PolyTO: Structural Topology Optimization with Convex Polygons
We propose a topology optimization (TO) framework where the structure is parameterized by a set of convex polygons. Extending feature mapping methods in TO, the representation allows for direct extraction of the geometry for further post processing. In addition, the method allows one to impose geometric constraints 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 the expression of diverse set of configurations of the polygons. Furthermore, the halfspaces are differentiably mapped onto a background mesh to allow for analysis and gradient driven optimization.
Each polygon is parameterized by the coordinates of its center, an angular offset and the offset of the half-spaces from the center. The design consists of numerous polygons.
Given a parameterization of a polygon, we first compute the signed distance field (SDF) of each of the half-spaces. Then, we compute the intersection of these fields to obtain the SDF of the polygon. Finally, the SDF is projected to obtain a density field.