  Users frequently seek to fabricate objects whose outer surfaces consist of
regions with different surface attributes, such as color or material.
Manufacturing such objects in a single piece is often challenging or even
impossible. The alternative is to partition them into single-attribute
volumetric parts that can be fabricated separately and then assembled to form
the target object. Facilitating this approach requires partitioning the input
model into parts that conform to the surface segmentation and that can be moved
apart with no collisions. We propose Surface2Volume, a partition algorithm
capable of producing such assemblable parts, each of which is affiliated with a
single attribute, the outer surface of whose assembly conforms to the input
surface geometry and segmentation. In computing the partition we strictly
enforce conformity with surface segmentation and assemblability, and optimize
for ease of fabrication by minimizing part count, promoting part simplicity,
and simplifying assembly sequencing. We note that computing the desired
partition requires solving for three types of variables: per-part assembly
trajectories, partition topology, i.e. the connectivity of the interface
surfaces separating the different parts, and the geometry, or location, of
these interfaces. We efficiently produce the desired partitions by addressing
one type of variables at a time: first computing the assembly trajectories,
then determining interface topology, and finally computing interface locations
that allow parts assemblability. We algorithmically identify inputs that
necessitate sequential assembly, and partition these inputs gradually by
computing and disassembling a subset of assemblable parts at a time. We
demonstrate our method....
