Graphics, Figures & Tables ⇒ tikZ | Quadratic Bézier Curves

[x42bn6]

I love TikZ but does anyone know how to do a quadratic Bézier curve on it?

TikZ only provides support for cubic Bézier curves, which is one too much for me.

Failing that, does anyone know how to convert a cubic Bézier curve into a quadratic one?

[localghost]

If you really need a quadratic Bézier curve on the points P0, P1 and P2, then a process called »degree elevation« yields the cubic control points (Q0, Q1, Q2 and Q3) as follows:

Code: Select all

Q0 = P0
Q1 = 1/3 P0 + 2/3 P1
Q2 = 2/3 P1 + 1/3 P2
Q3 = P2

A simple example looks like this.

Code: Select all

\documentclass{minimal}
\usepackage{tikz}

\begin{document}
  \begin{tikzpicture}
    \draw[help lines] (0,0) grid (3,1);
    \filldraw [gray] (0,0) circle (2pt)
                     (2,1) circle (2pt)
                     (3,0) circle (2pt);
    \draw (0,0) .. controls (1.334,0.667) and (2.334,0.667) .. (3,0);
  \end{tikzpicture}
\end{document}

This reduces the Bézier curve from cubic to quadratic.


Best regards and welcome to the board
Thorsten¹

[Atrix256]

Another way to do this is to plot the function of a quadratic bezier curve in Bernstein form.

a 1d explicit quadratic bezier function looks like this:

y = A*(1-x)^2 + B*2x(1-x) + C*x^2

I just did that to get a 1d bezier curve diagram for my paper. Not sure if tikZ can plot multi-dimensional functions or not where f(x,y)=0, but if so, you just have one of those explicit 1d bezier curves per axis, where A,B,C are the control points for that specific axis.

If it helps, here's how to draw a 1d quadratic bezier curve with control points 0,1,0

\draw[scale=1,domain=0:1,smooth,variable=\x,blue] plot ({\x},{2*\x-2*\x*\x});