[Tex/LaTex] stripe pattern tikz manual chapter 78

colordiagramsgraphicstikz-pgftransparency

Interleaving two colors in a stripes pattern

Aim: coloring a shape (rectangle, circle, etc.) in two interleaving colors with the aid of patterns.

One solution would be the definition of four patterns. As you can tell from the the following there are two interleaving patterns defined in each direction.

southwest — nordeast
swne
1- swnestripes: (blue stripes)
2- swneStripes: (white stripes)

southeast — nordwest
senw
3- senwstripes: (red stripes)
4- senwStripes: (white stripes)

Naturally, the other solution would be first filling the background in one color (e.g., white) and then applying a pattern on top of it (e.g.,blue). But I do like making things complicated 😉

Preamble:

\documentclass[a4paper]{article}
    \usepackage{graphicx}
    \usepackage{subfig}
    \usepackage{tikz}
    \usetikzlibrary{patterns}

Declarations:

    \begin{document}
    \def\boundb{(-3,2) rectangle (4,-2)}
    \def\setAa{(-1,0) circle (1)}
    \def\setBa{(2,0) circle (1)}
    \def\setAb{(0,0) circle (1)}
    \def\setBb{(1,0) circle (1)}

Patterns:

    \pgfdeclarepatternformonly{swnestripes}{\pgfpoint{0cm}{0cm}}{\pgfpoint{1cm}{1cm}}{\pgfpoint{1cm}{1cm}}
    {
        \foreach \i in {0.1cm, 0.3cm,...,0.9cm}
        {
         \pgfpathmoveto{\pgfpoint{\i}{0cm}}
         \pgfpathlineto{\pgfpoint{1cm}{1cm - \i}}
         \pgfpathlineto{\pgfpoint{1cm}{1cm - \i + 0.1cm}}
         \pgfpathlineto{\pgfpoint{\i - 0.1cm}{0cm}}
         \pgfpathclose%
         \pgfusepath{fill}
         \pgfpathmoveto{\pgfpoint{0cm}{\i}}
         \pgfpathlineto{\pgfpoint{1cm - \i}{1cm}}
         \pgfpathlineto{\pgfpoint{1cm - \i - 0.1cm}{1cm}}
         \pgfpathlineto{\pgfpoint{0cm}{\i + 0.1cm}}
         \pgfpathclose%
         \pgfusepath{fill}
        }
    }
    \pgfdeclarepatternformonly{swneStripes}{\pgfpoint{0cm}{0cm}}{\pgfpoint{1cm}{1cm}}{\pgfpoint{1cm}{1cm}}
    {
        \foreach \i in {0.1cm, 0.3cm,...,0.9cm}
        {
         \pgfpathmoveto{\pgfpoint{\i}{0cm}}
         \pgfpathlineto{\pgfpoint{1cm}{1cm - \i}}
         \pgfpathlineto{\pgfpoint{1cm}{1cm - \i - 0.1cm}}
         \pgfpathlineto{\pgfpoint{\i + 0.1cm}{0cm}}
         \pgfpathclose%
         \pgfusepath{fill}
         \pgfpathmoveto{\pgfpoint{0cm}{\i}}
         \pgfpathlineto{\pgfpoint{1cm - \i}{1cm}}
         \pgfpathlineto{\pgfpoint{1cm - \i + 0.1cm}{1cm}}
         \pgfpathlineto{\pgfpoint{0cm}{\i - 0.1cm}}
         \pgfpathclose%
         \pgfusepath{fill}
        }
    }
    \pgfdeclarepatternformonly{senwstripes}{\pgfpoint{0cm}{0cm}}{\pgfpoint{1cm}{1cm}}{\pgfpoint{1cm}{1cm}}
    {
        \foreach \i in {0.1cm, 0.3cm,...,0.9cm}
        {
         \pgfpathmoveto{\pgfpoint{0cm}{\i}}
         \pgfpathlineto{\pgfpoint{0cm}{\i + 0.1cm}}
         \pgfpathlineto{\pgfpoint{\i + 0.1cm}{0cm}}
         \pgfpathlineto{\pgfpoint{\i}{0cm}}
         \pgfpathclose%
         \pgfusepath{fill}
         \pgfpathmoveto{\pgfpoint{1cm}{\i}}
         \pgfpathlineto{\pgfpoint{\i}{1cm}}
         \pgfpathlineto{\pgfpoint{\i + 0.1cm}{1cm}}
         \pgfpathlineto{\pgfpoint{1cm}{\i + 0.1cm}}
         \pgfpathclose%
         \pgfusepath{fill}
        }
    }
    \pgfdeclarepatternformonly{senwStripes}{\pgfpoint{0cm}{0cm}}{\pgfpoint{1cm}{1cm}}{\pgfpoint{1cm}{1cm}}
    {
        \foreach \i in {0.0cm, 0.2cm,...,0.8cm}
        {
         \pgfpathmoveto{\pgfpoint{\i}{0cm}}
         \pgfpathlineto{\pgfpoint{0cm}{\i}}
         \pgfpathlineto{\pgfpoint{0cm}{\i + 0.1cm}}
         \pgfpathlineto{\pgfpoint{\i + 0.1cm}{0cm}}
         \pgfpathclose%
         \pgfusepath{fill}
         \pgfpathmoveto{\pgfpoint{1cm}{\i}}
         \pgfpathlineto{\pgfpoint{\i}{1cm}}
         \pgfpathlineto{\pgfpoint{\i + 0.1cm}{1cm}}
         \pgfpathlineto{\pgfpoint{1cm}{\i + 0.1cm}}
         \pgfpathclose%
         \pgfusepath{fill}
        }
    }

