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Let's take the flag of Germany as an example, because the flag is way quite simple and its waving state can be easily drawn "manually". But I am asking about general flag (the flag of any country/group, even the flag of my team).

Normal flag (1)

documentclass[tikz]{standalone}

usepackage{xcolor}

definecolor{gerbla}{RGB}{0,0,0}

definecolor{gerred}{RGB}{255,0,0}

definecolor{geryel}{RGB}{255,204,0}

begin{document}

begin{tikzpicture}

fill[gerbla] (0,2) rectangle (5,3);

fill[gerred] (0,1) rectangle (5,2);

fill[geryel] (0,0) rectangle (5,1);

end{tikzpicture}

end{document}

Waving flag (2) (the ratio may not be true)

documentclass[tikz]{standalone}

usepackage{xcolor}

definecolor{gerbla}{RGB}{0,0,0}

definecolor{gerred}{RGB}{255,0,0}

definecolor{geryel}{RGB}{255,204,0}

begin{document}

begin{tikzpicture}

fill[gerbla] (0,3) to[out=0,in=180] (4,2) -- (4,1) to[out=180,in=0] (0,2) -- cycle;

fill[gerred] (0,2) to[out=0,in=180] (4,1) -- (4,0) to[out=180,in=0] (0,1) -- cycle;

fill[geryel] (0,1) to[out=0,in=180] (4,0) -- (4,-1) to[out=180,in=0] (0,0) -- cycle;

end{tikzpicture}

end{document}

Advanced waving flag (3)

(unTikZified – image taken from Emojipedia)

Question

How to draw a waving flag? In other word, say I already have a rectangle-shape flag (1), with many patterns and items on it (even with some includegraphics), how can I "wave" (1) to get (2), where

1. The ratio length/width is still correct.


2. The images, patterns, etc. on the flag are waved too, and these items still fit correctly with the overall flag.

Bonus question

If I already have (1) or (2), how can I get shadow effects and light effects like (3)?

The code for the flag of the United States, as requested by @marmot:

documentclass[tikz]{standalone}

usetikzlibrary{shapes}

usepackage{xcolor}

begin{document}

begin{tikzpicture}

definecolor{usblue}{rgb}{.234,.233,.430}

definecolor{usared}{rgb}{.698,.132,.203}

fill[usared] (0,0) rectangle (1.9,1);

foreach i in {1,3,...,11}

    fill[white] (0,i/13) rectangle (1.9,{(i+1)/13});

fill [usblue] (0,6/13) rectangle ({1.9*2/5},1);

foreach i in {1,2,3,4,5,6} {

    foreach j in {1,2,3,4,5} {

        node[star,star points=5,star point ratio=2.25,fill=white,minimum size=0.0616cm,inner sep=0pt] at ({(1.9/15)*i-(1.9/30)},{6/13+(7/130)+(7*(j-1)/65)}) {};

    }

}

foreach i in {1,2,3,4,5} {

    foreach j in {1,2,3,4} {

        node[star,star points=5,star point ratio=2.25,fill=white,minimum size=0.0616cm,inner sep=0pt] at ({(1.9/15)*i},{6/13+(7*j/65)}) {};

    }

}

end{tikzpicture}

end{document}

You can use nonlinear transformations to achieve this effect.

documentclass[tikz,border=3.14mm]{standalone}

usepgfmodule{nonlineartransformations}

definecolor{gerbla}{RGB}{0,0,0}

definecolor{gerred}{RGB}{255,0,0}

definecolor{geryel}{RGB}{255,204,0}

makeatletter

defflagtransformation{%

pgf@xa=pgf@x%

pgf@ya=pgf@y%

%typeout{oldspace x=pgf@xaspace old space y=pgf@ya}%

pgfmathsetmacro{myy}{pgf@ya+7*sin(pgf@xa*3.6)-0.1*pgf@xa}%

%typeout{atspace x=thepgf@xa:space newspace y=myy}%

pgf@y=myy pt}

makeatother

newcommand{GermanFlag}{%

fill[gerbla] (0,2) rectangle (4,3);

fill[gerred] (0,1) rectangle (4,2);

fill[geryel] (0,0) rectangle (4,1);}

begin{document}

begin{tikzpicture}[font=sffamily,scale=1]

begin{scope}[local bounding box=linear]

