1 files changed, 59 insertions, 5 deletions
diff --git a/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-pgfsys-commands.tex b/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-pgfsys-commands.tex
index ae982952815..47b876cd1b1 100644
--- a/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-pgfsys-commands.tex
+++ b/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-pgfsys-commands.tex
@@ -637,8 +637,10 @@ done.
 \subsection{Pattern System Commands}
 
 \begin{command}{\pgfsys@declarepattern
-    \marg{name}\marg{$x_1$}\marg{$y_1$}\marg{$x_2$}\marg{$y_2$}
-    \marg{$x$ step}\marg{$y$ step}\marg{code}\marg{flag}%
+    \marg{name}\marg{$x_1$}\marg{$y_1$}\marg{$x_2$}\marg{$y_2$}%
+    \marg{$x$ step}\marg{$y$ step}%
+    \marg{$a$}\marg{$b$}\marg{$c$}\marg{$d$}\allowbreak\marg{$e$}\marg{$f$}%
+    \marg{code}\marg{flag}%
 }
     This command declares a new colored or uncolored pattern, depending on
     whether \meta{flag} is |0|, which means uncolored, or |1|, which means
@@ -652,14 +654,66 @@ done.
     The tiling step of the pattern is given by \meta{$x$ step} and \meta{$y$
     step}.
 
+    The parameters \meta{$a$} to \meta{$f$} are entries of the transformation
+    matrix that is applied to the pattern, see |\pgfsys@patternmatrix| for more
+    information.
+
     \example
     %
 \begin{codeexample}[code only]
-\pgfsys@declarepattern{hori}{-.5pt}{0pt}{.5pt}{3pt}{3pt}{3pt}
-{\pgfsys@moveto{0pt}{0pt}\pgfsys@lineto{0pt}{3pt}\pgfsys@stroke}
-{0}
+\pgfsys@declarepattern
+    {hori}{-.5pt}{0pt}{.5pt}{3pt}{3pt}{3pt}%
+    {1.0}{0.0}{0.0}{1.0}{0.0pt}{0.0pt}%
+    {\pgfsys@moveto{0pt}{0pt}\pgfsys@lineto{0pt}{3pt}\pgfsys@stroke}
+    {0}
+\end{codeexample}
+    %
+\end{command}
+
+
+\begin{command}{\pgfsys@patternmatrix}
+    For convenience \pgfname\ defines the transformation matrix that is applied
+    to all patterns defined with |\pgfdeclarepatternformonly| and
+    |\pgfdeclarepatterninherentlycolored| in a macro.  This can be used as an
+    extension point for ad-hoc transformation of existing patterns.  The
+    default definition is the
+    identity matrix:
+    %
+\begin{codeexample}[code only]
+\def\pgfsys@patternmatrix{{1.0}{0.0}{0.0}{1.0}{0.0pt}{0.0pt}}
 \end{codeexample}
     %
+    The entries of the enclosed array
+    |{|\meta{$a$}|}{|\meta{$b$}|}{|\meta{$c$}|}{|\meta{$d$}|}{|\meta{$e$}|}{|\meta{$f$}|}|
+    are entries in the transformation matrix, identified as in the following
+    transformation prescription:
+    \begin{equation*}
+        \begin{pmatrix}
+            x' \\
+            y' \\
+            1 \\
+        \end{pmatrix}
+        =
+        \begin{pmatrix}
+            a & c & e \\
+            b & d & f \\
+            0 & 0 & 1 \\
+        \end{pmatrix}
+        \begin{pmatrix}
+            x \\
+            y \\
+            1 \\
+        \end{pmatrix} .
+    \end{equation*}
+    Carrying out the matrix multiplication results in the following system of
+    equations
+    \begin{align*}
+        x' &= a x + c y + e , \\
+        y' &= b x + d y + f .
+    \end{align*}
+    Evidently, the parameters \marg{$a$} to \marg{$d$} have to be dimensionless
+    because they are scaling factors, but the parameters \marg{$e$} and
+    \marg{$f$} are offsets, therefore they have to carry a unit.
 \end{command}
 
 \begin{command}{\pgfsys@setpatternuncolored\marg{name}\marg{red}\marg{green}\marg{blue}}