Para uma espécie de ilustração matemática, considere o caso em que são necessárias diversas hachuras distinguíveis, todas em preto e branco, e em que a direção precisa tenha significado.
Dou um exemplo simples de padrão de hachura no MWE.
1Existe alguma maneira geral de simplesmente escrever uma macro para gerar um padrão de hachura desse tipo, mas com uma única variável numérica que controla a direção?
Para esclarecer todas as minhas tentativas de criar uma macro, chame-a de MCR, de forma que:
pattern=MCR x ,pattern color=...onde x=2 ou 1 ou 0 para horizontal, ou 0,5 para vertical, ou 0,25 para diagonal, e aproximadamente no meio.
OU
Até agora eu usei também uma macro para importar um gráfico em um nó para usá-lo como um padrão, dimensionando-o ou esticando-o, e muitas vezes usando a configuração [clip] de \draw e a ordem de execução dos comandos para obter o efeito desejado . Uma macro curta facilita o uso repetido.
2Então, alternativamente, é possível construir um gráfico de hachura, um de noroeste para sudeste, além daquele dado de sudoeste para nordeste, e então enviar para um arquivo, e usar gráficos de entrada em um nó para girar a imagem e usá-lo como padrão? A solução para1é preferível a isso, se1é possível.
\documentclass{standalone}\usepackage{pgfplots,tikz}\usetikzlibrary{patterns}
\def\dotshading{figuretonedots}
\def\toning #1 #2 #3 {\node at (#1) {\includegraphics[width=#3\textwidth]{\csname #2\endcsname}};}
\begin{document}\begin{tikzpicture}%
\pgfdeclarepatternformonly{ltrtoning}%
{\pgfqpoint{-1pt}{-1pt}}{\pgfqpoint{10pt}{10pt}}%
{\pgfqpoint{9pt}{9pt}}{
\pgfsetlinewidth{0.32pt}
\pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
\pgfpathlineto{\pgfqpoint{9.1pt}{9.1pt}}
\pgfusepath{stroke}}%
%\toning 6.78,6.78 dotshading 1.1 %removing this removes toning
\draw[draw=none,pattern=ltrtoning,pattern color=black!64]rectangle(13.4,13.4);
\end{tikzpicture}\end{document}
Responder1
Atualmente, o PGF não suporta a adição de uma matriz de transformação ao padrão, portanto uma rotação geral não é possível.
Poderíamos (com alguma sobrecarga computacional) usar imagens de caminho.
No entanto, o seguinte mostra uma maneira (reconhecidamente muito ruim) de obter padrões rotacionados, hackeando a camada do sistema para incluir uma matriz de transformação para padrões e explorando o fato de que padrões "mutáveis" (que na verdade não são mutáveis) são criados pouco antes de serem criados. são aplicados dependendo do valor das variáveis fornecidas na definição do padrão.
\documentclass[tikz, border=5]{standalone}
\usetikzlibrary{patterns}
\makeatletter
\def\pgfsys@patternmatrix{1.0 0.0 0.0 1.0 0.0 0.0}
\def\pgfsys@declarepattern#1#2#3#4#5#6#7#8#9{%
% Start building the pattern dictionary:
\pgf@xa=#2\relax%
\pgf@ya=#3\relax%
\pgf@xb=#4\relax%
\pgf@yb=#5\relax%
\pgf@xc=#6\relax%
\pgf@yc=#7\relax%
\pgf@sys@bp@correct\pgf@xa%
