  In this paper we present a novel two-scale framework to optimize the
structure and the material distribution of an object given its functional
specifications. Our approach utilizes multi-material microstructures as
low-level building blocks of the object. We start by precomputing the material
property gamut -- the set of bulk material properties that can be achieved with
all material microstructures of a given size. We represent the boundary of this
material property gamut using a level set field. Next, we propose an efficient
and general topology optimization algorithm that simultaneously computes an
optimal object topology and spatially-varying material properties constrained
by the precomputed gamut. Finally, we map the optimal spatially-varying
material properties onto the microstructures with the corresponding properties
in order to generate a high-resolution printable structure. We demonstrate the
efficacy of our framework by designing, optimizing, and fabricating objects in
different material property spaces on the level of a trillion voxels, i.e
several orders of magnitude higher than what can be achieved with current
systems.
