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The central axis line of a well or a wellbore or a  pipeline with a position vector 

LaTeX Math Inline
body\bf r
at each point of of trajectory given as:

LaTeX Math Block
anchor1
alignmentleft
{\bf r} = {\bf r}(l)

where

...

= \{ x(l), \, y(l), \, z(l) \}

where

LaTeX Math Inline
body{\bf r}(l)

space coordinates

with 

LaTeX Math Inline
bodyz

-ccordinate facing down to the Earth Centre

LaTeX Math Inline
body

{\bf r}_0intake pipeline coordinates 

l

path length from pipeline intake point 

LaTeX Math Inline
body

\

{

x_s = 0, \, y_s = 0, \, z_s = 0 \}pipeline length from inflow point 

\bf r}_0

LaTeX Math Inline
body

l = \int_0^l \sqrt{dx^2 + dy^2 + dz^2} = \int_0^l \sqrt{\dot x^2 + \dot y^2 + \dot z^2} dl

{\bf r}_0

well or pipeline intake point coordinates (usually  

LaTeX Math Inline
body

\{

--uriencoded--%7B\bf r%7D_0 = \%7B x_

s

0 = 0, \, y_

s

0 = 0, \, z_

s

0 = 0 \

}

%7D
)


In practice the trajectory is usually set by Deviation Data.

See also

...

Natural Science / Physics / Measuring / Positioning 

[ Deviation Data ] [ Inclination ]  [ Azimuth ]