% Copyright 2019 by Till Tantau
%
% This file may be distributed and/or modified
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% 2. under the GNU Free Documentation License.
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\section{Patterns}
\label{section-patterns}

\subsection{Overview}

There are many ways of filling a path. First, you can fill it using a solid
color and this is also the fastest method. Second, you can also fill it using a
shading, which means that the color changes smoothly between two (or more)
different colors. Third, you can fill it using a tiling pattern and it is
explained in the following how this is done.

A tiling pattern can be imagined as a rectangular tile (hence the name) on
which a small picture is painted. There is not a single tile, but
(conceptually) an infinite number of tiles, all showing the same picture, and
these tiles are arranged horizontally and vertically to fill the plane. When
you use a tiling pattern to fill a path, what happens is that the path clips
out a ``window'' through which we see part of this infinite plane.

Patterns come in two versions: \emph{inherently colored patterns} and
\emph{form-only patterns}. (These are often called ``color patterns'' and
``uncolored patterns'', but these names are misleading since uncolored patterns
do have a color and the color changes. As I said, the name is misleading\dots)
An inherently colored pattern is just a colored tile like, say, a red star with
a black outline. A form-only pattern can be imagined as a tile that is a kind
of rubber stamp. When this pattern is used, the stamp is used to print copies
of the stamp picture onto the plane, but we can use a different stamp color
each time we use a form-only pattern.

\pgfname\ provides a special support for patterns. You can declare a pattern
and then use it very much like a fill color. \pgfname\ directly maps patterns
to the pattern facilities of the underlying graphic languages (PostScript,
\textsc{pdf}, and \textsc{svg}). This means that filling a path using a pattern
will be nearly as fast as if you used a uniform color.

There are a number of pitfalls and restrictions when using patterns. First,
once a pattern has been declared, you cannot change it anymore. In particular,
it is not possible to enlarge it or change the line width. Such flexibility
would require that the repeating of the pattern were not done by the graphic
language, but on the \pgfname\ level. This would make patterns orders of
magnitude slower to produce and to render. However, \pgfname{} does provide a
more-or-less successful emulation of ``mutable'' patterns, although internally,
a new (fixed) instance of a pattern is declared when the parameters of a
pattern change.

Second, the phase of patterns is not well-defined, that is, it is not clear
where the origin of the ``first'' tile is. To be more precise, PostScript and
\textsc{pdf} on the one hand and \textsc{svg} on the other hand define the
origin differently. PostScript and \textsc{pdf} define a fixed origin that is
independent of where the path lies. This has the highly desirable effect that
if you use the same pattern to fill multiple paths, the outcome is the same as
if you had filled a single path consisting of the union of all these paths. By
comparison, \textsc{svg} uses the upper-left (?) corner of the path to be
filled as the origin. However, the \textsc{svg} specification is a bit vague on
this question.


\subsection{Declaring a Pattern}

Before a pattern can be used, it must be declared. The following command is
used for this:

\begin{command}{\pgfdeclarepatternformonly%
    \opt{\oarg{variables}}%
    \marg{name}%
    \marg{bottom left}%
    \marg{top right}%
    \marg{tile size}%
    \marg{code}%
}
    This command declares a new form-only pattern. The \meta{name} is a name
    for later reference. The two parameters \meta{lower left} and \meta{upper
    right} must describe a bounding box that is large enough to encompass the
    complete tile.

    The size of a tile is given by \meta{tile size}, that is, a tile is a
    rectangle whose lower left   corner is the origin and whose upper right
    corner is given by \meta{tile size}. This might make you wonder why the
    second and third parameters are needed. First, the bounding box might be
    smaller than the tile size if the tile is larger than the picture on the
    tile. Second, the bounding box might be bigger, in which case the picture
    will ``bleed'' over the tile.

    The \meta{code} should be \pgfname\ code that can be protocolled. It should
    not contain any color code.
    %
\begin{codeexample}[preamble={\usetikzlibrary{patterns}}]
\pgfdeclarepatternformonly{stars}
{\pgfpointorigin}{\pgfpoint{1cm}{1cm}}
{\pgfpoint{1cm}{1cm}}
{
  \pgftransformshift{\pgfpoint{.5cm}{.5cm}}
  \pgfpathmoveto{\pgfpointpolar{0}{4mm}}
  \pgfpathlineto{\pgfpointpolar{144}{4mm}}
  \pgfpathlineto{\pgfpointpolar{288}{4mm}}
  \pgfpathlineto{\pgfpointpolar{72}{4mm}}
  \pgfpathlineto{\pgfpointpolar{216}{4mm}}
  \pgfpathclose%
  \pgfusepath{fill}
}
\begin{tikzpicture}
  \filldraw[pattern=stars] (0,0)   rectangle (1.5,2);
  \filldraw[pattern=stars,pattern color=red]
                           (1.5,0) rectangle (3,2);
\end{tikzpicture}
\end{codeexample}

    The optional argument \meta{variables} consists of a comma separated list
    of macros, registers or keys, representing the parameters of the pattern
    that may vary. If a variable is a key, then the full path name must be used
    (specifically, it must start with |/|). As an example, a list might look
    like the following: |\mymacro,\mydimen,/pgf/my key|. Note that macros and
    keys should be ``simple''. They should only store values in themselves.

    The effect of \meta{variables}, is the following: Normally, when this
    argument is empty, once a pattern has been declared, it becomes ``frozen''.
    This means that it is not possible to enlarge the pattern or change the
    line width later on. By specifying \meta{variables}, no pattern is actually
    created. Instead, the arguments are stored away (so the macros, registers
    or keys do not have to be defined in advance).

