# TikZ-PGF – Drawing Easy Curves in TikZ

tikz-pgf

I find myself needing to draw lots of elegantly curved paths in TikZ. Ideally, I'd just specify a series of points, and TikZ would calculate the extra data itself to draw a nice series of curves passing smoothly through these points, perhaps with an optional "looseness" parameter that I could specify. But the only way I can find to draw nice curves is by explicitly giving control points, or by manually specifying in and out angles.

I can think up a simple algorithm to do this, which would certainly be within TikZ's power to perform: just choose the in and out angles in a simple fashion based on the relative angles between each adjacent pair of line segments.

Is something like this already built-in? Or can someone cook something up that does the job?

Edit: Jake has provided an answer using the plot [smooth] functionality. This is almost perfect! But it can't do what I need, because it doesn't let me specify tangent angles manually where needed, which is especially important at the beginning and end of the curve. I would have thought this would be a natural and straightforward addition to the existing plot [smooth] algorithm: for every coordinate, an optional angle should be able to be specified as an argument, which if supplied is treated as the tangent angle for the curve at that point. And while we're at it, it wouldn't hurt to also allow the tension to be modified along the path.

A minimal extension to the algorithm would just accept two optional parameters, for the curve tangent at the beginning and end.

You can use the \draw plot [smooth] coordinates {<coordinate1> <coordinate2> <coordinate3> ...}; syntax, which uses an algorithm similar to the one you described.

The looseness is controlled by the tension parameter. If you want to close the line, you can use [smooth cycle] instead of smooth:

\documentclass{article}

\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
\draw [gray!50]  (0,0) -- (1,1) -- (3,1) -- (1,0)  -- (2,-1) -- cycle;
\draw [red] plot [smooth cycle] coordinates {(0,0) (1,1) (3,1) (1,0) (2,-1)};

\draw [gray!50, xshift=4cm]  (0,0) -- (1,1) -- (2,-2) -- (3,0);
\draw [cyan, xshift=4cm] plot [smooth, tension=2] coordinates { (0,0) (1,1) (2,-2) (3,0)};
\end{tikzpicture}
\end{document}


The smooth algorithm is quite simple: it sets the support points so that the tangent at each corner is parallel to the line from the previous to the next corner. The distance of the support points to the corner is the same in either direction, and proportional to the distance from the previous corner to the next corner. The tension is used as a multiplier for the support point distance. It can not be changed along the curve, and neither can the starting and finishing angles of the line be specified. The algorithm can be found in pgflibraryplothandlers.code.tex as \pgfplothandlercurveto.

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing,shapes.misc}

\begin{document}
\begin{tikzpicture}
\tikzset{
show curve controls/.style={
decoration={
show path construction,
curveto code={
\draw [blue, dashed]
(\tikzinputsegmentfirst) -- (\tikzinputsegmentsupporta)
node [at end, cross out, draw, solid, red, inner sep=2pt]{};
\draw [blue, dashed]
(\tikzinputsegmentsupportb) -- (\tikzinputsegmentlast)
node [at start, cross out, draw, solid, red, inner sep=2pt]{};
}
}, decorate
}
}

\draw [gray!50]  (0,0) -- (1,1) -- (3,1) -- (1,0)  -- (2,-1) -- cycle;
\draw [show curve controls] plot [smooth cycle] coordinates {(0,0) (1,1) (3,1) (1,0) (2,-1)};
\draw [red] plot [smooth cycle] coordinates {(0,0) (1,1) (3,1) (1,0) (2,-1)};

\draw [gray!50, xshift=4cm]  (0,0) -- (1,1) -- (3,-1) -- (5,1) -- (7,-2);
\draw [cyan, xshift=4cm] plot [smooth, tension=2] coordinates { (0,0) (1,1) (3,-1) (5,1) (7,-2)};
\draw [show curve controls,cyan, xshift=4cm] plot [smooth, tension=2] coordinates { (0,0) (1,1) (3,-1) (5,1) (7,-2)};
\end{tikzpicture}
\end{document}


Here is a slightly modified version of the plothandler, which allows you to specify the first and last support point using the TikZ key first support={<point>} and last support={<point>}, where <point> can be any TikZ coordinate expression, such as(1,2), (1cm,2pt), (A.south west), ([xshift=1cm] A.south west) (thanks to Andrew Stacey's wonderful answer to Extract x, y coordinate of an arbitrary point in TikZ).

