Anastasis: Recovering CAD Modeling History from Meshes via Search over Feature Proposals

CAD reverse engineering is essential for recovering editable models from existing designs. In industrial workflows, meshes are widely used as representations for downstream applications such as simulation. Reconstructing the underlying parametric CAD structure from meshes is therefore important when the original editable model is unavailable. Existing approaches tackle this inverse problem from different perspectives. Geometry-driven methods directly fit the observed shape but rely on weak design priors, often yielding feature decompositions inconsistent with the original modeling logic, whereas learned models offer stronger priors for feature alignment but struggle with precise parameter recovery. We present Anastasis, a mesh-to-CAD framework that recursively explains the input geometry by recovering executable parametric features from proposals and searching over their composition into a modeling history. Specifically, a learned proposal model identifies feature-level surface evidence and Boolean roles from the input mesh, which are then converted into executable parametric features by a geometry-based recovery stage that recovers their continuous parameters. Finally, a learned feature prior ranks and filters the recovered candidates, after which combinatorial search selects and orders them into a modeling history, while unresolved geometric residuals are recursively processed by the same procedure. Experiments on public CAD reconstruction benchmarks show that Anastasis achieves state-of-the-art performance with 0.981 IoU in-distribution, generalizes well across datasets, and produces modeling histories that better reflect the underlying design process.