Interactive CAD Reverse Modeling via Variational Curve Approximation

Reconstructing editable CAD models from mesh data remains a fundamental yet challenging problem in reverse engineering. Existing methods often struggle to achieve both geometric accuracy and topological consistency, especially when recovering analytic design intent from complex meshes. We present an interactive CAD reverse modeling framework based on variational curve approximation, which bridges mesh segmentation and parametric reconstruction in a unified manner. Our method extracts surface-aligned cutting curves from segmented regions and refines them through a variational approximation process that encodes primitive attributes and geometric constraints. This enables the automatic recovery of closed loops, constraint relations, and operation parameters, leading to a compact and topologically consistent CAD representation. In addition, a coplanar profile detection and voxel-similarity-based Boolean inference are developed to restore the topological order of the original modeling sequence. Extensive experiments demonstrate that our approach achieves higher geometric fidelity, better structural consistency, and improved automation compared with state-of-the-art techniques. The reconstructed models are watertight, topologically consistent, and readily applicable to downstream CAD design tasks.