# sketching a polar curve using tikz and orientation counterclockwise

I would like to modify the code below so that

1. Can I indicate the counterclockwise directions with arrow

-- from O to B -- from B to A -- from A to O

Also, 2. Can we indicate theta_1 and theta_2 starting from x-axis to OB and OA as in the picture attached.

1. How can I change the thickness of the curves?

Thanks a bunch for your help.

\documentclass[tikz,border=3.14mm]{standalone}
\makeatletter % https://tex.stackexchange.com/a/127045/121799
\makeatother

\usetikzlibrary{patterns,intersections,backgrounds}
\begin{document}

\begin{tikzpicture}
\draw[latex-latex] (0,4) node[left]{$y$} -- (0,0) coordinate[label=below:$O$](O) -- (5,0) node[below]{$x$};
\draw[save path=\pathA,name path=A](0,0) -- (50:4) coordinate[label=above:$A$](A)
to[out=0,in=130] ++(0.7,-0.5) coordinate (aux)
to[out=-50,in=90] ++(0.7,-0.5) coordinate[label=right:$B$] (B)
-- (B|-O)
--cycle;
\draw[dashed] (A) -- (A-|O) coordinate[label=left:$E$] (E)
(B) -- (B|-O) coordinate[label=below:$C$] (C);
\draw[name path=BF,dashed] (B) -- (B-|O) coordinate[label=left:$F$] (F);
\draw[name path=AD,dashed](A) -- (A|-O) coordinate[label=below:$D$] (D);
\fill[name intersections={of=A and BF,by=H}] (H) coordinate[label=above left:$H$]
circle(1pt);
\draw[name path=BO] (B) -- (O);
\fill[name intersections={of=BO and AD,by={J}}] (J) coordinate[label=below left:$J$]
circle(1pt);
\fill[name intersections={of=BF and AD,by={G}}] (G) coordinate[label=above right:$G$]
circle(1pt);
\draw[latex-] (aux) to[out=50,in=180] ++(0.5,0.5) node[right]{$r=f(\theta)$};
\draw[latex-] (B) to[out=0,in=130] ++(0.3,+0.5) node[right]{$\theta=\theta_1$};
\draw[latex-] (A) to[out=0,in=130] ++(0.3,+0.5) node[right]{$\theta=\theta_2$};

%\begin{scope}
%\clip [use path=\pathA];
%\fill[yellow,opacity=0.2] ([yshift=5pt]A) rectangle (B|-F);
%\end{scope}

\end{tikzpicture}

\end{document}


Using decorantions.markings, arrows.meta and calc libraries, then contour package to avoid text-line crossing, and get the desired result.

RESULT:

MWE:

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage[outline]{contour}
\contourlength{2pt}
\usetikzlibrary{patterns,intersections,backgrounds,arrows.meta,decorations.markings,calc}

\begin{document}
\begin{tikzpicture}[
%Environment config
>={Stealth[inset=0pt,length=5pt]},
%Environment Styles
InLineArrow/.style={
draw,
thick,
postaction={
decorate,
decoration={
markings,
mark=at position #1 with {
\fill(0:3.5pt) -- (120:3.5pt) -- (240:3.5pt);
}
}
}
}
]

\draw[<->]
(0,4) node[left]{$y$}
-- (0,0) coordinate[label=below:$O$](O)
-- (5,0) node[below]{$x$};

\path[save path=\pathA,name path=A] %  Change to path to redraw the lines with certain style.
(0,0)
-- (50:4) coordinate[label=above:$A$](A)
to[out=0,in=130] ++(0.7,-0.5) coordinate (aux)
to[out=-50,in=90] ++(0.7,-0.5) coordinate[label={[inner sep=7pt]right:$B$}] (B)
-- (B|-O)
--cycle;
\draw[dashed]
(A)
-- (A-|O) coordinate[label=left:$E$](E)
(B)
-- (B|-O) coordinate[label=below:$C$] (C);

\draw[name path=BF,dashed]
(B)
-- (B-|O) coordinate[label=left:$F$] (F);
A)
-- (A|-O) coordinate[label=below:$D$] (D);

\fill[name intersections={of=A and BF,by=H}](H)coordinate[label=above left:$H$] circle (1.5pt);
\path[name path=BO] (B) -- (O);%  Change to path to redraw the lines with certain style.
\fill[name intersections={of=BO and AD,by={J}}] (J) coordinate[label=below left:$J$]circle(1.5pt);
\fill[name intersections={of=BF and AD,by={G}}] (G) coordinate[label=above right:$G$]circle(1.5pt);
\draw[<-] (aux) to[out=50,in=180] ++(0.5,0.5) node[right]{$r=f(\theta)$};
\draw[<-] (B) to[out=0,out looseness=1.5,in=130] ++(0.3,+0.5) node[right]{$\theta=\theta_1$};
\draw[<-] (A) to[out=0,out looseness=1.5,in=130] ++(0.3,+0.5) node[right]{$\theta=\theta_2$};

\begin{scope}[on background layer]
\definecolor{Col1}{HTML}{01FDFF}
\definecolor{Col2}{HTML}{FF40FF}
\definecolor{Col3}{HTML}{921AB8}
\draw[-Triangle,Col2,line width=1.2pt]
(0:2)
arc (0:50:2) node [pos=0.85,anchor=south west,color=Col3]{\small $\theta=\theta_2$};
\draw[-Triangle,Col1,line width=1.2pt]
let \p1 = (B), %To access cartesian coordinates x, and y.
\n1 = {atan2(\y1,\x1)} % Get the angle.
in (0:1.5)
arc (0:\n1:1.5)node [pos=0.25,anchor=south west,color=Col3]{\contour{white}{\small $\theta=\theta_1$}}; % Draw the arrow.
\draw[InLineArrow=0.43,blue,line width=1.2pt]
(A)
-- (O);
\draw[InLineArrow=0.8,blue,line width=1.2pt]
(O)
-- (B);
\draw[
InLineArrow=0.25,
blue,
line width=1.2pt,
%line width=0.75pt, % uncoment to get the result as in your example.
%draw=black
]
(B)
to [out=90,in=-50] (aux)
to[out=130,in=0] (A);

\end{scope}
\end{tikzpicture}

\end{document}

• Ok thanks, I trusted since it did not cause any error in my compilation and also I did not remove it because I thought it affected the code of the intersections without checking it, how lazy I am... – J Leon V. Aug 19 '18 at 15:54
• Thanks! I really like the outline trick! (But I might have used bent arrows, yet this might be considered overkill.) – user121799 Aug 19 '18 at 22:54