  This article proposes to integrate two Reeb graphs with the information of
their isosurfaces' inclusion relation. As computing power evolves, there arise
numerical data that have small-scale physics inside larger ones -- for example,
small clouds in a simulation can be contained inside an atmospheric layer,
which is further contained in an enormous hurricane. Extracting such inclusions
between isosurfaces is a challenge for isosurfacing: the user would have to
explore the vast combinations of isosurfaces $(f_1^{-1}(l_1), f_2^{-1}(l_2))$
from scalar fields $f_i: M(n) \to \mathbb{R}$, $i = 1, 2$, where $M$ is an
$n$-dimensional domain manifold and $f_i$ are physical quantities, to find
inclusion of one isosurface within another. For this, we propose the
\textit{Reeb complement}, a topological space that integrates two Reeb graphs
with the inclusion relation. The Reeb complement has a natural partition that
classifies equivalent containment of isosurfaces. This is a handy
characteristic that lets the Reeb complement serve as an overview of the
inclusion relationship in the data. We also propose level-of-detail control of
the inclusions through simplification of the Reeb complement. We demonstrate
that the relationship of two independent scalar fields can be extracted by
taking the product of Reeb graphs (which we call the Reeb product) and by then
subtracting the projection of the Reeb space, which opens up a new possibility
for feature analysis.
