The central axis line of a wellbore or a pipeline with a position vector $\begin{array}{l}\bf r\end{array}$ at each point of trajectory given as:

(1)	$\begin{array}{l}\displaystyle {\bf r} = {\bf r}(l)= \{ x(l), \, y(l), \, z(l) \}\end{array}$

where

$\begin{array}{l}{\bf r}(l)\end{array}$	position vector of trajectory point with $\begin{array}{l}z(l)\end{array}$ being a ture vertical direction
$\begin{array}{l}l\end{array}$	path length from pipeline intake point $\begin{array}{l}{\bf r}_0\end{array}$
$\begin{array}{l}{\bf r}_0\end{array}$	well or pipeline intake point coordinates (usually $\begin{array}{l}{\bf r}_0 = \{ x_0 = 0, \, y_0 = 0, \, z_0 = 0 \}\end{array}$ )

In practice the trajectory is usually set by Deviation Data.

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See also