    When the fill pattern is set, \pgfname{} checks if the pattern has already
    been created with the \meta{variables} set to their current values
    (\pgfname{} is usually ``smart enough'' to distinguish between macros,
    registers and keys). If so, this already-declared-pattern is used as the
    fill pattern. If not, a new instance of the pattern (which will have a
    unique internal name) is declared using the current values of
    \meta{variables}. These values are then saved and the fill pattern set
    accordingly.

    The following shows an example of a pattern which varies according to the
    values of the macro |\size|, the key |/tikz/radius|, and the \TeX{}
    dimension |\thickness|.
    %
\begin{codeexample}[preamble={\usetikzlibrary{patterns}}]
\pgfdeclarepatternformonly[/tikz/radius,\thickness,\size]{rings}
{\pgfpoint{-0.5*\size}{-0.5*\size}}
{\pgfpoint{0.5*\size}{0.5*\size}}
{\pgfpoint{\size}{\size}}
{
  \pgfsetlinewidth{\thickness}
  \pgfpathcircle\pgfpointorigin{\pgfkeysvalueof{/tikz/radius}}
  \pgfusepath{stroke}
}
\newdimen\thickness
\tikzset{
  radius/.initial=4pt,
  size/.store in=\size, size=20pt,
  thickness/.code={\thickness=#1},
  thickness=0.75pt
}
\begin{tikzpicture}[rings/.style={pattern=rings}]
  \filldraw [rings, radius=2pt, size=6pt]      (0,0)   rectangle +(1.5,2);
  \filldraw [rings, radius=2pt, size=8pt]      (2,0)   rectangle +(1.5,2);
  \filldraw [rings, radius=6pt, thickness=2pt] (0,2.5) rectangle +(1.5,2);
  \filldraw [rings, radius=8pt, thickness=4pt] (2,2.5) rectangle +(1.5,2);
\end{tikzpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfdeclarepatterninherentlycolored
    \opt{\oarg{variables}}
    \marg{name}
    \marg{lower left}
    \marg{upper right}
    \marg{tile size}
    \marg{code}%
}
    This command works like |\pgfdeclarepatternuncolored|, only the pattern
    will have an inherent color. To set the color, you should use \pgfname's
    color commands, not the |\color| command, since this fill is not
    protocolled.
    %
\begin{codeexample}[preamble={\usetikzlibrary{patterns}}]
\pgfdeclarepatterninherentlycolored{green stars}
{\pgfpointorigin}{\pgfpoint{1cm}{1cm}}
{\pgfpoint{1cm}{1cm}}
{
  \pgfsetfillcolor{green!50!black}
  \pgftransformshift{\pgfpoint{.5cm}{.5cm}}
  \pgfpathmoveto{\pgfpointpolar{0}{4mm}}
  \pgfpathlineto{\pgfpointpolar{144}{4mm}}
  \pgfpathlineto{\pgfpointpolar{288}{4mm}}
  \pgfpathlineto{\pgfpointpolar{72}{4mm}}
  \pgfpathlineto{\pgfpointpolar{216}{4mm}}
  \pgfpathclose%
  \pgfusepath{stroke,fill}
}
\begin{tikzpicture}
  \filldraw[pattern=green stars] (0,0) rectangle (3,2);
\end{tikzpicture}
\end{codeexample}
    %
\end{command}


\subsection{Setting a Pattern}

Once a pattern has been declared, it can be used.

\begin{command}{\pgfsetfillpattern\marg{name}\marg{color}}
    This command specifies that paths that are filled should be filled with the
    ``color'' by the pattern \meta{name}. For an inherently colored pattern,
    the \meta{color} parameter is ignored. For form-only patterns, the
    \meta{color} parameter specifies the color to be used for the pattern.
    %
\begin{codeexample}[
    preamble={\usetikzlibrary{patterns}
\pgfdeclarepatternformonly{stars}
{\pgfpointorigin}{\pgfpoint{1cm}{1cm}}
{\pgfpoint{1cm}{1cm}}
{
  \pgftransformshift{\pgfpoint{.5cm}{.5cm}}
  \pgfpathmoveto{\pgfpointpolar{0}{4mm}}
  \pgfpathlineto{\pgfpointpolar{144}{4mm}}
  \pgfpathlineto{\pgfpointpolar{288}{4mm}}
  \pgfpathlineto{\pgfpointpolar{72}{4mm}}
  \pgfpathlineto{\pgfpointpolar{216}{4mm}}
  \pgfpathclose%
  \pgfusepath{fill}
}
\pgfdeclarepatterninherentlycolored{green stars}
{\pgfpointorigin}{\pgfpoint{1cm}{1cm}}
{\pgfpoint{1cm}{1cm}}
{
  \pgfsetfillcolor{green!50!black}
  \pgftransformshift{\pgfpoint{.5cm}{.5cm}}
  \pgfpathmoveto{\pgfpointpolar{0}{4mm}}
  \pgfpathlineto{\pgfpointpolar{144}{4mm}}
  \pgfpathlineto{\pgfpointpolar{288}{4mm}}
  \pgfpathlineto{\pgfpointpolar{72}{4mm}}
  \pgfpathlineto{\pgfpointpolar{216}{4mm}}
  \pgfpathclose%
  \pgfusepath{stroke,fill}
}}]
\begin{tikzpicture}
  \pgfsetfillpattern{stars}{red}
  \filldraw (0,0) rectangle (1.5,2);

  \pgfsetfillpattern{green stars}{red}
  \filldraw (1.5,0) rectangle (3,2);
\end{tikzpicture}
\end{codeexample}
    %
\end{command}


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