How can I draw a water lily in LaTeX?

Question

I wonder, can anyone draw a picture like this?

I tried, but I'm at the very beginning... There should be four semicircles and one full circle. I've managed to draw only two of them so far. Here's my code:

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{shapes,backgrounds}
\newcommand\radius{3}
\newcommand\y{\sqrt{3*\radius^2 /4}}

\begin{document}
\pagestyle{empty}
\def\firstcircle{(0,0) circle (\radius)}
\def\secondcircle{(3,0) circle (\radius)}
\def\thirdcircle{({\radius , \y}) circle (\radius)}
%\def\fourthcircle{(3,0) circle (3cm)}
%\def\fifthcircle{(3,0) circle (3cm)}
\begin{tikzpicture}
    \draw \firstcircle;
    \draw \secondcircle;
%    \draw \thirdcircle;

\end{tikzpicture}
\end{document}

Why wouldn't the third circle draw?

Answer 1

Are you looking for this 5-petal "water-lily" ?

% a 5-petal rose (or "water-lily" if you like ^^)
\documentclass[tikz,border=3mm]{standalone}
\begin{document}
\begin{tikzpicture}
\def\R{3}   
\draw (0,0) circle(\R); 
\draw[smooth,magenta] plot[domain=0:36*5,samples=200] (\x:{\R*cos(5*\x)});
\end{tikzpicture}
\end{document}

I update the Asymptote version of @Jairo

//http://asymptote.ualberta.ca/
unitsize(3cm);
draw(unitcircle);
path petal=(1,0) .. (0,0) .. dir(144);
for(int i=1; i<=5; ++i) {draw(rotate(72*i+30)*petal,red);}

Answer 2

You can use \clip to cut away the outside parts, and use polar coordinates.

\documentclass[tikz,border=3mm]{standalone}
\begin{document}
\begin{tikzpicture}[declare function={R=3;alpha=-20;},thick]
 \draw circle[radius=R]; 
 \clip circle[radius=R]; 
 \draw foreach \X in {0,...,6}
 {(alpha+60*\X:R) circle[radius=R]};
\end{tikzpicture}
\end{document}

Answer 3

Using LuaTeX, it is easy to generate some more generic results.

\documentclass{article}
\usepackage{tikz}
\usepackage{luacode}

\begin{document}

\tikzset{
  arcstyle/.style={
    thick
  }
}

\begin{luacode*}
one_degree = math.pi / 180

function get_inscribed_point(radius, n_poly, index, rotation)
  local ang = (360.0 / n_poly * index + rotation) * one_degree
  local x = radius * math.cos(ang)
  local y = radius * math.sin(ang)
  return {x,y}
end


function get_arc_info(p1, p2, p3)
  local xa, ya = table.unpack(p1)
  local xb, yb = table.unpack(p2)
  local xc, yc = table.unpack(p3)
  
  local coef1 = xb*xb - xc*xc + yb*yb - yc*yc
  local coef2 = xa*xa - xb*xb + ya*ya - yb*yb
  local coef3 = 2.0 * ((xa-xb)*(yb-yc)-(xb-xc)*(ya-yb))
  
  -- calculate center
  local center_x = (-(ya-yb)*coef1+(yb-yc)*coef2)/coef3
  local center_y = ((xa-xb)*coef1-(xb-xc)*coef2)/coef3
  
  -- calculate radius
  local radius = math.sqrt(math.pow(xa-center_x, 2)+math.pow(ya-center_y, 2))
  
  -- calculate arc angle range
  local arc_ang1 = math.asin((0.5*math.sqrt(math.pow(xb-xa,2)+math.pow(yb-ya,2))/radius))
  local arc_ang2 = math.asin((0.5*math.sqrt(math.pow(xc-xb,2)+math.pow(yc-yb,2))/radius))
  local arc_angle = (arc_ang1 + arc_ang2) * 2.0
  