\pgf@sys@bp@correct\pgf@ya%
\pgf@sys@bp@correct\pgf@xb%
\pgf@sys@bp@correct\pgf@yb%
\pgf@sys@bp@correct\pgf@xc%
\pgf@sys@bp@correct\pgf@yc%
% Now create the pattern object:
\immediate\pdfobj stream
attr
{
/Type /Pattern
/PatternType 1
/PaintType \ifnum#9=0 2 \else 1 \fi
/TilingType 1
/BBox [\pgf@sys@tonumber\pgf@xa\space\pgf@sys@tonumber\pgf@ya\space\pgf@sys@tonumber\pgf@xb\space\pgf@sys@tonumber\pgf@yb]
/XStep \pgf@sys@tonumber\pgf@xc\space
/YStep \pgf@sys@tonumber\pgf@yc\space
/Matrix [\pgfsys@patternmatrix]
/Resources << >> %<<
}
{#8}%
\pgfutil@addpdfresource@patterns{/pgfpat#1\space \the\pdflastobj\space 0 R}%
}
\def\pgf@sp{ }%
\def\pgftransformextractmatrix#1#2{%
\begingroup%
\pgftransformreset%
#2%
\xdef\pgf@tmp{\pgf@pt@aa\pgf@sp\pgf@pt@ab\pgf@sp\pgf@pt@ba\pgf@sp\pgf@pt@bb\pgf@sp\pgf@sys@tonumber\pgf@pt@x\pgf@sp\pgf@sys@tonumber\pgf@pt@y}%
\endgroup%
\let#1=\pgf@tmp}
\pgfdeclarepatternformonly[\patternangle]{rotated hatch}%
{\pgfqpoint{-.1pt}{-1.pt}}{\pgfqpoint{5pt}{5pt}}
{\pgfqpoint{5pt}{5pt}}
{
\pgfsetlinewidth{.5pt}
\pgfpathmoveto{\pgfqpoint{-.1pt}{-.1pt}}
\pgfpathlineto{\pgfqpoint{5pt}{5pt}}
\pgfpathmoveto{\pgfqpoint{5pt}{-.1pt}}
\pgfpathlineto{\pgfqpoint{-.1pt}{5pt}}
\pgfusepath{stroke}
}
\tikzset{%
pattern angle/.code={%
\pgfmathparse{#1}\let\patternangle=\pgfmathresult
\pgftransformextractmatrix\pgfsys@patternmatrix{\pgftransformrotate{\patternangle}}%
},
pattern angle=0
}
\begin{document}
\begin{tikzpicture}[x=3cm,y=3cm];
\foreach \i [count=\j from 0] in {0,7,...,105}{
\draw [pattern=rotated hatch, pattern angle=\i]
({mod(\j,4)}, {floor(\j/4)}) rectangle ++(0.75,0.75)
node [above] {$\i^\circ$};
}
\end{tikzpicture}
\end{document}
Ou...
Aqui está uma implementação incompleta de padrões mutáveis com transformações. Parece um pouco diferente quando tentei traduzir a maneira como a nova arrows.metabiblioteca cria setas para uma nova maneira de definir padrões:
\pgfdeclarepattern{name=hatch,
type=uncolored,
parameters={\hatchsize, \hatchangle, \hatchlinewidth},
bottom left={x=-.1pt, y=-.1pt},
top right={x=\hatchsize+.1pt, y=\hatchsize+.1pt},
tile size={width=\hatchsize, height=\hatchsize},
transformation={rotate=\hatchangle},
code={
\pgfsetlinewidth{\hatchlinewidth}
\pgfpathmoveto{\pgfpoint{-.1pt}{-.1pt}}
\pgfpathlineto{\pgfpoint{\hatchsize+.1pt}{\hatchsize+.1pt}}
\pgfpathmoveto{\pgfpoint{-.1pt}{\hatchsize+.1pt}}
\pgfpathlineto{\pgfpoint{\hatchsize+.1pt}{-.1pt}}
\pgfusepath{stroke}
}}
Podem parametersser macros ou dimensões e assim por diante, mas se forem usadas dimensões ou contagens, elas deverão ser prefixadas com \the. É possível (não tentei) que as chaves possam ser incluídas usando \pgfkeysvalueof{mykey}.
Ele hackeia tanto a camada do sistema quanto a camada básica, então você foi avisado...
\documentclass[tikz, border=5]{standalone}
\usetikzlibrary{patterns}
\makeatletter
% Alternate system layer pattern definition.