Figure:

    \begin{figure}[p]
    \centering
    \subfloat[Two separate Sets $\overline{A\cup B}$]{
     \begin{tikzpicture}[scale=0.6, auto, swap]
       \filldraw[pattern=senwStripes, pattern color=magenta!60]\boundb;
       \filldraw[pattern=swnestripes, pattern color=blue!60]\boundb;
       \filldraw[fill=white, draw=blue, line width=2pt]\setAa;
       \filldraw[fill=white, draw=magenta, line width=2pt]\setBa;
       \node at (-2,1) [above left] {$A$};
       \node at (1,1) [above left] {$B$};
     \end{tikzpicture}
    }\qquad
    \caption{Set Examples}
    \label{fig:Sets}
    \end{figure}
\end{document}

Issues:

pdflatex produces

ptptpt    pt    ptptpt    pt    ptptpt    pt    ptptpt    pt

(The desired figure is also created, on a separate page, as expected.)

Dominant Color

When drawing two or more patterns on one shape (e.g., pattern shifted, different color, see interleaved stripes above, multiple possible combinations) in the end, one shape or color is overlapping the other, i.e., one color is more dominant in the whole figure.

   \filldraw[pattern=senwStripes, pattern color=magenta!60]\boundb;
   \filldraw[pattern=swnestripes, pattern color=blue!60]\boundb;

blue is the dominant in the figure.

   \filldraw[pattern=swnestripes, pattern color=blue!60]\boundb;
   \filldraw[pattern=senwStripes, pattern color=magenta!60]\boundb;

magenta is. You can have a look at the effect if you compile the following code:

    \begin{figure}[p]
    \centering
    \subfloat[blue dominant $\overline{A\cup B}$]{
     \begin{tikzpicture}[scale=0.6, auto, swap]
       \filldraw[pattern=senwStripes, pattern color=magenta!60]\boundb;
       \filldraw[pattern=swnestripes, pattern color=blue!60]\boundb;
       \filldraw[fill=white, draw=blue, line width=2pt]\setAa;
       \filldraw[fill=white, draw=magenta, line width=2pt]\setBa;
       \node at (-2,1) [above left] {$A$};
       \node at (1,1) [above left] {$B$};
     \end{tikzpicture}
    }\qquad
    \subfloat[magenta dominant $\overline{A\cup B}$]{
     \begin{tikzpicture}[scale=0.6, auto, swap]
       \filldraw[pattern=swnestripes, pattern color=blue!60]\boundb;
       \filldraw[pattern=senwStripes, pattern color=magenta!60]\boundb; % swapped
       \filldraw[fill=white, draw=blue, line width=2pt]\setAa;
       \filldraw[fill=white, draw=magenta, line width=2pt]\setBa;
       \node at (-2,1) [above left] {$A$};
       \node at (1,1) [above left] {$B$};
     \end{tikzpicture}
    }\qquad
    \caption{Set Examples}
    \label{fig:Sets}
    \end{figure}
\end{document}

Hypothetical question: is there a way to make them both "equal" dominant?

