[Tex/LaTex] pgflayer: background and foreground and tikz: pattern for water

patternpgflayerstikz-pgf

I am attempting to draw a barrel floating in water. I am trying to use pgfonlayer so that when the water line intersects the barrel, the line will be removed.

Also, I looked through small section in the manual on patterns, but I couldn't find a suitable pattern for water.

Here is the image I am trying to re-create:

enter image description here

Here is the code I have and the image:

\documentclass[tikz]{standalone}
\usetikzlibrary{patterns}

\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,foreground}

\begin{document}
\begin{tikzpicture}
  \begin{pgfonlayer}{foreground}
    % draw a barrel
    \draw (0, 0) ellipse[x radius = 1.5cm, y radius = 0.5cm]
    coordinate (B) at (-1.5cm, 0) coordinate (A) at (1.5cm, 0);
    \draw[dashed] (-1.5cm, -1cm) arc[x radius = 1.5cm, y radius = 0.5cm,
    start angle = 180, end angle = 360];
    \draw[dashed] (-1.5cm, -1.1cm) arc[x radius = 1.5cm, y radius = 0.5cm,
    start angle = 180, end angle = 360];
    \draw[dashed] (-1.5cm, -2cm) arc[x radius = 1.5cm, y radius = 0.5cm,
    start angle = 180, end angle = 360];
    \draw[dashed] (-1.5cm, -2.1cm) arc[x radius = 1.5cm, y radius = 0.5cm,
    start angle = 180, end angle = 360];
    \draw (-1.5cm, -3cm) coordinate (C) arc[x radius = 1.5cm, y radius = 0.5cm,
    start angle = 180, end angle = 360] coordinate (D);
    \draw (A) -- (D);
    \draw (B) -- (C);

    % draw the direction of the W = mg
    \fill[black] (0, -1.85cm) coordinate (W) circle[radius = 0.025cm];
    \draw[-stealth] (W) -- ++(0, -0.35cm) node[right, font = \scriptsize] {$mg$};

    % draw the barrel dimensions
    \begin{scope}[>=stealth]
      \draw[|<->|] (-1.5cm, 1cm) -- ++(3cm, 0) node[pos = 0.5,
      fill = white, font = \scriptsize, inner sep = 0.05cm] {$d$};
      \draw[|<->|] (-2cm, 0cm) -- ++(0, -3.5cm) node[pos = 0.5,
      fill = white, font = \scriptsize, inner sep = 0.05cm] {$\ell$};
    \end{scope}
  \end{pgfonlayer}

  % draw the water
  \begin{pgfonlayer}{background}
    \draw (-2.5cm, -1.5cm) -- ++(7cm, 0);
  \end{pgfonlayer}
\end{tikzpicture}
\end{document}

enter image description here

Best Answer

I have re-drawn the cylinder and filled it with white so that whatever is drawn on background layer, is not visible. Further, by manipulating the dash pattern and using \foreach loop with some xshift, the desired effect can be achieved.

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{patterns}

\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,foreground}

\begin{document}
\begin{tikzpicture}
  \begin{pgfonlayer}{foreground}
    % draw a barrel
    \draw[fill=white] (-1.5cm, 0) -- (-1.5cm, -3cm) coordinate (C) arc[x radius = 1.5cm, y radius = 0.5cm,
    start angle = 180, end angle = 360] coordinate (D) -- (1.5cm, 0) --(-1.5cm, 0) -- cycle;
%    \draw[red] (A) -- (D);
%    \draw[red] (B) -- (C);
    \draw[fill=white] (0, 0) ellipse[x radius = 1.5cm, y radius = 0.5cm]
    coordinate (B) at (-1.5cm, 0) coordinate (A) at (1.5cm, 0);
    \draw[dashed] (-1.5cm, -1cm) arc[x radius = 1.5cm, y radius = 0.5cm,
    start angle = 180, end angle = 360];
    \draw[dashed] (-1.5cm, -1.1cm) arc[x radius = 1.5cm, y radius = 0.5cm,
    start angle = 180, end angle = 360];
    \draw[dashed] (-1.5cm, -2cm) arc[x radius = 1.5cm, y radius = 0.5cm,
    start angle = 180, end angle = 360];
    \draw[dashed] (-1.5cm, -2.1cm) arc[x radius = 1.5cm, y radius = 0.5cm,
    start angle = 180, end angle = 360];


    % draw the direction of the W = mg
    \fill[black] (0, -1.85cm) coordinate (W) circle[radius = 0.025cm];
    \draw[-stealth] (W) -- ++(0, -0.35cm) node[right, font = \scriptsize] {$mg$};

