Node-based shape optimization is a promising tool for form finding of thin-walled structures. Especially in the automotive industry, where engineers are faced with increasingly stringent functional requirements for structural components, free-form shape optimization can be a remedy. In the first step, shape optimization is used in the early-stage development of mechanical parts. The resulting shapes are usually reinterpreted and recreated in the realm of CAD (Computer Aided Design). However, interpreting free-form shape-optimized geometries can be challenging. This is mainly due to the typically organic appearance, which is a limitation for the industry. Lately, a focus has been drawn towards creating shape parameterizations that are better suited for the interpretation of engineered-looking features. One method employs a node-based shape parameterization to generate bead-like features, thereby facilitating the interpretation of geometric features. However, manually recreating the optimized geometries with CAD is still very time-consuming and costly. Automatic CAD reconstruction can be a remedy. In fact, the method for generating beading patterns is based on the explicit regularization technique called Vertex Morphing. A special case, in which linear filter and shape functions are employed, generates bi-cubic B-Spline surfaces. This enables the generation of CAD-quality surfaces, although we are not operating in the CAD realm. Catmull-Clark subdivision surfaces also generate bi-cubic B-Spline surfaces for regular control polygons. In this work, we present a CAD reconstruction scheme that utilizes the feature curves of the bead pattern generated by the method to create a Catmull-Clark control polygon. This control polygon can represent the engineering features, enabling future changes by engineers.