  In this paper, we propose a topology optimization (TO) framework where the
design is parameterized by a set of convex polygons. Extending feature mapping
methods in TO, the representation allows for direct extraction of the geometry.
In addition, the method allows one to impose geometric constraints such as
feature size control directly on the polygons that are otherwise difficult to
impose in density or level set based approaches. The use of polygons provides
for more more varied shapes than simpler primitives like bars, plates, or
circles. The polygons are defined as the feasible set of a collection of
halfspaces. Varying the halfspace's parameters allows for us to obtain diverse
configurations of the polygons. Furthermore, the halfspaces are differentiably
mapped onto a background mesh to allow for analysis and gradient driven
optimization. The proposed framework is illustrated through numerous examples
of 2D structural compliance minimization TO. Some of the key limitations and
future research are also summarized.