    % draw the barrel dimensions
    \begin{scope}[>=stealth]
      \draw[|<->|] (-1.5cm, 1cm) -- ++(3cm, 0) node[pos = 0.5,
      fill = white, font = \scriptsize, inner sep = 0.05cm] {$d$};
      \draw[|<->|] (-2cm, 0cm) -- ++(0, -3.5cm) node[pos = 0.5,
      fill = white, font = \scriptsize, inner sep = 0.05cm] {$\ell$};
    \end{scope}
  \end{pgfonlayer}

  % draw the water
  \begin{pgfonlayer}{background}
    \draw[dash pattern=on 20pt off 10pt] (-2.5cm, -1.5cm) -- ++(6cm, 0);
    \foreach \x in {-1.7,-1.9,...,-4.1}{
      \draw[gray!30,dash pattern=on 4pt off 4pt] ([xshift=4pt]-2.5cm, \x cm) -- ++([xshift=-4pt]6cm, 0);
    }
    \foreach \x in {-1.6,-1.8,...,-4}{
      \draw[gray!30,dash pattern=on 4pt off 4pt] (-2.5cm, \x cm) -- ++(6cm, 0);
    }
  \end{pgfonlayer}
\end{tikzpicture}
\end{document}

enter image description here

Code

\documentclass[tikz, border=2mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.9}
\usetikzlibrary{arrows.meta}
\tikzset{>=Latex}

\begin{document}
\begin{tikzpicture}
\def\tilt{45}
\def\azimuth{30}
\begin{axis}[%
axis equal,
width=14cm,
height=14cm,
hide axis,
enlargelimits=0.3,
view/h=\tilt,
view/v=\azimuth,
scale uniformly strategy=units only,
colormap={bluewhite}{color=(blue) color=(white)},   
]
\coordinate (X) at (axis cs: 1,0,0);
\coordinate (-X) at (axis cs: -1,0,0);
\coordinate (Y) at (axis cs: 0,1,0);
\coordinate (-Y) at (axis cs: 0,-1,0);
\coordinate (Z) at (axis cs: 0,0,1);
\coordinate (-Z) at (axis cs: 0,0,-1);
\filldraw[ball color=white] (axis cs: 0,0,0) circle (2.47cm);
    \pgfplotsinvokeforeach {-80,-60,...,80}{
        \pgfplotsextra{ 
            \pgfmathsetmacro\sinVis{sin(#1)/cos(#1)*sin(\azimuth)/cos(\azimuth)}
            % angle of "visibility"
            \pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
            \coordinate (X) at (axis cs: {cos(#1)},0,{sin(#1)});
            \draw [densely dashed] (X) arc (0:360:{100*cos(#1)});
        } }
    \pgfplotsinvokeforeach {-80,-60,...,80}{
    \pgfplotsextra{ 
        \pgfmathsetmacro\sinVis{sin(#1)/cos(#1)*sin(\azimuth)/cos(\azimuth)}
         % angle of "visibility"
        \pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
        \coordinate (X) at (axis cs: {cos(#1)},0,{sin(#1)});
        \draw (X) arc (0:\tilt+\angVis:{100*cos(#1)}) (X) arc (0:-180+\tilt-\angVis:{100*cos(#1)});
    } }

\foreach \a in {0,20,...,359}
{ \pgfmathsetmacro{\Bound}{-60*cos(\a+45)}
    \addplot3[domain=\Bound:90, samples=45,samples y=0] ({cos(\a)*cos(x)},{sin(\a)*cos(x)},{sin(x)});
    \addplot3[domain=-90:\Bound, samples=45,samples y=0, densely dashed] ({cos(\a)*cos(x)},{sin(\a)*cos(x)},{sin(x)});
}
\end{axis}  
\end{tikzpicture}   
\end{document}

Output

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

A solution which allows to draw intersection segments of any two intersections is available as tikz library fillbetween.

This library works as general purpose tikz library, but it is shipped with pgfplots and you need to load pgfplots in order to make it work:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}];

\end{tikzpicture}

\end{document}

enter image description here

The key intersection segments is described in all detail in the pgfplots reference manual section "5.6.6 Intersection Segment Recombination"; the key idea in this case is to

create a temporary path temp1 which is the first intersection segment of red and blue, more precisely, it is the first intersection segment in the Left argument in red and blue : red. This path is drawn as thin black path. Substitute its \draw statement by \path to make it invisible.
Compute the desired intersection segment by intersecting temp1 and green and use the correct intersection segment. By trial and error I figured that it is the third segment of path temp1 which is written as L3 (L = left argument in temp1 and green and 3 means third segment of that path).

The argument involves some trial and error because fillbetween is unaware of the fact that end and startpoint are connected -- and we as end users do not see start and end point.

Note that you can connect these path segments with other paths. If such an intersection segment should be the continuation of another path, use -- as before the first argument in sequence. This allows to fill paths segments:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,fill=blue,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}]  
    [intersection segments={of=temp1 and green, sequence={--R2}}]
;

\end{tikzpicture}

\end{document}

enter image description here

Best Answer

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Code

Output

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

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