Here is another example:

    \begin{figure}[p]
    \centering
    \subfloat[Set B overlapping set A $\overline{A\cup B}$]{
    \begin{tikzpicture}[scale=0.6, auto, swap]

      \node at (-3,1.5) [above left] {$\scriptstyle U$};
      \begin{scope}[fill opacity=0.2]
       \filldraw[pattern=swnestripes, pattern color=blue!80, ultra thin]\boundb;
       \filldraw[pattern=senwStripes, pattern color=orange, ultra thin]\boundb;
      \end{scope}

      \begin{scope}
       \clip\boundb;
       \fill[fill=white]\setAb;
      \end{scope}
      \begin{scope}
       \clip\boundb;
       \fill[fill=white]\setBb;
      \end{scope}

      \begin{scope}
       \clip\setAb;
       \fill[fill=red!10]\setBb;
      \end{scope}
      \begin{scope}
       \clip\setBb;
       \fill[fill=red!10]\setAb;
      \end{scope}

      \draw[draw=blue, line width=1pt]\setAb;
      \draw[draw=orange, line width=1pt]\setBb;

      \node at (-1,1) [above left] {$\scriptstyle A$};
      \node at (2,1) [above right] {$\scriptstyle B$};
    \end{tikzpicture}
    }\qquad
    \caption{Set Examples}
    \label{fig:Sets}
    \end{figure}
\end{document}

In the following figure, orange circle is overlapping blue circle at intersection points.

enter image description here

Since transparency does not "equally" distribute the dominance of colors in the overlapping parts (the lower color contributes less on the overall effect), one solution for "equal rights" for the colors is structured drawing.

enter image description here

Can you think of a "hack" to get there?

How can I get rid of the "ptptpt"? Any help appreciated. Thanks.

If this looks a bit strange to you, here is a compromise I decided on:

compromise

One color may overlap in the upper part, and one in the lower!

    \begin{figure}[p]
    \centering
    \subfloat[Set B overlapping set A and set A overlapping set B $\overline{A\cup B}$]{
    \begin{tikzpicture}[scale=0.6, auto, swap]

      \node at (-3,1.5) [above left] {$\scriptstyle U$};
      \begin{scope}[fill opacity=0.2]
       \filldraw[pattern=swnestripes, pattern color=blue!80, ultra thin]\boundb;
       \filldraw[pattern=senwStripes, pattern color=orange, ultra thin]\boundb;
      \end{scope}

      \begin{scope}
       \clip\boundb;
       \fill[fill=white]\setAb;
      \end{scope}
      \begin{scope}
       \clip\boundb;
       \fill[fill=white]\setBb;
      \end{scope}

      \begin{scope}
       \clip\setAb;
       \fill[fill=red!10]\setBb;
      \end{scope}
      \begin{scope}
       \clip\setBb;
       \fill[fill=red!10]\setAb;
      \end{scope}

      \node at (-1,1) [above left] {$\scriptstyle A$};
      \node at (2,1) [above right] {$\scriptstyle B$};

      \begin{scope}
        \clip (-2,0) rectangle (4,2);
        \draw[draw=blue, line width=1pt]\setAb;
        \draw[draw=orange, line width=1pt]\setBb;
      \end{scope}
      \begin{scope}
        \clip (-2,0) rectangle (4,-2);
        \draw[draw=orange, line width=1pt]\setBb;
        \draw[draw=blue, line width=1pt]\setAb;
      \end{scope}
    \end{tikzpicture}
    }\qquad
    \caption{Set Examples}
    \label{fig:Sets}
    \end{figure}

