Accurate 3D shape representation is essential in engineering applications such as design, optimization, and simulation. In practice, engineering workflows require structured, part-aware representations, as objects are inherently designed as assemblies of distinct components. However, most existing methods either model shapes holistically or decompose them without predefined part structures, limiting their applicability in real-world design tasks. We propose PartSDF, a supervised implicit representation framework that explicitly models composite shapes with independent, controllable parts while maintaining shape consistency. Despite its simple single-decoder architecture, PartSDF outperforms both supervised and unsupervised baselines in reconstruction and generation tasks. We further demonstrate its effectiveness as a structured shape prior for engineering applications, enabling precise control over individual components while preserving overall coherence. Code available at https://github.com/cvlab-epfl/PartSDF.

CAD modeling typically involves the use of simple geometric primitives whereas recent advances in deep-learning based 3D surface modeling have opened new shape design avenues. Unfortunately, these advances have not yet been accepted by the CAD community because they cannot be integrated into engineering workflows. To remedy this, we propose a novel approach to effectively combining geometric primitives and free-form surfaces represented by implicit surfaces for accurate modeling that preserves interpretability, enforces consistency, and enables easy manipulation.