% Takes 15(!) arguments
\def\pgfsys@declarepattern@alt#1#2#3#4#5#6#7{%
% Start building the pattern dictionary:
\pgf@xa=#2\relax%
\pgf@ya=#3\relax%
\pgf@xb=#4\relax%
\pgf@yb=#5\relax%
\pgf@xc=#6\relax%
\pgf@yc=#7\relax%
\pgf@sys@bp@correct\pgf@xa%
\pgf@sys@bp@correct\pgf@ya%
\pgf@sys@bp@correct\pgf@xb%
\pgf@sys@bp@correct\pgf@yb%
\pgf@sys@bp@correct\pgf@xc%
\pgf@sys@bp@correct\pgf@yc%
\pgfsys@@declarepattern@alt{#1}}
\def\pgfsys@@declarepattern@alt#1#2#3#4#5#6#7#8#9{%
\pgfutil@tempdima=#6\relax%
\pgfutil@tempdimb=#7\relax%
\pgf@sys@bp@correct\pgf@xa%
\pgf@sys@bp@correct\pgf@ya%
% Now create the pattern object:
\immediate\pdfobj stream
attr
{
/Type /Pattern
/PatternType 1
/PaintType \ifnum#9=0 2 \else 1 \fi
/TilingType 1
/BBox [\pgf@sys@tonumber\pgf@xa\space\pgf@sys@tonumber\pgf@ya\space\pgf@sys@tonumber\pgf@xb\space\pgf@sys@tonumber\pgf@yb]
/XStep \pgf@sys@tonumber\pgf@xc\space
/YStep \pgf@sys@tonumber\pgf@yc\space
/Matrix [#2\space#3\space#4\space#5\space\pgf@sys@tonumber\pgfutil@tempdima\space\pgf@sys@tonumber\pgfutil@tempdimb]
/Resources << >> %<<
}
{#8}%
\pgfutil@addpdfresource@patterns{/pgfpat#1\space \the\pdflastobj\space 0 R}%
}
% Pattern keys
\pgfkeys{/pgf/patterns/.cd,
name/.code=\edef\pgf@pat@name{#1},
type/.is choice,
type/uncolored/.code=\def\pgf@pat@type{0},
type/colored/.code=\def\pgf@pat@type{1},
parameters/.store in=\pgf@pat@parameters,
bottom left/.store in=\pgf@pat@bottomleft,
top right/.store in=\pgf@pat@topright,
tile size/.store in=\pgf@pat@tilesize,
transformation/.store in=\pgf@pat@transformation,
code/.store in=\pgf@pat@code,
name=,
type=uncolored,
parameters=,
bottom left=,
top right=,
transformation=,
code=,
points/.style={/pgf/patterns/points/.cd, #1},
transformations/.style={/pgf/patterns/transformations/.cd,#1},
/pgf/patterns/points/.cd,
x/.store in=\pgf@pat@x,
y/.store in=\pgf@pat@y,
width/.store in=\pgf@pat@x,
height/.store in=\pgf@path@y,
/pgf/patterns/transformations/.cd,
rotate/.code=\pgftransformrotate{#1},
xscale/.code=\pgftransformxscale{#1},
yscale/.code=\pgftransformyscale{#1},
% Plus others...
}
% Points can be specified using PGF commands
% or x and y keys
\def\pgf@pat@processpoint#1{%
\def\pgf@marshal{\pgfutil@in@=}%
\expandafter\pgf@marshal\expandafter{#1}%
\ifpgfutil@in@%
\pgfkeys{/pgf/patterns/points/.expanded=#1}%
\pgf@process{\pgfpoint{\pgf@pat@x}{\pgf@pat@y}}%
\else%
\pgf@process{#1}%
\fi%
}
% Transformations can be specified using PGF commands
% or keys (currently only rotate, xscale and yscale)
\def\pgf@pat@processtransformations#1{%
\def\pgf@marshal{\pgfutil@in@=}%
\expandafter\pgf@marshal\expandafter{#1}%
\ifpgfutil@in@%
\pgfkeys{/pgf/patterns/transformations/.expanded=#1}%
\else%
#1%
\fi%
}
% New pattern definition command
%
% #1 is a list of keys.
