A key step during industrial design is the passing of design information from computer aided design (CAD) to analysis tools (CAE) and vice versa. Here, one is faced with a severe incompatibility in geometry representation: While CAD is usually based on surface representations, analysis mostly relies on volumetric representations. The forward pass, i.e., converting CAD data to computational meshes, is well understood and established. However, the same does not hold for the inverse direction, i.e., CAD reconstruction of deformed geometries resulting from analysis. This is particularly important for industrial workflows in which the shape optimization of an initial product is outsourced. Such shape optimization is the focus of this work. The few reconstruction methods reported mainly rely on spline fitting, in particular on creating new splines similar to shape reconstruction from 3D imaging. In contrast, this paper studies a novel approach that reuses the CAD data given in the initial design. We show that this concept enables one to shape reconstruct mediocre deformations while preserving the initial notion of features defined during design. Furthermore, reusing the initial CAD representation reduces the shape reconstruction problem to a shape modification problem. We study this unique feature and show that it enables the reconstruction of CAD data from computational meshes by composing each spline in the initial CAD data with a single, global deformation spline. While post-processing is needed for use in current CAD software, most notably, this novel approach enables reconstructing complete CAD models even from defeatured computational meshes.