# How make the domain of a 2 variable function figure?

I am writing some notes about 2-variable calculus and I wondering how to reproduces this figure in TikZ.

• Welcome to TeX.SX! The short answer is that, yes, this is possible but I have to warn you that questions of the form "Please draw this for me" that show no effort on the part of OP, often don't get answered. You will get more help if you post some code showing what you have tried and give a minimal working example. A quick search on TeX.SX for drawing functions (with tikz or pstricks) will give you an idea of where to start from. – user30471 Mar 19 '20 at 5:03
• Same kind of diagram here How to make this diagram on Tikz? – AndréC Jul 31 '20 at 15:35

Welcome! Several post of this type already exist, here is one more. One way to draw irregular shapes is to use smooth cycle through a set of coordinates.

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{arrows.meta,bending}
\begin{document}
\begin{tikzpicture}[>=Triangle,
dot/.style={circle,fill=blue!70!black,inner sep=1.3pt}]
\draw[orange,thick,fill=orange!50,xshift=1cm] plot[smooth cycle]
coordinates {(10:0.5) (80:2) (140:2.8) (200:2.5) (250:2.7)   (290:2.2)
(310:1.8)};
\draw[thick,->] (-2,0) -- (3,0) node[below left]{$x$};
\draw[thick,->] (0,-3) -- (0,3) node[below left]{$y$};
\draw[thick,->] (4,-3) -- (4,3) node[below left]{$z$}
node[pos=0.2,dot,label={right:$f(a,b)$}] (fab){}
node[pos=0.8,dot,label={right:$f(x,y)$}] (fxy){};
\draw[thick,blue!70!black,-{Stealth[bend]}]
(0.3,1.2) node[dot,label={right:$(x,y)$}] (xy){}
to[bend left=50] (fxy);
\draw[thick,blue!70!black,-{Stealth[bend]}]
(0.5,-1.2) node[dot,label={right:$(a,b)$}] (ab){}
to[bend right=40] (fab);
\draw (3.9,0) -- (4.1,0) node[right]{$0$}
(0,0) node[below left] {$O$} (-135:1) node{$D$};
\end{tikzpicture}
\end{document}


I add my answer...also just for fun with...Mathcha. If you like to draw :-) ...this is the original picture:

\documentclass[a4paper,12pt]{article}
\usepackage{tikz}
\usepackage{xcolor}
\usepackage{newtxtext,newtxmath}
\begin{document}
\tikzset{every picture/.style={line width=0.75pt}}
\begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1]
\draw    (289.5,251) -- (290.49,28) ;
\draw [shift={(290.5,25)}, rotate = 450.25] [fill={rgb, 255:red, 0; green, 0; blue, 0 }  ][line width=0.08]  [draw opacity=0] (8.93,-4.29) -- (0,0) -- (8.93,4.29) -- cycle    ;

