  Two-scale topology optimization, combined with the design of microstructure
families with a broad range of effective material parameters, is increasingly
widely used in many fabrication applications to achieve a target deformation
behavior for a variety of objects. The main idea of this approach is to
optimize the distribution of material properties in the object partitioned into
relatively coarse cells, and then replace each cell with microstructure
geometry that mimics these material properties. In this paper, we focus on
adapting this approach to complex shapes in situations when preserving the
shape's surface is important. Our approach extends any regular (i.e. defined on
a regular lattice grid) microstructure family to complex shapes, by enriching
it with individually optimized cut-cell tiles adapted to the geometry of the
cut-cell. We propose an automated and robust pipeline based on this approach,
and we show that the performance of the regular microstructure family is only
minimally affected by our extension while allowing its use on 2D and 3D shapes
of high complexity.