\def\pgfdeclarepattern#1{%
\begingroup%
\def\pgf@pat@opts{#1}%
\pgfkeys{/pgf/patterns/.cd,#1}%
\pgfutil@ifundefined{pgf@pattern@name\pgf@pat@name}{%
\ifx\pgf@pat@parameters\pgfutil@empty%
\expandafter\global\expandafter\let\csname pgf@pattern@name@\pgf@pat@name @parameters\endcsname=\pgfutil@empty%
\pgf@declarepattern%
\else%
\expandafter\global\expandafter\let\csname pgf@pattern@name@\pgf@pat@name @parameters\endcsname=\pgf@pat@parameters
\expandafter\global\expandafter\let\csname pgf@pattern@name@\pgf@pat@name\endcsname=\pgf@pat@opts%
\fi%
}{%
\pgferror{Pattern `\pgf@pat@type' already defined}%
}%
\endgroup%
}
\def\pgf@declarepattern{%
\pgfsysprotocol@getcurrentprotocol\pgf@pattern@temp%
{%
\pgfinterruptpath%
\pgfpicturetrue%
\pgf@relevantforpicturesizefalse%
\pgftransformreset%
\pgfsysprotocol@setcurrentprotocol\pgfutil@empty%
\pgfsysprotocol@bufferedtrue%
\pgfsys@beginscope%
\pgfsetarrows{-}%
\pgf@pat@code%
\pgfsys@endscope%
\pgfsysprotocol@getcurrentprotocol\pgf@pattern@code%
\global\let\pgf@pattern@code=\pgf@pattern@code%
\endpgfinterruptpath%
\pgf@pat@processpoint{\pgf@pat@bottomleft}%
\pgf@xa=\pgf@x%
\pgf@ya=\pgf@y%
\pgf@pat@processpoint{\pgf@pat@topright}%
\pgf@xb=\pgf@x%
\pgf@yb=\pgf@y%
\pgf@pat@processpoint{\pgf@pat@tilesize}%
\pgf@xc=\pgf@x%
\pgf@yc=\pgf@y%
\begingroup%
\pgftransformreset%
\pgf@pat@processtransformations\pgf@pat@transformation%
\pgfgettransformentries\aa\ab\ba\bb\shiftx\shifty%
\global\edef\pgf@pattern@matrix{{\aa}{\ab}{\ba}{\bb}{\shiftx}{\shifty}}%
\endgroup%
% Now, build a name for the pattern
\pgfutil@tempcnta=\pgf@pattern@number%
\advance\pgfutil@tempcnta by1\relax%
\xdef\pgf@pattern@number{\the\pgfutil@tempcnta}%
\expandafter\xdef\csname pgf@pattern@name@\pgf@pat@name\endcsname{\the\pgfutil@tempcnta}%
\expandafter\xdef\csname pgf@pattern@type@\pgf@pat@name\endcsname{\pgf@pat@type}%
\xdef\pgf@marshal{\noexpand\pgfsys@declarepattern@alt%
{\csname pgf@pattern@name@\pgf@pat@name\endcsname}
{\the\pgf@xa}{\the\pgf@ya}{\the\pgf@xb}{\the\pgf@yb}{\the\pgf@xc}{\the\pgf@yc}\pgf@pattern@matrix{\pgf@pattern@code}{\pgf@pat@type}}%
}%
\pgf@marshal%
\pgfsysprotocol@setcurrentprotocol\pgf@pattern@temp%
}
\def\pgfsetfillpattern#1#2{%
\pgfutil@ifundefined{pgf@pattern@name@#1}%
{%
\pgferror{Undefined pattern `#1'}%
}%
{%
% Patterns from library won't have pgf@pattern@name@#1@parameters
\pgfutil@ifundefined{pgf@pattern@name@#1@parameters}{%
\pgf@set@fillpattern{#1}{#2}%
}{%
\expandafter\ifx\csname pgf@pattern@name@#1@parameters\endcsname\pgfutil@empty%
\pgf@set@fillpattern{#1}{#2}%
\else
\edef\pgf@pat@currentparameters{\csname pgf@pattern@name@#1@parameters\endcsname}%
\edef\pgf@pat@mutablename{#1@\pgf@pat@currentparameters}%
\pgfutil@ifundefined{pgf@pattern@name@\pgf@pat@mutablename}%
{%
\expandafter\expandafter\expandafter\pgfdeclarepattern\expandafter\expandafter\expandafter{\csname pgf@pattern@name@#1\endcsname,
