseteorule
  \pgfpathcircle{\pgfpoint{0mm}{0cm}}{7mm}
  \pgfpathcircle{\pgfpoint{5mm}{0cm}}{7mm}
  \pgfusepath{fill}
\end{pgfpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfsetnonzerorule}
    Dictates that the nonzero winding number rule is used in subsequent
    fillings in the current \TeX\ scope. This is the default.
    %
\begin{codeexample}[]
\begin{pgfpicture}
  \pgfsetnonzerorule
  \pgfpathcircle{\pgfpoint{0mm}{0cm}}{7mm}
  \pgfpathcircle{\pgfpoint{5mm}{0cm}}{7mm}
  \pgfusepath{fill}
\end{pgfpicture}
\end{codeexample}
    %
\end{command}


\subsubsection{Graphic Parameter: Filling Color}

\begin{command}{\pgfsetfillcolor\marg{color}}
    Sets the color used for filling paths to \meta{color}. Like the stroke
    color, the effect lasts only till the next use of |\color|.
\end{command}


\subsubsection{Graphic Parameter: Fill Opacity}

You can set the fill opacity using |\pgfsetfillopacity|. This command is
described in Section~\ref{section-transparency}.


\subsection{Clipping a Path}
\label{section-clip}

When you add the |clip| option, the current path is used for clipping
subsequent drawings. The same rule as for filling is used to decide whether a
point is inside or outside the path, that is, either the even-odd rule or the
nonzero rule.

Clipping never enlarges the clipping area. Thus, when you clip against a
certain path and then clip again against another path, you clip against the
intersection of both.

The only way to enlarge the clipping path is to end the |{pgfscope}| in which
the clipping was done. At the end of a |{pgfscope}| the clipping path that was
in force at the beginning of the scope is reinstalled.


\subsection{Using a Path as a Bounding Box}
\label{section-using-bb}

When you add the |use as bounding box| option, the bounding box of the picture
will be enlarged such that the path in encompassed, but any \emph{subsequent}
paths of the current \TeX\ scope will not have any effect on the size of the
bounding box. Typically, you use this command at the very beginning of a
|{pgfpicture}| environment. Alternatively, you can use |\pgfresetboundingbox|,
followed by |\pgfusepath{use as bounding box}| to overrule the picture's
bounding box completely.
%
\begin{codeexample}[]
Left
\begin{pgfpicture}
  \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{2ex}{1ex}}
  \pgfusepath{use as bounding box} % draws nothing

  \pgfpathcircle{\pgfpointorigin}{2ex}
  \pgfusepath{stroke}
\end{pgfpicture}
right.
\end{codeexample}