[Tex/LaTex] Concentric Cylinders with tikz

diagramsmetaposttikz-pgftikz-shape

I am trying to draw two concentric cylinders with tikz to show the change in volume with respect to radius, while the height remains fixed. The left ilustration below is the first drawing, where the height changes with fixed radius. Much of this code was borrowed from
here. The illustration at the right is where I have questions.

enter image description here

1) Is there a way to shade the region between the two top bases? I know how to do this for a regular 2-d illustration using tikz rules between regions, but I can't quite reference these two separate bases.

2) This illustration isn't ideal, obviously, so would there be a more efficient way to generate it where the cylinders appear truly concentric? Perhaps manually draw a similar ellipse inside the outer cylinder and experiment with placement?

the MWE is:

\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows,snakes,backgrounds,patterns,shapes.geometric,calc}

\begin{document}

\begin{tikzpicture}[scale=1]
\node [draw, cylinder, cylinder uses custom fill, cylinder body fill=lightgray!20, 
cylinder end fill=lightgray!20, shape aspect=4, rotate=90, minimum width=3cm] (c1) at 
(0,1.8){};

\coordinate(dhtop) at ($(c1.after top)!-1*.1!(c1.before top)$);
\coordinate(dhbot) at ($(c1.before bottom)!-1*.1!(c1.after bottom)$);
\coordinate(dhlabel) at ($(dhtop)!.5!(dhbot)$);
\draw[|-|] (dhbot)--(dhtop);
\path (dhlabel) node[right, outer sep = 2pt] {$dh$};

\node [draw, cylinder, shape aspect=4, rotate=90, minimum height=4cm, minimum 
width=3cm] (c) {};

\coordinate(htop) at ($(c.before top)!-1*.1!(c.after top)$);
\coordinate(hbot) at ($(c.after bottom)!-1*.1!(c.before bottom)$);
\coordinate(hlabel) at ($(htop)!.5!(hbot)+(c.north)!.9!(c.center)$);

\draw[|-|] (hbot)--(htop);
\path (hlabel) node[left] {$h$}; %Modify height label here

\coordinate (center) at ($(c.before top)!0.5!(c.after top)$);
\filldraw (center) circle (1pt);

\coordinate (rlabel) at ($(center) !0.5!(c.after top)$);
\coordinate (rtop) at ($(center)!-1*.1!(c.after top)$);

\coordinate (rend) at ($(c.mid east)!0.5!(c.after top)$);
\draw[-, shorten >=-10] (center) -- (rend);
\path (rend) node[outer sep = 5pt, left] {$r$};
\end{tikzpicture}

\bigskip

\begin{tikzpicture}[scale=1]
\node [draw, cylinder, shape aspect=6, rotate=90, cylinder uses custom fill, cylinder 
body fill=lightgray!20, minimum height=4cm, minimum width=4cm] (c1) at (0,0){};

\coordinate(htop) at ($(c1.after top)!-1*.1!(c1.before top)$);
\coordinate(hbot) at ($(c1.before bottom)!-1*.1!(c1.after bottom)$);
\coordinate(hlabel) at ($(htop)!.5!(hbot)$);
\draw[|-|] (hbot)--(htop);
\path (hlabel) node[right, outer sep = 2pt] {$h$};

\node [draw, cylinder, shape aspect=5, rotate=90, minimum height=3.9cm, minimum 
width=3cm] (c) {};

\coordinate (center) at ($(c.before top)!0.5!(c.after top)$);
\filldraw (center) circle (1pt);

\coordinate (rlabel) at ($(center) !0.5!(c.after top)$);
\coordinate (rtop) at ($(center)!-1*.1!(c.after top)$);

\coordinate (rend) at ($(c.mid east)!0.5!(c.after top)$);
\draw[-, shorten >=-10] (center) -- (rend);
\path (rend) node[outer sep = 5pt, left] {$r$};
\end{tikzpicture}

\end{document}

Best Answer

In Metapost, you can shade an annulus by filling the outer circle with the shade and then filling the inner circle with the background. Here's an attempt at your figure, which might give you a starting point.

