Relation (4.12) can be rewritten in the form
where
This form allow for the construction of contours of 
in the 
-wave number plane.
A contour of constant is a circle of radius
centered at 
,
. Since the maximum
,
, zero value being for maximum
. A sketch is shown below for
sample .
Consider some sample point P in the wave number
diagram for which 
is the vector wave number.
This phase velocity associated with P has the direction
, however the group velocity has a direction
normal to the contour at P and directed inwards
towards the center of curvature which occurs
at 
on the 
axis.