Best Answer

To get the circles as you draw them, use a clip. Draw one of the circles twice, once clipped against the rectangle \clip (-2,2) rectangle (.5,-2); and once against \clip (2,2) rectangle (.5,-2);. So in your code above, put:

  \begin{scope}
  \clip (2,2) rectangle (.5,-2);
  \draw[draw=blue, line width=1pt]\setAb;
  \end{scope}
  \draw[draw=orange, line width=1pt]\setBb;
  \begin{scope}
  \clip (-2,2) rectangle (.5,-2);
  \draw[draw=blue, line width=1pt]\setAb;
  \end{scope}

With vastly exaggerated line width you get:

overlapping circles

Related Solutions

[Tex/LaTex] TikZ: Cropping the Bounding Box

The code adds some completely useless invisible (or rather white) stuff. The lines

\clip(0pt,403pt) -- (389.957pt,403pt) -- (389.957pt,99.6166pt) -- (0pt,99.6166pt) -- (0pt,403pt);
\color[rgb]{1,1,1}
\fill(3.76406pt,399.236pt) -- (380.923pt,399.236pt) -- (380.923pt,253.19pt) -- (3.76406pt,253.19pt) -- (3.76406pt,399.236pt);
\fill(53.4497pt,394.719pt) -- (374.901pt,394.719pt) -- (374.901pt,289.325pt) -- (53.4497pt,289.325pt) -- (53.4497pt,394.719pt);

draw a white background that is larger than the actual picture. TikZ sees that and thinks it is part of the picture. Simply removing/uncommenting these lines removes most of the whitespace.

Near the end of the first scope,

\color[rgb]{1,1,1}
\fill(3.76406pt,249.426pt) -- (386.193pt,249.426pt) -- (386.193pt,103.381pt) -- (3.76406pt,103.381pt) -- (3.76406pt,249.426pt);

does the same. Additionally (near the end of the second scope),

\pgftext[center, base, at={\pgfpoint{220.95pt}{106.392pt}}]{\sffamily\fontsize{9}{0}\selectfont{\textbf{ }}}

adds a blank node below the picture, again enlarging the bounding box.

Removing all those lines gives a tight bounding box.

As far as I know, TikZ cannot do the cropping for you, as it can't know whether the white stuff is intentional or not (there might for example be a dark background behind the image so that white is visible).

[Tex/LaTex] Rotate a node but not its content: the case of the ellipse decoration

The source of the difficulty is that ellipses are constructed in a particular way in TikZ. They are paths that start from the x-axis and proceed counter-clockwise around their centre. The vast majority of the time, the exact parametrisation doesn't matter. You appear to have found the one situation where it does!

In the actual question, you only want to be able to mirror the ellipse, and so draw it starting from the negative x-axis (the title of the question suggests a more flexible approach). That's actually not too hard since we can exploit the symmetry of the ellipse. The key is to provide it with a negative x-radius, since then it will start from the negative x-axis (and proceed clockwise, but we could correct for that by negating the y-radius as well). To do this, we interrupt the call from the node shape to the drawing command and flip the sign of the x-radius. The simplest way to do this is to redefine the \pgfpathellipse macro to do the negation and then call the original macro. The following code does this.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations,shapes,decorations.markings}
\makeatletter
\let\origpgfpathellipse=\pgfpathellipse
\def\revpgfpathellipse#1#2#3{%
  #2%
  \pgf@xa=-\pgf@x
  \origpgfpathellipse{#1}{\pgfqpoint{\pgf@xa}{0pt}}{#3}}
\makeatother

\tikzset{
  reversed ellipse/.style={
    ellipse,
    reverse the ellipse%
  },
  reverse the ellipse/.code={
    \let\pgfpathellipse=\revpgfpathellipse
  }
}
\begin{document}
\begin{tikzpicture}
\node[ellipse,
  draw,
  postaction={
    decorate,
    decoration={
      markings,
      mark=at position 1 with {
        \arrow[line width=5pt,blue]{>}
      }
    }
  }
] at (0,0) {hello world};

\node[reversed ellipse,
  draw,
  postaction={
    decorate,
    decoration={
      markings,
      mark=at position 1 with {
        \arrow[line width=5pt,blue]{>}
      }
    }
  }
] at (0,-2) {hello world};
\end{tikzpicture}

\end{document}

Here's the result:

rotated ellipse

(the arrow got clipped, but you can see where it lies)