  -- find out if (xc,yc) or (xa,ya) has the smallest angle
  -- make sure xc has the smallest angle (if not, swap two points)
  local ang_a = math.atan2(ya-center_y,xa-center_x)
  local ang_c = math.atan2(yc-center_y,xc-center_x)
  if ang_a < ang_c then
    ang_a = ang_a + 2 * math.pi
  end
  
  -- determine start angle
  local start_angle =ang_c
  local end_angle = ang_a
  
  -- return results
  return {
    ["center_x"] = center_x,
    ["center_y"] = center_y,
    ["radius"] = radius,
    ["start_angle"] = start_angle / one_degree,
    ["end_angle"] = end_angle / one_degree,
    ["arc_start_x"] = xc,
    ["arc_start_y"] = yc
  }
end

function draw_arc(p1, p2, p3)
    local arc = get_arc_info(p1, p2, p3)
      
    tex.print(string.format([[\draw[arcstyle] (%f cm, %f cm) arc (%f:%f:%f cm);]],
      arc["arc_start_x"],
      arc["arc_start_y"],
      arc["start_angle"],
      arc["end_angle"],
      arc["radius"]))
end

function draw_lily(radius, n_poly, offset, rotation)
  for i=1,n_poly do
    local ind1 = i - 1
    local ind2 = (i+offset - 1)%n_poly
    local p1 = get_inscribed_point(radius, n_poly, ind1, rotation)
    local p2 = {0.0,0.0}
    local p3 = get_inscribed_point(radius, n_poly, ind2, rotation)
    draw_arc(p1, p2, p3)
  end
end

\end{luacode*}


\begin{tikzpicture}
\draw (0,0) circle (2cm);
\directlua{
  draw_lily(2.0, 6, 2, 0.0)
}
\end{tikzpicture}
\begin{tikzpicture}
\draw (0,0) circle (2cm);
\directlua{
  draw_lily(2.0, 6, 2, 15.0)
}
\end{tikzpicture}
\begin{tikzpicture}
\draw (0,0) circle (2cm);
\directlua{
  draw_lily(2.0, 8, 2, 15.0)
}
\end{tikzpicture}
\begin{tikzpicture}
\draw (0,0) circle (2cm);
\directlua{
  draw_lily(2.0, 12, 2, 15.0)
}
\end{tikzpicture}
\begin{tikzpicture}
\draw (0,0) circle (2cm);
\directlua{
  draw_lily(2.0, 12, 3, 15.0)
}
\end{tikzpicture}
\begin{tikzpicture}
\draw (0,0) circle (2cm);
\directlua{
  draw_lily(2.0, 12, 4, 15.0)
}
\end{tikzpicture}
\begin{tikzpicture}
\draw (0,0) circle (2cm);
\directlua{
  draw_lily(2.0, 36, 2, 15.0)
}
\end{tikzpicture}

\end{document}

Answer 4

Another pstricks solution, with pst-eucl, which has commands to draw regular polygons and the circumscribed circle of a triangle:

\documentclass[svgnames]{standalone}
\usepackage{pst-eucl}

\begin{document}

\begin{pspicture}(-2.2,-2.2)(1.6,2.2)
\SpecialCoor
\psset{PointSymbol=none, PointName=none}
\pstGeonode(0,0){O}(2;40){A}
\pstRegularPolygonOA{O}{A}{5}{B, C, D, E}
\psclip{\pscircle[linecolor=PaleVioletRed](O){2}}%
\foreach \b/\e/\c in {A/D/H, B/E/I, C/A/J, D/B/K, E/C/L}{\pstCircleABC[linecolor=LightPink]{O}{\b}{\e}{\c}}
 \endpsclip
\end{pspicture}
\end{document}
 

Answer 5

An extra light pure LaTeX solution (``Small is beautiful''):

\documentclass {article}
\usepackage{pict2e}
\usepackage{comment}
\begin{document}