\draw  [color={rgb, 255:red, 245; green, 166; blue, 35 }  ,draw opacity=1 ][fill={rgb, 255:red, 247; green, 212; blue, 116 }  ,fill opacity=1 ][line width=1.5]  (182.5,87) .. controls (202.5,109) and (172.54,114.33) .. (166.5,126) .. controls (160.46,137.67) and (200.5,141) .. (197.5,163) .. controls (194.5,185) and (120.5,203) .. (87.5,182) .. controls (54.5,161) and (63,85.73) .. (87.5,71) .. controls (112,56.27) and (162.5,65) .. (182.5,87) -- cycle ;
\draw    (117.5,210.33) -- (117.5,38) ;
\draw [shift={(117.5,35)}, rotate = 450] [fill={rgb, 255:red, 0; green, 0; blue, 0 }  ][line width=0.08]  [draw opacity=0] (8.93,-4.29) -- (0,0) -- (8.93,4.29) -- cycle    ;
\draw  [color={rgb, 255:red, 60; green, 20; blue, 237 }  ,draw opacity=1 ][fill={rgb, 255:red, 63; green, 13; blue, 210 }  ,fill opacity=1 ] (124,80) .. controls (124,77.79) and (125.79,76) .. (128,76) .. controls (130.21,76) and (132,77.79) .. (132,80) .. controls (132,82.21) and (130.21,84) .. (128,84) .. controls (125.79,84) and (124,82.21) .. (124,80) -- cycle ;
\draw  [color={rgb, 255:red, 60; green, 20; blue, 237 }  ,draw opacity=1 ][fill={rgb, 255:red, 63; green, 13; blue, 210 }  ,fill opacity=1 ] (286,71) .. controls (286,68.79) and (287.79,67) .. (290,67) .. controls (292.21,67) and (294,68.79) .. (294,71) .. controls (294,73.21) and (292.21,75) .. (290,75) .. controls (287.79,75) and (286,73.21) .. (286,71) -- cycle ;
\draw    (278.25,140) -- (301.75,140) ;
\draw  [color={rgb, 255:red, 60; green, 20; blue, 237 }  ,draw opacity=1 ][fill={rgb, 255:red, 63; green, 13; blue, 210 }  ,fill opacity=1 ] (139,165) .. controls (139,162.79) and (140.79,161) .. (143,161) .. controls (145.21,161) and (147,162.79) .. (147,165) .. controls (147,167.21) and (145.21,169) .. (143,169) .. controls (140.79,169) and (139,167.21) .. (139,165) -- cycle ;
\draw [color={rgb, 255:red, 38; green, 7; blue, 211 }  ,draw opacity=1 ]   (128,80) .. controls (167.6,50.3) and (213.57,25.5) .. (283.86,69.64) ;
\draw [shift={(286,71)}, rotate = 212.76] [fill={rgb, 255:red, 38; green, 7; blue, 211 }  ,fill opacity=1 ][line width=0.08]  [draw opacity=0] (8.93,-4.29) -- (0,0) -- (8.93,4.29) -- cycle    ;
\draw  [color={rgb, 255:red, 60; green, 20; blue, 237 }  ,draw opacity=1 ][fill={rgb, 255:red, 63; green, 13; blue, 210 }  ,fill opacity=1 ] (88,111) .. controls (88,108.79) and (89.79,107) .. (92,107) .. controls (94.21,107) and (96,108.79) .. (96,111) .. controls (96,113.21) and (94.21,115) .. (92,115) .. controls (89.79,115) and (88,113.21) .. (88,111) -- cycle ;
\draw  [color={rgb, 255:red, 60; green, 20; blue, 237 }  ,draw opacity=1 ][fill={rgb, 255:red, 63; green, 13; blue, 210 }  ,fill opacity=1 ] (286,196) .. controls (286,193.79) and (287.79,192) .. (290,192) .. controls (292.21,192) and (294,193.79) .. (294,196) .. controls (294,198.21) and (292.21,200) .. (290,200) .. controls (287.79,200) and (286,198.21) .. (286,196) -- cycle ;
\draw  [color={rgb, 255:red, 60; green, 20; blue, 237 }  ,draw opacity=1 ][fill={rgb, 255:red, 63; green, 13; blue, 210 }  ,fill opacity=1 ] (286,111) .. controls (286,108.79) and (287.79,107) .. (290,107) .. controls (292.21,107) and (294,108.79) .. (294,111) .. controls (294,113.21) and (292.21,115) .. (290,115) .. controls (287.79,115) and (286,113.21) .. (286,111) -- cycle ;
\draw [color={rgb, 255:red, 38; green, 7; blue, 211 }  ,draw opacity=1 ]   (88,111) .. controls (163.12,123.14) and (181.32,67.76) .. (284.44,110.35) ;
\draw [shift={(286,111)}, rotate = 202.74] [fill={rgb, 255:red, 38; green, 7; blue, 211 }  ,fill opacity=1 ][line width=0.08]  [draw opacity=0] (8.93,-4.29) -- (0,0) -- (8.93,4.29) -- cycle    ;
\draw    (83.5,139.33) -- (232.7,139.2) ;
\draw [shift={(235.7,139.2)}, rotate = 539.95] [fill={rgb, 255:red, 0; green, 0; blue, 0 }  ][line width=0.08]  [draw opacity=0] (8.93,-4.29) -- (0,0) -- (8.93,4.29) -- cycle    ;
\draw [color={rgb, 255:red, 38; green, 7; blue, 211 }  ,draw opacity=1 ]   (143,165) .. controls (164.68,180.05) and (209.98,240.96) .. (283.76,197.35) ;
\draw [shift={(286,196)}, rotate = 508.4] [fill={rgb, 255:red, 38; green, 7; blue, 211 }  ,fill opacity=1 ][line width=0.08]  [draw opacity=0] (8.93,-4.29) -- (0,0) -- (8.93,4.29) -- cycle    ;

