[Tex/LaTex] Drawing a curve knowing its parametric equations

tikz-pgf

I want to draw with TikZ a curve, knowing its parametric equations.

The curve is given by:

$\gamma :\left\{
\begin{array}{c}
x=t, \\
y=t^{2}, \\
z=t^{3},%
\end{array}%
\right. t\in \left[ 0,1\right] .$

Which would be the code for this plotting?

Best Answer

You can do it either TikZ or pgfplots way

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\begin{document}
In TikZ

\begin{tikzpicture}
\draw[domain=0:1,smooth,variable=\t]plot (\t,\t^2,\t^3);
\end{tikzpicture}

In pgfplots

\begin{tikzpicture}
    \begin{axis}[samples y=0]
        \addplot3+[domain=0:1] (x,x^2,x^3);
    \end{axis}
\end{tikzpicture}

\end{document}

The extra option is due to Artificial Line in PGFPlots 3D Parametric Plots?

Related Solutions

[Tex/LaTex] How to draw a parametric 3D curve in tikz

pgfplots is an option:

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}
\begin{document}
\begin{tikzpicture}
\begin{axis}
\addplot3[variable=t,mesh,domain=0:1] (t^2,{ t*(1-t)}, 1-t);
\end{axis}
\end{tikzpicture}
\end{document}

which looks like

With view={<azimuth>}{<elevation>} you can rotate the view to an angle where the features of the curve are easier visible. If you want to help further with depth perception, you can for instance add e.g. support lines:

\documentclass[tikz, border=2mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}

\begin{document}

\begin{tikzpicture}
\begin{axis}
[   view={60}{30},
    enlargelimits=false,
]
    \pgfplotsinvokeforeach{0,0.1,...,1}
    { \draw[gray] (#1*#1,#1-#1*#1,1-#1) -- (#1*#1,#1-#1*#1,0);
    }

    \addplot3[variable=t,mesh,domain=0:1] (t^2,t-t^2,1-t);

    \end{axis}
\end{tikzpicture}

\end{document}

Best Answer

Related Solutions

[Tex/LaTex] How to draw a parametric 3D curve in tikz

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