enter image description here

prologues := 3;
outputtemplate := "%j%c.eps";

beginfig(1);

path c, d, r, h; 

p = 89; q = 34;
c = fullcircle xscaled p yscaled q;
d = c scaled 1.4;

fill d withcolor .9 white;
fill c withcolor white;

forsuffixes $=c,d:
  draw $; 
  draw point 4 of $ -- subpath (4,8) of $ shifted (0,-p) -- point 0 of $;
  draw subpath (0,4) of $ shifted (0,-p) dashed withdots scaled .4;
endfor

r = origin -- point 1 of c;
draw r; label.ulft(btex $r$ etex, point 0.5 of r);
fill c scaled 1/25;

h = (point 0 of d -- point 0 of d shifted (0,-p)) shifted 20 right;
ahangle := 180; ahlength := 3;
drawdblarrow h; label.rt(btex $h$ etex, point 0.5 of h);

endfig;
end.

Related Solutions

[Tex/LaTex] Top-align text in a TikZ node of given size for single- and multiline case

You could work around this by using two nodes instead of one: The first contains just the text, the second uses the fit library to draw a rectangle of a specified minimum height around the text.

I've written a style called add rectangle that takes an optional height and uses the append after command style to add a second node directly after the text node.

In order to fill the background, you can use the backgrounds library and place the rectangle on the background layer using the pgfonlayer environment.

\documentclass{scrreprt}

\usepackage{tikz}
\usetikzlibrary{positioning,fit,calc,backgrounds}

\usepackage{varwidth}

\tikzset{
    add rectangle/.style={
        alias=tempname,
        append after command={
            ; \begin{pgfonlayer}{background}
        \node [
            fill=yellow,
                draw=yellow!80!black,
                        fit={(tempname) ($(tempname.north)+(0,-#1)$)},
                        inner sep=0pt] {};
        \end{pgfonlayer} \path
        }
    },
    add rectangle/.default=2cm
}

\begin{document}

\begin{tikzpicture}
\node (left) [
    add rectangle=2cm
] {%
\begin{varwidth}{3cm}%
Short%
\end{varwidth}%
};

\node at (left.north east) [name=middle,anchor=north west,add rectangle=2cm] {%
\begin{varwidth}{3cm}%
Somehow a longer text for testing%
\end{varwidth}%
};

\node at (middle.north east) [anchor=north west,add rectangle=2cm] {%
\begin{varwidth}{3cm}%
Somehow a longer text for testing. This is a really long text that will stretch the box vertically.%
\end{varwidth}%
};
\end{tikzpicture}


\end{document}

[Tex/LaTex] defining a region to fill in a tikz shape

TikZ doesn't allow you to apply the fill and draw commands to separate pieces of a path. The relevant part is in the macro \tikz@finish. On a normal path, the drawing and filling is done by the piece:

  \edef\tikz@temp{\noexpand\pgfusepath{%
    \iftikz@mode@fill fill,\fi%
    \iftikz@mode@draw draw,\fi%
    \iftikz@mode@clip clip,\fi%
    }}%
  \tikz@temp%

In a node shape, the \backgroundpath is the path used at this point. Now you don't want this: you want to be able to specify part of the \backgroundpath as for draw and part for fill. So you have to specify two paths. Neither can actually be in place at the point where TikZ normally draws or fills since neither should have both actions applied. Normally, I'd recommend using the fact that a node shape can have several paths associated to it (\beforebackgroundpath and so forth), but then you get into complications with passing styles to the different parts (in the TQFT package I use this to style the various parts of a cobordism, but there it is reasonable as there are different components. Here you just have one thing and splitting it is less user-friendly.).

So we just need to subvert the normal TikZ mechanism and replace it with our own. This means using the \backgroundpath at definition time rather than leaving it to later. You do this already in the hackgenuspic (and other) shapes. The only bit you don't do is use it conditionally.

