Hfrhyu

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
usepackagexcolor
definecolorgerblaRGB0,0,0
definecolorgerredRGB255,0,0
definecolorgeryelRGB255,204,0
begindocument
begintikzpicture
fill[gerbla] (0,2) rectangle (5,3);
fill[gerred] (0,1) rectangle (5,2);
fill[geryel] (0,0) rectangle (5,1);
endtikzpicture
enddocument

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

documentclass[tikz]standalone
usepackagexcolor
definecolorgerblaRGB0,0,0
definecolorgerredRGB255,0,0
definecolorgeryelRGB255,204,0
begindocument
begintikzpicture
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;
endtikzpicture
enddocument

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
usetikzlibraryshapes
usepackagexcolor
begindocument
begintikzpicture
definecolorusbluergb.234,.233,.430
definecolorusaredrgb.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)) ;
 

endtikzpicture
enddocument

You can use nonlinear transformations to achieve this effect.

documentclass[tikz,border=3.14mm]standalone
usepgfmodulenonlineartransformations
definecolorgerblaRGB0,0,0
definecolorgerredRGB255,0,0
definecolorgeryelRGB255,204,0
makeatletter
defflagtransformation%
pgf@xa=pgf@x%
pgf@ya=pgf@y%
%typeoutoldspace x=pgf@xaspace old space y=pgf@ya%
pgfmathsetmacromyypgf@ya+7*sin(pgf@xa*3.6)-0.1*pgf@xa%
%typeoutatspace x=thepgf@xa:space newspace y=myy%
pgf@y=myy pt
makeatother
newcommandGermanFlag%
fill[gerbla] (0,2) rectangle (4,3);
fill[gerred] (0,1) rectangle (4,2);
fill[geryel] (0,0) rectangle (4,1);
begindocument
begintikzpicture[font=sffamily,scale=1]
beginscope[local bounding box=linear]
 GermanFlag
endscope
node[anchor=south] (lin) at (linear.north)linear;
beginscope[xshift=5cm,local bounding box=nonlinear,transform shape
nonlinear=true]
 pgftransformnonlinearflagtransformation
 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);
endscope
node[anchor=south] at (lin.south-|nonlinear.north)nonlinear;
endtikzpicture
enddocument

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
usetikzlibraryshapes
usepgfmodulenonlineartransformations
definecolorusbluergb.234,.233,.430
definecolorusaredrgb.698,.132,.203
makeatletter
defflagtransformation%
pgf@xa=pgf@x%
pgf@ya=pgf@y%
%typeoutoldspace x=pgf@xaspace old space y=pgf@ya%
pgfmathsetmacromyypgf@ya+7*sin(pgf@xa*3.6)-0.1*pgf@xa%
%typeoutatspace x=thepgf@xa:space newspace y=myy%
pgf@y=myy pt
makeatother
newcommandUSFlag%
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)) ;
 

begindocument
begintikzpicture[font=sffamily,scale=2,transform shape]
beginscope[local bounding box=linear]
 USFlag
endscope
node[anchor=south] (lin) at (linear.north)linear;
beginscope[xshift=2.5cm,local bounding box=nonlinear,transform shape
nonlinear=true]
 pgftransformnonlinearflagtransformation
 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);
endscope
node[anchor=south] at (lin.south-|nonlinear.north)nonlinear;
endtikzpicture
enddocument

And here is something for Black Mild.

documentclass[tikz,border=3.14mm]standalone
usetikzlibraryshapes
usepgfmodulenonlineartransformations
definecolorusbluergb.234,.233,.430
definecolorusaredrgb.698,.132,.203
makeatletter
defflagtransformation%
pgf@xa=pgf@x%
pgf@ya=pgf@y%
%typeoutoldspace x=pgf@xaspace old space y=pgf@ya%
pgfmathsetmacromyypgf@ya+7*sin(pgf@xa*3.6)-0.1*pgf@xa%
%typeoutatspace x=thepgf@xa:space newspace y=myy%
pgf@y=myy pt
tikzdeclarecoordinatesystemflag% https://tex.stackexchange.com/a/434247/121799
 tikz@scan@one@pointrelax(#1)
 flagtransformation

makeatother
newcommandUSFlag%
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)) ;
 

begindocument
foreach X in 0,5,...,95
begintikzpicture[font=sffamily,scale=2,transform shape]
beginscope[xshift=X pt,
local bounding box=nonlinear,transform shape
nonlinear=true]
 pgftransformnonlinearflagtransformation
 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); 
 shade[left color=gray,right color=gray!70,middle color=gray!20] 
(0,1.05) rectangle ++ (-0.1,-3);
endscope
endtikzpicture
enddocument

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
usepgfmodulenonlineartransformations
makeatletter
defflagtransformation%
pgf@xa=pgf@x%
pgf@ya=pgf@y%
%typeoutoldspace x=pgf@xaspace old space y=pgf@ya%
pgfmathsetmacromyypgf@ya+7*sin(pgf@xa*3.6)-0.1*pgf@xa%
%typeoutatspace x=thepgf@xa:space newspace y=myy%
pgf@y=myy pt
makeatother
definecolorSkyBluergb0.00784314,0.32156864,0.61176473
definecolorFireRedrgb0.86274511,0.11764706,0.20784314
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);
begindocument
begintikzpicture[font=sffamily,scale=0.15]
beginscope[local bounding box=linear]
 IcelandFlag
endscope
node[anchor=south] (lin) at (linear.north)linear;
beginscope[xshift=35cm,local bounding box=nonlinear]
 pgftransformnonlinearflagtransformation
 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);
endscope
node[anchor=south] at (lin.south-|nonlinear.north)nonlinear;
endtikzpicture
enddocument

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

documentclass[tikz]standalone
usepackagetikz-3dplot 
definecolorgerblaRGB0,0,0
definecolorgerredRGB255,0,0
definecolorgeryelRGB255,204,0
begindocument
tdplotsetmaincoords7020 
begintikzpicture[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);
endtikzpicture
enddocument