% Text Node
\draw (111,147) node    {$0$};
% Text Node
\draw (91,165) node    {$D$};
% Text Node
\draw (150,88) node    {$(x,y)$};
% Text Node
\draw (310,147) node    {$0$};
% Text Node
\draw (322,69) node    {$f(x,y)$};
% Text Node
\draw (324,191) node    {$f(a,b)$};
% Text Node
\draw (164,160) node    {$(a,b)$};
% Text Node
\draw (106,36.33) node    {$y$};
% Text Node
\draw (306,28.33) node    {$z$};
\end{tikzpicture}

\end{document}


and with some metamorphosis, your figure appears almost similar to the original...😉😉😉...

Excuse me @Zarko and @Schrödinger's cat ...but I like the drawing...😏😏😏😏,

• How interesting. :) – azetina Mar 19 '20 at 13:36
• @azetina So I'm emotional ahahahha...look I'm scarce and you all know it. – Sebastiano Mar 19 '20 at 13:46
• :) Good job at the diagram. – azetina Mar 19 '20 at 13:50
• You guys are awsome – Eduardo Mar 19 '20 at 15:11
• @Eduardo Here we are a great group ("Io sono il più scarso")! Don't forget it! :-) – Sebastiano Mar 19 '20 at 22:36

Compile here: http://asymptote.ualberta.ca/

unitsize(1cm);
path c= (2.8,3)..{(.75,0)}(3.5,2)..{(-1,0)}(3.5,-1.5)..(0,2)..cycle;
path xaxis=(-3,0)--(3,0), yaxis=(0,-3.5)--(0,4);
draw(Label("$x$",Relative(0.99)),xaxis,Arrow);
draw(Label("$y$",Relative(0.99),align=LeftSide),yaxis,Arrow);
filldraw(rotate(-50,(0,3))*c,orange+opacity(.5));
label(Label("$D$",Relative(.5)),rotate(-50,(0,3))*c);
draw(Label("$z$",Relative(0.99),align=LeftSide),shift((5,0))*yaxis,Arrow);
draw((0.3,1.5){dir(80)}..{dir(-40)}relpoint(shift((5,0))*yaxis,.8),Arrow);
draw((-0.8,0.8){dir(-20)}..(1,0.3)..{dir(-10)}relpoint(shift((5,0))*yaxis,.6),Arrow);
draw((0.6,-1.3){dir(-40)}..{dir(20)}relpoint(shift((5,0))*yaxis,.3),Arrow);
dot(Label("$(x,y)$",black),(0.3,1.5),dir(-5),blue);
dot(Label("$(a,b)$",black),(0.6,-1.3),dir(90),blue);
dot((-0.8,0.8),blue);
dot(Label("$f(x,y)$",black),relpoint(shift((5,0))*yaxis,.8),blue);
dot(Label("$f(a,b)$",black),relpoint(shift((5,0))*yaxis,.3),blue);
dot(relpoint(shift((5,0))*yaxis,.6),blue);
draw(Label("$0$",EndPoint),(4.9,0)--(5.1,0));
label("$0$",0,dir(-135));


Just for fun.

