# Spiral cone

For drawing a spiral cone, we need to find an appropriate parametrization.

This code was written by Gonzalo Medina on TeX.SE. Edit and compile if you like:
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{width=7cm,compat=1.8}
\usetikzlibrary{decorations.markings}
\def\Point{36.9}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
view       = {-25}{-25},
axis lines = middle,
zmax       = 60,
height     = 8cm,
xtick      = \empty,
ytick      = \empty,
ztick      = \empty
]
ytick      = \empty,
yticklabel = \empty,
domain     = 0:14.7*pi,
samples    = 400,
samples y  = 0,
mark       = none,
thick,
red,
]
( {x*sin(0.28*pi*deg(x))},{x*cos(0.28*pi*deg(x)},{x});
mark options = {color=blue},
mark         = *
]
coordinates {({\Point*sin(0.28*pi*deg(\Point))},
{\Point*cos(0.28*pi*deg(\Point)}, {\Point})};
domain    = 0:12*pi,
samples   = 100,
samples y = 0,
mark      = none,
dashed,
]
( {\Point*sin(0.28*pi*deg(\Point))}, {\Point*cos(0.28*pi*deg(\Point)}, {x} );
mark=none,
dashed
]
coordinates {(0,0,0) ({\Point*sin(0.28*pi*deg(\Point))},
{\Point*cos(0.28*pi*deg(\Point)}, {0})};
\draw[
decoration = {
markings,
mark= at position 0.99 with {\arrow{latex}}
},
postaction=decorate
]
(axis cs:0,10,0) arc[start angle=80,end angle=14] (axis cs:14,0,0);
\node at (axis cs:20,0,30) {$P$};
\node at (axis cs:24,0,7) {$z$};
\node [font=\footnotesize] at (axis cs:20,17,0) {$\varrho$};
\node [font=\footnotesize] at (axis cs:6,15,0) {$\varphi$};
\end{axis}
\end{tikzpicture}
\end{document}

\end{document}