 GermanFlag

end{scope}

node[anchor=south] (lin) at (linear.north){linear};

begin{scope}[xshift=5cm,local bounding box=nonlinear,transform shape

nonlinear=true]

 pgftransformnonlinear{flagtransformation}

 GermanFlag

 shade[left color=black,right color=black,middle color=white,opacity=0.15]

 (0,0) rectangle (2,3);

 shade[left color=black,right color=black,middle color=white,opacity=0.15]

 (2,0) rectangle (4,3);

end{scope}

node[anchor=south] at (lin.south-|nonlinear.north){nonlinear};

end{tikzpicture}

end{document}

Of course, this works with any flag you have the TikZ code for, including of course your nice US flag.

documentclass[tikz,border=3.14mm]{standalone}

usetikzlibrary{shapes}

usepgfmodule{nonlineartransformations}

definecolor{usblue}{rgb}{.234,.233,.430}

definecolor{usared}{rgb}{.698,.132,.203}

makeatletter

defflagtransformation{%

pgf@xa=pgf@x%

pgf@ya=pgf@y%

%typeout{oldspace x=pgf@xaspace old space y=pgf@ya}%

pgfmathsetmacro{myy}{pgf@ya+7*sin(pgf@xa*3.6)-0.1*pgf@xa}%

%typeout{atspace x=thepgf@xa:space newspace y=myy}%

pgf@y=myy pt}

makeatother

newcommand{USFlag}{%

fill[usared] (0,0) rectangle (1.9,1);

foreach i in {1,3,...,11}

    fill[white] (0,i/13) rectangle (1.9,{(i+1)/13});

fill [usblue] (0,6/13) rectangle ({1.9*2/5},1);

foreach i in {1,2,3,4,5,6} {

    foreach j in {1,2,3,4,5} {

        node[star,star points=5,star point ratio=2.25,fill=white,

        minimum size=0.0616cm,inner sep=0pt] at ({(1.9/15)*i-(1.9/30)},{6/13+(7/130)+(7*(j-1)/65)}) {};

    }

}

foreach i in {1,2,3,4,5} {

    foreach j in {1,2,3,4} {

        node[star,star points=5,star point ratio=2.25,fill=white,minimum size=0.0616cm,inner sep=0pt] at ({(1.9/15)*i},{6/13+(7*j/65)}) {};

    }

}}

begin{document}

begin{tikzpicture}[font=sffamily,scale=2,transform shape]

begin{scope}[local bounding box=linear]

 USFlag

end{scope}

node[anchor=south] (lin) at (linear.north){linear};

begin{scope}[xshift=2.5cm,local bounding box=nonlinear,transform shape

nonlinear=true]

 pgftransformnonlinear{flagtransformation}

 USFlag

 shade[left color=black,right color=black,middle color=white,opacity=0.15]

 (0,0) rectangle (0.95,1);

 shade[left color=black,right color=black,middle color=white,opacity=0.15]

 (0.95,0) rectangle (1.9,1);

end{scope}

node[anchor=south] at (lin.south-|nonlinear.north){nonlinear};

end{tikzpicture}

end{document}

And here is something for Black Mild.

documentclass[tikz,border=3.14mm]{standalone}

usetikzlibrary{shapes}

usepgfmodule{nonlineartransformations}

definecolor{usblue}{rgb}{.234,.233,.430}

definecolor{usared}{rgb}{.698,.132,.203}

makeatletter

defflagtransformation{%

pgf@xa=pgf@x%

pgf@ya=pgf@y%

%typeout{oldspace x=pgf@xaspace old space y=pgf@ya}%

pgfmathsetmacro{myy}{pgf@ya+7*sin(pgf@xa*3.6)-0.1*pgf@xa}%

%typeout{atspace x=thepgf@xa:space newspace y=myy}%

pgf@y=myy pt}

makeatother

newcommand{USFlag}{%

fill[usared] (0,0) rectangle (1.9,1);

foreach i in {1,3,...,11}

    fill[white] (0,i/13) rectangle (1.9,{(i+1)/13});

fill [usblue] (0,6/13) rectangle ({1.9*2/5},1);

foreach i in {1,2,3,4,5,6} {

    foreach j in {1,2,3,4,5} {

        node[star,star points=5,star point ratio=2.25,fill=white,

        minimum size=0.0616cm,inner sep=0pt] at ({(1.9/15)*i-(1.9/30)},{6/13+(7/130)+(7*(j-1)/65)}) {};