By default, the points are assumed to refer to coordinates relative to the first/last point of the path. You can specify that the support points are given as absolute coordinates by using the keys absolute first support, absolute last support, or absolute supports.

 \documentclass{article}

\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing,shapes.misc}

\begin{document}
\begin{tikzpicture}
\tikzset{
show curve controls/.style={
decoration={
show path construction,
curveto code={
\draw [blue, dashed]
(\tikzinputsegmentfirst) -- (\tikzinputsegmentsupporta)
node [at end, cross out, draw, solid, red, inner sep=2pt]{};
\draw [blue, dashed]
(\tikzinputsegmentsupportb) -- (\tikzinputsegmentlast)
node [at start, cross out, draw, solid, red, inner sep=2pt]{};
}
}, decorate
}
}

\makeatletter
\newcommand{\gettikzxy}[3]{%
\tikz@scan@one@point\pgfutil@firstofone#1\relax
\edef#2{\the\pgf@x}%
\edef#3{\the\pgf@y}%
}

\newif\iffirstsupportabsolute
\newif\iflastsupportabsolute

\tikzset{
absolute first support/.is if=firstsupportabsolute,
absolute first support=false,
absolute last support/.is if=lastsupportabsolute,
absolute last support=false,
absolute supports/.style={
absolute first support=#1,
absolute last support=#1
},
first support/.code={
\gettikzxy{#1}{\pgf@plot@firstsupportrelx}{\pgf@plot@firstsupportrely}
},
first support={(0pt,0pt)},
last support/.code={
\gettikzxy{#1}{\pgf@plot@lastsupportrelx}{\pgf@plot@lastsupportrely}
},
last support={(0pt,0pt)}
}

\def\pgf@plot@curveto@handler@initial#1{%
\pgf@process{#1}%
\pgf@xa=\pgf@x%
\pgf@ya=\pgf@y%
\pgf@plot@first@action{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
\xdef\pgf@plot@curveto@first{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
\iffirstsupportabsolute
\pgf@xa=\pgf@plot@firstsupportrelx%
\pgf@ya=\pgf@plot@firstsupportrely%
\else
\fi
\xdef\pgf@plot@curveto@firstsupport{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
\global\let\pgf@plot@curveto@first@support=\pgf@plot@curveto@firstsupport%
\global\let\pgf@plotstreampoint=\pgf@plot@curveto@handler@second%
}

\def\pgf@plot@curveto@handler@finish{%
\ifpgf@plot@started%
\pgf@process{\pgf@plot@curveto@second}
\pgf@xa=\pgf@x%
\pgf@ya=\pgf@y%
\iflastsupportabsolute
\pgf@xa=\pgf@plot@lastsupportrelx%
\pgf@ya=\pgf@plot@lastsupportrely%
\else
\fi
\pgfpathcurveto{\pgf@plot@curveto@first@support}{\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}{\pgf@plot@curveto@second}%
\fi%
}
\makeatother

\coordinate (A) at (2,-1);

\draw [gray!50]  (-1,-0.5) -- (1.5,1) -- (3,0);
\draw [
cyan,
postaction=show curve controls
] plot [
smooth, tension=2,
absolute supports,
first support={(A)},
last support={(A)}] coordinates { (-1,-0.5) (1.5,1) (3,0)};

\draw [
yshift=-3cm,
magenta,
postaction=show curve controls
] plot [
smooth, tension=2,
first support={(-0.5cm,1cm)},
last support={(0.5cm,1cm)}] coordinates { (-1,-0.5) (1.5,1) (3,0)};

\end{tikzpicture}
\end{document}