name=\pgf@pat@mutablename,parameters=}%
}%
{}%
\expandafter\pgf@set@fillpattern\expandafter{\pgf@pat@mutablename}{#2}%
\fi%
}%
}%
}
\def\pgf@set@fillpattern#1#2{%
% Pattern types are 0 (uncolored) or 1 (colored)
\ifcase\csname pgf@pattern@type@#1\endcsname\relax%
\pgfutil@colorlet{pgf@tempcolor}{#2}%
\pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgf@tempcolor}}%
\pgfutil@extractcolorspec{pgf@tempcolor}{\pgf@tempcolor}%
\expandafter\pgfutil@convertcolorspec\pgf@tempcolor{rgb}{\pgf@rgbcolor}%
\expandafter\pgf@set@fill@patternuncolored\pgf@rgbcolor\relax{#1}%
\or
\pgfsys@setpatterncolored{\csname pgf@pattern@name@#1\endcsname}%
\else
\fi
}
\def\tikzdeclarepattern#1{%
\begingroup%
\pgfkeys{/pgf/patterns/code/.code={\def\pgf@pat@code{%
\let\tikz@transform=\relax\tikz@installcommands##1}}}
\pgfdeclarepattern{#1,type=colored}%
\endgroup%
}
\makeatother
\pgfdeclarepattern{name=hatch,
type=uncolored,
parameters={\hatchsize, \hatchangle, \hatchlinewidth},
bottom left={x=-.1pt, y=-.1pt}, % or \pgfqpoint{-.1pt}{-.1pt} will also work
top right={x=\hatchsize+.1pt, y=\hatchsize+.1pt},
tile size={width=\hatchsize, height=\hatchsize},
transformation={rotate=\hatchangle},
code={
\pgfsetlinewidth{\hatchlinewidth}
\pgfpathmoveto{\pgfpoint{-.1pt}{-.1pt}}
\pgfpathlineto{\pgfpoint{\hatchsize+.1pt}{\hatchsize+.1pt}}
\pgfpathmoveto{\pgfpoint{-.1pt}{\hatchsize+.1pt}}
\pgfpathlineto{\pgfpoint{\hatchsize+.1pt}{-.1pt}}
\pgfusepath{stroke}
}}
\tikzset{%
hatch size/.store in=\hatchsize,
hatch angle/.store in=\hatchangle,
hatch line width/.store in=\hatchlinewidth,
hatch size=5pt,
hatch angle=0pt,
hatch line width=.5pt,
}
\begin{document}
\begin{tikzpicture}
\foreach \r in {1,...,4}
\draw [pattern=hatch, pattern color=red]
(\r*3,0) rectangle ++(2,2);
\foreach \r in {1,...,4}
\draw [pattern=hatch, pattern color=green, hatch size=2pt]
(\r*3,3) rectangle ++(2,2);
\foreach \r in {1,...,4}
\draw [pattern=hatch, pattern color=blue, hatch size=10pt, hatch angle=21]
(\r*3,6) rectangle ++(2,2);
\foreach \r in {1,...,4}
\draw [pattern=hatch, pattern color=orange, hatch line width=2pt]
(\r*3,9) rectangle ++(2,2);
\end{tikzpicture}
\end{document}
Além disso, abre a possibilidade de especificação de padrões usando TikZ (o código \tikzdeclarepatternestá incluído acima):
\tikzdeclarepattern{name=flower,
type=uncolored,
bottom left={x=-.1pt, y=-.1pt},
top right={x=10.1pt, y=10.1pt},
tile size={width=10pt, height=10pt},
code={
\tikzset{x=1pt,y=1pt}
\path [draw=green] (5,2.5) -- (5, 7.5);
\foreach \i in {0,60,...,300}
\path [fill=pink, shift={(5,7.5)}, rotate=-\i]
(0,0) .. controls ++(120:4) and ++(60:4) .. (0,0);
\path [fill=red] (5,7.5) circle [radius=1];
\foreach \i in {-45,45}
\path [fill=green, shift={(5,2.5)}, rotate=-\i]
(0,0) .. controls ++(120:4) and ++(60:4) .. (0,0);
}}
Que é então usado da maneira usual:
\tikz\draw [pattern=flower] circle [radius=1];
e produz:
