# Drawing "blobs"

I would like to draw diagrams representing sets as blobs using tikz, that is an object having no distinct shape (this is one definition of blob.) It doesn't have to be tikz specifically : any solution is welcome, it just happens to be the only way I am aware of to draw diagrams in LaTeX. Also, I have to be able to fit the drawings in commutative diagrams containing standard arrows etc, which is why I felt compelled to use tikz.

At any rate, I would like to create drawings that look like the one below

How do I create these "generic shapes"?

Here's a drawing more in line with the result I want to achieve.

The bent line in X is supposed to represent the inverse image under the map f of the point drawn in f(X), and the two points on it are the images of the two points on the left under the map alpha.

## 2 Answers

This is a MWE with the Asymptote,

// blobs.asy :
//
size(7cm);

import graph;
import patterns;

import fontsize;
defaultpen(fontsize(9pt));

texpreamble("\usepackage{lmodern}");

pen hatchPen=orange+0.4bp;
pen borderPen=deepblue+1bp;
pen arrPen=red+1bp;
pen areaBG=palegreen;

pair[] dots={
(25,280),
(60,280),
(25,140),
};

pair star=(60,137);

guide[] arrows={(25,265)--(25,160),
(60,265){dir(-90)}..(60,200)..(40,160),
};

guide[] markedArrows={
(150,280)--(200,280),
(150,140)--(200,140),
(360,240)--(360,200),
};

pair[] xArea={
(409,257),
(415,272),
(400,289),
(383,291),
(367,292),
(358,300),
(355,307),
(344,317),
(330,317),
(320,312),
(311,319),
(303,308),
(302,303),
(306,298),
(306,287),
(312,277),
(319,269),
(330,267),
(346,260),
(366,259),
};

pair[] xAreaInside={
(341,272),
(332,282),
(333,301),
(339,312),
(385,270),
};

pair[] yArea={
(379,35),
(398,36),
(422,39),
(453,52),
(468,63),
(484,86),
(478,107),
(453,110),
(426,111),
(393,129),
(361,149),
(349,157),
(335,157),
(323,173),
(303,173),
(283,153),
(267,134),
(266,113),
(280,100),
(297,93),
(313,82),
(329,64),
(341,45),
};

pair[] smallShArea={
(400,41),
(403,46),
(399,51),
(406,58),
(408,66),
(398,63),
(387,59),
(380,57),
(369,62),
(360,57),
(366,48),
(376,46),
(384,48),
};

pair[] bigShArea={
(380,74),
(390,83),
(396,99),
(389,111),
(376,115),
(358,123),
(340,130),
(326,144),
(307,151),
(295,146),
(295,140),
(299,129),
(304,119),
(321,116),
(334,107),
(348,87),
};

pair[] yAreaInside={
(315,136),
(370,97),
(436,85),
(460,82),
};

dot(dots,UnFill);

draw(arrows[0],arrPen,Arrow(HookHead,size=4));
draw(arrows[1],arrPen,Arrow(HookHead,size=4));

for(int i=0;i<markedArrows.length;++i){
draw(markedArrows[i],arrPen,Arrow(HookHead,size=4));
}

filldraw(graph(xArea,operator..)..cycle,areaBG,borderPen);
draw(graph(xAreaInside[0:4],operator..),borderPen);

dot(xAreaInside[1:3],UnFill);
label("$X$",xAreaInside[4]);

filldraw(graph(yArea,operator..)..cycle,areaBG,borderPen);

guide gsmallShArea=graph(smallShArea,operator..)..cycle;
guide gbigShArea=graph(bigShArea,operator..)..cycle;

add("hatch",hatch(1mm,hatchPen));
fill(gsmallShArea,pattern("hatch"));
fill(gbigShArea,pattern("hatch"));

draw(gsmallShArea,borderPen);
draw(gbigShArea,borderPen);

dot(yAreaInside[0],UnFill);
label("$f(X)$",yAreaInside[1]);
label("*",yAreaInside[2]);
label("Y",yAreaInside[3]);

label("$\alpha$",markedArrows[0],N);
label("$\beta$",markedArrows[1],N);
label("$f$",markedArrows[2],E);

label("*",star);


To get a standalone blobs.pdf, run asy -f pdf blobs.asy, it will automatically run pdflatex to typeset the labels.

• This is absolutely stunning! Please tell me, how did you produce all the coordinates? Nov 16, 2013 at 2:42
• Also, can the same be done in tikz? Nov 16, 2013 at 2:48
• This is my first time using asymptote, do I have to add a preamble to what you wrote? I'm sorry to ask such a basic question, but I have no idea what an asy file looks like :( Nov 16, 2013 at 3:34
• Forget about the asy question, I got it to work. But please tell me how you produced all of those coordinates! Nov 16, 2013 at 4:07
• @Olivier Bégassat: You can use any digitizer to get coordinates from the sketch, for example plotdigitizer. Nov 16, 2013 at 5:45

This should get you started. You can draw blobs using tikz and the hobby library.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\begin{document}

\begin{tikzpicture}
%% Blob
\path[draw,use Hobby shortcut,closed=true]
(0,0) .. (.5,1) .. (1,3) .. (.3,4) .. (-1,2) .. (-1,.5);
\begin{scope}[xshift=4cm]
\draw (0,0) to [quick curve through={(0,0) (.5,1) .. (1,3) .. (.3,4) .. (-1,2)}] (0,0) ;
\end{scope}
%% Curvy line using hobby
\path[draw,-stealth,use Hobby shortcut,closed=false]
(-1.5,0) .. (-2.2,-2.2) .. (-2.8,-3);
\draw[xshift=-.5cm,-stealth] (-1.5,0) to [quick curve through={(-2.2,-2.2)}] (-2.8,-3) ;
%% Cury line without hobby
\path[draw,xshift=.5cm]
(-1.5,0) edge[out=-95,in=45,-stealth] (-2.8,-3);
\path[draw,xshift=1cm,-stealth]
(-1.5,0) to[out=-95,in=45] (-2.8,-3);
\end{tikzpicture}
\end{document}


• Thanks! The one on the left looks very nice. Can I use the same command without the closed=true to draw a generic curvy line? Nov 16, 2013 at 0:06
• Great! I don't know how to install the hobby package though. I don't understand the instructions given here at all, could you please help? Nov 16, 2013 at 0:46
• I'm not sure, I'm using TeXmaker, so I guess the distribution is MikTeX? I use a computer at my university, it runs Linux Mint. Is the package manager something I can acess from the TeXmaker interface? Nov 16, 2013 at 0:51
• @OlivierBégassat Texmaker is only an editor. May be this question: How do I update my TeX distribution? is useful
– user11232
Nov 16, 2013 at 0:53
• Thanks, how can I find out which distribution I'm using? Nov 16, 2013 at 0:55