To build the colorful set, I used the curve to operation with the show curve controls style from page 646 of the 3.1.5b manual (see below)

# Final result

\documentclass[tikz,border=5mm]{standalone}

\usetikzlibrary{arrows.meta}                                                         \usetikzlibrary {decorations.pathreplacing,shapes.misc}

\tikzset{
show curve controls/.style={
decoration={
show path construction,
curveto code={
\draw [blue, dashed]
(\tikzinputsegmentfirst) -- (\tikzinputsegmentsupporta)
node [at end, cross out, draw, solid, red, inner sep=2pt]{};
\draw [blue, dashed]
(\tikzinputsegmentsupportb) -- (\tikzinputsegmentlast)
node [at start, cross out, draw, solid, red, inner sep=2pt]{};
}
},decorate
}
}
\tikzset{>=Stealth,
every path/.style={very thick},
every node/.style={font=\bf},
point/.style={inner sep=1.3pt,fill,circle}
}
\begin{document}

\begin{tikzpicture}
\begin{scope}% left figure
% set
\draw[draw=red,fill=orange!80!green!20]%[postaction=show curve controls]
(-2.5,0) to[out=-90,in=180,in looseness=1,out looseness=1]
(.5,-2.5) to [out=0,in=-90,in looseness=1,out looseness=.5] (2.8,-1)to[out=90,in=-90,in looseness=1,out looseness=1]
(1.5,.5) to[out=90,in=-90,in looseness=.5,out looseness=.5]
(1.9,1.5)to[out=90,in=0,in looseness=1,out looseness=1]
(.5,2.5)to[out=180,in=90,in looseness=1,out looseness=1]
cycle;
% axis
\node[below left] at(0,0){$0$};
\draw[->] (-3,0)--(3.5,0)node[below left]{$x$};
\draw[->] (0,-3)--(0,3)node[below left]{$y$};
% (x,y)
\node[point,label={right:$(x,y)$}](xy) at (.3,1){};
% (a,b)
\node[point,label={above:$(a,b)$}](ab) at (.5,-1.3){};
% point M
\node[point](M) at (-1,.5){};
\end{scope}

\begin{scope}[xshift=5cm]% right figure
% axis
\draw[->] (0,-3.5)--(0,3.5)node[below left]{$z$};
% central point 0
\node [inner sep=1.5pt,fill,circle,label=right:$0$] at (0,0){};
% f(a,b)
\node [point,label={right:$f(a,b)$}] (fab) at (0,-1){};
% f(x,y)
\node [point,label={right:$f(x,y)$}] (fxy) at (0,2){};
% point M'
\node[point] (M') at (0,.8){};
\end{scope}

% arrows
\draw [->,violet] (xy)to[bend left](fxy);
\draw [->,violet] (ab) to[bend right](fab);
\draw [->,violet] (M) to[out=-20,in=180](M');
\end{tikzpicture}

\end{document}


# "show curve controls" style

\documentclass[tikz,border=5mm]{standalone}

\usetikzlibrary{arrows.meta}                                                         \usetikzlibrary {decorations.pathreplacing,shapes.misc}

\tikzset{
show curve controls/.style={
decoration={
show path construction,
curveto code={
\draw [blue,densely dashed]
(\tikzinputsegmentfirst) -- (\tikzinputsegmentsupporta)
node [at end, cross out, draw, solid, red, inner sep=2pt]{};
\draw [blue,densely dashed]
(\tikzinputsegmentsupportb) -- (\tikzinputsegmentlast)
node [at start, cross out, draw, solid, red, inner sep=2pt]{};
}
},decorate
}
}

\begin{document}

\begin{tikzpicture}
\draw[draw=red,fill=orange!80!green!20][postaction=show curve controls]
(-2.5,0) to[out=-90,in=180,in looseness=1,out looseness=1]
(.5,-2.5) to [out=0,in=-90,in looseness=1,out looseness=.5] (2.8,-1)to[out=90,in=-90,in looseness=1,out looseness=1]
(1.5,.5) to[out=90,in=-90,in looseness=.5,out looseness=.5]
(1.9,1.5)to[out=90,in=0,in looseness=1,out looseness=1]
(.5,2.5)to[out=180,in=90,in looseness=1,out looseness=1]
cycle;

\end{tikzpicture}

\end{document}

• Truly a good work....+1, but the $D$ don't like? :-) – Sebastiano Jul 31 '20 at 19:14
• Indded. People will say that we should leave a bit of work for the person who asked the question – AndréC Jul 31 '20 at 19:36
• Ah, now I have undertsood. – Sebastiano Jul 31 '20 at 21:04