In industrial applications, the outcome of a shape optimization is rarely a final, manufacturable design. Instead, shape optimization typically serves as an initial source of inspiration, after which the geometry is reconstructed and refined in a CAD (Computer-Aided Design) environment.

This CAD reconstruction step is often tedious and costly. Consequently, significant research effort is currently devoted to the development of automated CAD reconstruction methods to accelerate the overall design workflow.

At the Chair of Structural Analysis, we have developed an explicit regularization technique known as Vertex Morphing. In addition to addressing common numerical issues associated with finite element methods and node-based shape optimization, Vertex Morphing produces geometries of CAD quality. When employing the simplest filter function—the hat-function filter—the resulting shapes can be represented as bi-cubic B-spline surfaces. This raises the central question: how can explicit bi-cubic B-spline surface generation be leveraged within an automated CAD reconstruction framework?

Subdivision surfaces, like B-splines, are defined by control polygons that are recursively refined using predefined subdivision schemes, referred to as subdivision masks. In theory, the surface is defined as the limit obtained after an infinite number of subdivision steps, commonly termed the limit surface. In practice, however, only three or four refinement steps are typically sufficient to approximate this limit.

One of the most widely used subdivision schemes, the Catmull–Clark method, yields bi-cubic B-spline surfaces in the limit. The focus of this ongoing research is the reconstruction of shape-optimized geometries generated via Vertex Morphing by means of Catmull–Clark subdivision surface control polygons.