Consider a colorSpec object x with type equal to responsivity.material.
The set of all possible material reflectance functions (or transmittance functions)
is convex, closed, and bounded (in any reasonable function space),
and this implies that the set of all possible output responses
from x is also convex, closed, and bounded.
The latter set is called the object-color solid or Rösch Farbkörper for x.
A color on the boundary of the object-color solid is called an optimal color.
The special points W (the response to the perfect reflecting diffuser)
and 0 are on the boundary of this set.
The interior of the line segment of neutrals joining 0 to W is in the interior of the
object-color solid.
It is natural to parameterize this segment from 0 to 1 (from 0 to W).
The solid is symmetrical about the neutral gray midpoint G=W/2.
Now suppose that x has 3 spectra (3 responses)
and consider a color response R not equal to G.
There is a ray based at G and passing through R
that intersects the boundary of the
object-color solid at an optimal color B on the boundary
with Logvinenko coordinates \((\delta,\omega)\).
If these 2 coordinates are combined with \(\alpha\), where
R = \((1-\alpha)\)G + \(\alpha\)B,
it yields the Logvinenko coordinates
\((\alpha,\delta,\omega)\) of R.
These coordinates are also denoted by ADL; see References.
A response is in the object-color solid iff \(\alpha \le 1\).
A response is optimal iff \(\alpha=1\).
The coordinates of 0 are \((\alpha,\delta,\omega)\)=(1,0,0).
The coordinates of W are \((\alpha,\delta,\omega)\)=(1,1,0).
The coordinates of G are undefined.