\unitlength=5cm
\begin{picture}(2,2)(-1,-1)
    
\begin{comment}
; Elisp code to generate the repetitive LaTeX code for petals.
; only if you are an Emacs user. C-x C-e to evaluate.
(dolist (i (number-sequence 0 4)
    (insert (format "\n\n\\put(0,0){\\circle{%.3f}}" (* 4 (cos (* 2 (/ float-pi 5)))))))
(let* 
   ((angle-d (- (* (+ i 4) 72) 90))
    (angle-r (* angle-d(/ float-pi 180))))
 (insert 
  (format "\n\\put(%.3f,%.3f){\\arc[%d,%d]{1}}"
         (cos angle-r)
         (sin angle-r)
         (-(* i 72)18) 
         (+(* i 72)54)))))
\end{comment}
  \put(-0.951,-0.309){\arc[-18,54]{1}}
  \put(-0.000,-1.000){\arc[54,126]{1}}
  \put(0.951,-0.309){\arc[126,198]{1}}
  \put(0.588,0.809){\arc[198,270]{1}}
  \put(-0.588,0.809){\arc[270,342]{1}}

  \put(0,0){\circle{1.236}}
 \end{picture}
\end{document} 

A more sophisticated solution using the xpicture package :

     \documentclass{article}
     \usepackage{xpicture}
     \usepackage{multido}
    
    \begin{document}
    
    
\newcommand{\xrosace}[1]{%
        \polarreference\degreesangles%
        \newcommand{\Depart}{\ifodd#1-90\else0\fi}%
        \DIVIDE{360}{#1}{\Rot}  %
        \DIVIDE{\Rot}{2}{\DemRot}%
        \ifodd#1\SUBTRACT{90}{\DemRot}{\Orig}%
        \else\SUBTRACT{180}{\Rot}{\Orig}%
        \fi
        \ifodd#1\ADD{\Orig}{\Rot}{\Extr}%
        \else\ADD{180}{\Rot}{\Extr}%
        \fi
        \DIVIDE{\Rot}{4}{\QrtRot}%
        \ifodd#1\DEGREESSIN{\QrtRot}{\Drayon}%
        \else\DEGREESSIN{\DemRot}{\Drayon}%
        \fi
        \MULTIPLY{2}{\Drayon}{\rayon}%
        \DIVIDE{1}{\rayon}{\Irayon}%
        \Circle{1}%
        \multido{\rangle=\Depart+\Rot,%
                \rorig=\Orig+\Rot,%
                \rextr=\Extr+\Rot}{#1}%
        {\Put(\Irayon,\rangle){\circularArc{\Irayon}{\rorig}{\rextr}}}
}% fin xrosace

    
    
    \unitlength=2cm
    
    \begin{xpicture}(9,4)(-3,-1)
    
            \Put(-4, 0){\xrosace{3}}
            \Put(-2, 0){\xrosace{4}}
            \Put( 0, 0){\xrosace{5}}
            \Put( 2, 0){\xrosace{6}}
            \Put( 4, 0){\xrosace{7}}
            \Put(-4,-2){\xrosace{8}}
            \Put(-2,-2){\xrosace{9}}
            \Put( 0,-2){\xrosace{10}}
            \Put( 2,-2){\xrosace{11}}
            \Put( 4,-2){\xrosace{12}}
    
    \end{xpicture}
    
    \end{document}

Answer 6

Is a Metapost alternative allowed?

\documentclass{standalone}
\usepackage[shellescape,latex]{gmp}
\begin{document}
\begin{mpost}[name=lily]
numeric unit;
unit := 2cm;
path Circle; Circle := (fullcircle shifted -center fullcircle) scaled (2*unit);
path Form; Form := (unit*right) .. origin .. (unit*dir(144));
draw Circle;
for i = 1 upto 5:
    draw Form rotated (72*i+30);
endfor;
\end{mpost}%
\usempost{lily}%
\end{document}

Answer 7

A PSTricks solution only for either fun or comparison purposes.

\documentclass[pstricks,border=3mm]{standalone}
\begin{document}
\pspicture[linecolor=blue,linewidth=2pt](-5,-5)(5,5)
\psclip{\pscircle{5}}
    \foreach \i in {0,60,...,300}{\pscircle(5;\i){5}}
\endpsclip
\endpspicture
\end{document}