    }

}

foreach i in {1,2,3,4,5} {

    foreach j in {1,2,3,4} {

        node[star,star points=5,star point ratio=2.25,fill=white,minimum size=0.0616cm,inner sep=0pt] at ({(1.9/15)*i},{6/13+(7*j/65)}) {};

    }

}}

begin{document}

foreach X in {0,5,...,355}

{begin{tikzpicture}[font=sffamily,scale=2,transform shape]

begin{scope}[xshift=X pt,local bounding box=nonlinear,transform shape

nonlinear=true]

 pgftransformnonlinear{flagtransformation}

 USFlag

 shade[left color=black,right color=black,middle color=white,opacity=0.15]

 (0,0) rectangle (0.95,1);

 shade[left color=black,right color=black,middle color=white,opacity=0.15]

 (0.95,0) rectangle (1.9,1);

end{scope}

end{tikzpicture}}

end{document}

This answer has the codes for many flags, out of which I picked Iceland. (Note that if the flag contains shapes, you need to say transform shape nonlinear=true.) The shading can be added on top.

documentclass[tikz,border=3.14mm]{standalone}

usepgfmodule{nonlineartransformations}

makeatletter

defflagtransformation{%

pgf@xa=pgf@x%

pgf@ya=pgf@y%

%typeout{oldspace x=pgf@xaspace old space y=pgf@ya}%

pgfmathsetmacro{myy}{pgf@ya+7*sin(pgf@xa*3.6)-0.1*pgf@xa}%

%typeout{atspace x=thepgf@xa:space newspace y=myy}%

pgf@y=myy pt}

makeatother

definecolor{SkyBlue}{rgb}{0.00784314,0.32156864,0.61176473}

definecolor{FireRed}{rgb}{0.86274511,0.11764706,0.20784314}

newcommandIcelandFlag{

fill[SkyBlue] (0,0) rectangle (25,18);

fill[white] (7,0) rectangle (11,18);

fill[white] (0,7) rectangle (25,11);

fill[FireRed] (8,0) rectangle (10,18);

fill[FireRed] (0,8) rectangle (25,10);}

begin{document}

begin{tikzpicture}[font=sffamily,scale=0.15]

begin{scope}[local bounding box=linear]

 IcelandFlag

end{scope}

node[anchor=south] (lin) at (linear.north){linear};

begin{scope}[xshift=35cm,local bounding box=nonlinear]

 pgftransformnonlinear{flagtransformation}

 IcelandFlag

 shade[left color=black,right color=black,middle color=white,opacity=0.15]

 (0,0) rectangle (12.5,18);

 shade[left color=black,right color=black,middle color=white,opacity=0.15]

 (12.5,0) rectangle (25,18);

end{scope}

node[anchor=south] at (lin.south-|nonlinear.north){nonlinear};

end{tikzpicture}

end{document}

In order to draw a 3d flag, you may use tikz-3dplot.
With shade you can get something like this.

documentclass[tikz]{standalone}

usepackage{tikz-3dplot} 

definecolor{gerbla}{RGB}{0,0,0}

definecolor{gerred}{RGB}{255,0,0}

definecolor{geryel}{RGB}{255,204,0}

begin{document}

tdplotsetmaincoords{70}{20} 

begin{tikzpicture}[tdplot_main_coords]

% draw[-stealth] (0,0,0) -- (2,0,0) node[pos=1.1]{$x$};

% draw[-stealth] (0,0,0) -- (0,2,0) node[pos=1.1]{$y$};

foreach X [count=Y] in {gerbla,gerred,geryel}

{shade[left color=X,right color=X!70!black,middle color=X!70!white] 

plot[variable=x,domain=0:2] (x,{0.2*sin(x*90)},4-Y)

-- 

plot[variable=x,domain=2:0] (x,{0.2*sin(x*90)},3-Y);

shade[left color=X!70!black,right color=X,middle color=X!70!white] 

plot[variable=x,domain=2:4] (x,{0.2*sin(x*90)},4-Y)

-- 

plot[variable=x,domain=4:2] (x,{0.2*sin(x*90)},3-Y);}

end{tikzpicture}

end{document}