Andersen (1995) surveys research indicating that
the transformation from retina-centered coordinates to head-
or body-centered coordinates can be understood in terms of
fields associated with neurons in area 7a of the posterior
parietal cortex.
When the eye position is fixed, these neurons exhibit an
ordinary receptive field (defined over retinal coordinates)
in their response to a stimulus.
On the other hand, when the position of the stimulus on the
retina is fixed, then these neurons exhibit a response that
varies linearly with eye position; this is described by a
linear gain field, defined over eye position, and has
a characteristic direction.
Specifically, a linear gain field 
is described by a
direction vector 
, which is its gradient,
; thus,
at all positions 
.
Under normal conditions the response of the neuron is a
product of the receptive field and the linear gain field, and
so its response is defined over the four dimensions of
retinal and eye position.
The result is a neuron tuned to particular locations in
head-centered space, but only for certain ranges of eye
position.
Therefore, single neurons cannot encode locations in
head-centered space, but a field of neurons can combine their
responses into a population code for head-centered locations.
The resulting field has a well-defined minimum in
head-centered space, which can represent the destination of a
motion (such as a saccade) and, by means of its gradient, a
path to that destination.
Andersen (1995) also surveys studies of ocular
motion planning in the lateral intraparietal area of the
posterior parietal cortex
(see also Goodman & Andersen 1989).
Microstimulation of neurons create eye movements that can be
described as vector fields (giving the direction and amount
of motion) over head-centered coordinates.
Three kinds of fields 
are typically found:
(1) constant vector fields
( 
for all locations 
),
(2) vector fields of constant direction but decreasing
amplitude
( 
, that is,
the positive part of 
),
and (3) weakly convergent vector fields, which rarely reverse
direction.
On the other hand, in simulation studies, microstimulation of
two or more neurons created strongly convergent motion fields
by vector summation of the individual fields of the
neurons.
The gradient of such s field defines the paths, in head-centered space,
to the location defined by the minimum.