At the time that the \backgroundpath is processed, all of TikZ's path options have been processed. So TikZ knows the fill colour, the line width, the draw colour, and so forth. The only bit it doesn't know is whether or not to fill or draw the path. This is only figured out at the finish. (This is reasonable: the definition of the path can depend on the options, but doesn't usually depend on the action to be taken.) Fortunately, it isn't hard to find out what the desired actions are: we simply execute \tikz@mode. This sets a few conditionals, namely \iftikz@mode@fill and \iftikz@mode@draw (there's also \iftikz@mode@clip and a few more - for a truly robust solution we should consider them as well).

And from that, the rest is fairly easy. We execute \tikz@mode and if we need to fill the path, we define and fill the hole, and if we need to draw it, we define and draw the outer part. Given that we're using \tikz@mode a little earlier than usual, I've put it inside a group. I suspect I'm just being overcautious on this, though, as TikZ is fairly careful about not making assumptions.

Here's my code. The shape is based on hackgenuspic (but I renamed it to just genus). It's quite likely that I've missed something - I haven't stress-tested it! Please let me know if it breaks. (If not, it would seem a reasonable addition to the TQFT package - what do you think?)

\documentclass[convert]{standalone}
%\documentclass{article}
\usepackage{tikz, pgf}
\usetikzlibrary{shapes}

\makeatletter

\pgfdeclareshape{genus}{
 \anchor{center}{\pgfpointorigin}
\backgroundpath{
    \begingroup
    \tikz@mode
    \iftikz@mode@fill

         \pgfpathmoveto{\pgfqpoint{-0.78cm}{-.17cm}}
     \pgfpathcurveto %
            {\pgfpoint{-0.35cm}{-.44cm}}
        {\pgfpoint{0.35cm}{-.44cm}}
        {\pgfpoint{.78cm}{-0.17cm}} 
     \pgfpathmoveto{\pgfqpoint{-0.78cm}{-0.17cm}}
     \pgfpathcurveto %
            {\pgfpoint{-0.25cm}{.25cm}}
        {\pgfpoint{.25cm}{.25cm}}
        {\pgfpoint{0.78cm}{-0.17cm}}
        \pgfusepath{fill}
        \fi

        \iftikz@mode@draw
     \pgfpathmoveto{\pgfqpoint{-1cm}{0cm}}
     \pgfpathcurveto %
            {\pgfpoint{-0.5cm}{-.5cm}}
        {\pgfpoint{0.5cm}{-.5cm}}
        {\pgfpoint{1cm}{0cm}}

     \pgfpathmoveto{\pgfqpoint{-0.75cm}{-0.15cm}}
     \pgfpathcurveto %
            {\pgfpoint{-0.25cm}{.25cm}}
        {\pgfpoint{.25cm}{.25cm}}
        {\pgfpoint{0.75cm}{-0.15cm}}
              \pgfusepath{stroke}
        \fi
        \endgroup
    }
    }

    \makeatother

\begin{document}
\begin{tikzpicture}[scale=.5]
\fill[color=black!10] (-6,3) arc (-180:0:2 cm and 1 cm) 
 (-2,3) .. controls +(-60:1) and +(-120:1) .. (2,3)
(2,3)  arc (-180:0:2 cm and 1 cm)
(6,3) .. controls +(-90:2) and +(0:4) .. (0,-10) .. controls +(180:4) and +(-90:2) .. (-6,3);

\node [genus, scale=1, fill=green] at (0,0) {};
\node [genus, draw, scale=1, fill=orange] at (0,-2) {};
\node [genus, draw, ultra thick, scale=1, fill=green] at (0, -4) {};
\node [genus, draw, scale=.7] at (0, -6) {};
\node [genus, draw, dashed, scale=.5, fill=green] at (0, -8) {};


\draw (-4,3) ellipse (2 cm and 1 cm) 
 (-2,3) .. controls +(-60:1) and +(-120:1) .. (2,3)
(4,3)  ellipse (2cm and 1cm)
(6,3) .. controls +(-90:2) and +(0:4) .. (0,-10) .. controls +(180:4) and +(-90:2) .. (-6,3);
\end{tikzpicture}
\end{document}

with result:

Riemann surface with genus

Best Answer

Related Solutions

[Tex/LaTex] Top-align text in a TikZ node of given size for single- and multiline case

[Tex/LaTex] defining a region to fill in a tikz shape

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