We call this disambiguation rule Knit High Above, Knit Low Below, and it is illustrated in the series of figures 6 through 9. Our disambiguation rule is similar to and generalizes the bilinear interpolation method of Nelson (See [6] ) to disambiguate Marching Cubes (See [7], [8], [9], and [10]). We multilinearly interpolate the disambiguation value c.
Disambiguation Rule:
In 2 dimensions we bilinearly interpolate the disambiguation value as follows:
For each 4-hit face we
linearly interpolate 
across each edge. Now interpolate the position of the point p,
called the disambiguation point,
such that both the vertical and horizontal lines (with respect to the two coordinate
directions on the face) that pass through this point intersect identical
values on the opposite edges. Interpolate the value 
of this point, called the
disambiguation value, and we
extend the domain of 
to include p (we call this the extended 
).
In 3 dimensions we use trilinear interpolation to determine the maximum
value c at which the diagonally opposite Highs are path connected
through the interior of either cube that shares the face F.
In higher dimensions we similarly use multi-linear
interpolation to choose the maximum value c
for which the Highs are connected through the interior of any hypercube
sharing F. As in 2 dimensions, we interpolate an interior point p with value c.
The interior point p so interpolated is
called the disambiguation point and is associated with the face F.
For specific 
,
if 
with respect to face F, regard
the Lows as adjacent (knit High), else regard the Highs as adjacent (knit Low),
with respect to F.
Note that the path may not actually be through the face F, but since we are concerned with topology, this will not alter our results.
See figure 10 and figure 11 for clarification of the rule in
2 dimensions.
For example the disambiguation point of figure 11 is
,
and the disambiguation value is
.