1.2 Parametric Plots (\draw and \node)

Required package(s): \usepackage{tikz}.

  • The \draw function can handle parametric plot. The common options (inside the brackets) are
    • variable=: the parameter. By default, the parameter is \x.
    • domain=: the domain of the parameter.
    • samples=: the length of a eqidistance sequence that spans the domain.
    • color=: the color of the curve. Default is black.
    • fill=: the color of the enclosed area.
    • Arrow at the end of the curve: ->, ->>, |<->|
    • Line style: dotted, densely dotted, loosely dotted, dashed, etc. Default is solid.
    • Line thickness: thick, very thick, ultra thick, thin, etc. More precise control can be achieved with the option width=.
  • The \node function adds a label to the graph.
    • anchor=: the place of the anchor relative to the label. Accepted key words are east, west, north, south, or combinations such as north west.
    • scale=: the size of the text/symbol.
  • Other notable mentions for the example below.
    • sin(\t r): \t is a parameter and r indicates \t is measured in radians.
    • \path behaves exactly as \draw except it hides the curve.
    • Coordinates can be given by cartesian (x, y) or polar form (θ:r). For example, (0, 1) is equivalent to (90:1) in polar coordinates.
    • (90:1) circle (1pt) is a circle centered at (90:1) with a radius 1 pt.
\begin{figure}[htbp]
\begin{tikzpicture}[scale = 1]

% Draw and fill a circle
\draw [variable=\t, domain=0:2*pi, samples=200, thin, color=black] plot({cos(\t r)}, {sin(\t r)});

\draw [->] (-2, 0) -- (2, 0); % Add the x-axis 
\draw [->] (0, -2.2) -- (0, 2.2); % Add the y-axis

\node [anchor=north west, scale=0.5] at (1, 0) {$1$}; % Add tickmark label

\draw [fill=white] (90:1) circle (1pt);  % A empty circle at theta=90 and r=1, with radius 1 pt.
\path [fill=black] (30:1) circle (1pt);  % A filled circle at theta=30 and r=1, with radius 1 pt.
\path [fill=black] (0:{sqrt(3)}) circle (1pt);  
\draw [dashed, domain=-0.5:2, very thin] plot(\x, {1-\x/sqrt(3)});

\end{tikzpicture}
\end{figure}

The \draw command allows multiple parametric curves and points to be joined head to tail.

In the next example, the curve starts at the point (1, 0), goes counterclockwise around a unit circle for 180 degrees, then moves clockwise along a smaller circle for another 180 degrees before finally returns to the point (1, 0).

\begin{figure}[htbp]
\begin{tikzpicture}[scale = 1]
\draw (1,0) 
-- plot[domain=0:pi] ({cos(\x r)}, {sin(\x r)})  
-- plot[domain=pi:0] ({0.3*cos(\x r)}, {0.3*sin(\x r)}) 
-- cycle;
\end{tikzpicture}
\end{figure}