Hybrid surface fitting framework using local parametric optimization and adaptive truncated hierarchical refinement

Accurate reconstruction of freeform engineering surfaces from measured point clouds is essential in modern CAD, CAM, CAE and industrial reverse-engineering pipelines. Conventional B-spline fitting often struggles to balance geometric fidelity, parameterization quality and computational efficiency, particularly when input data contain both smooth regions and localized irregularities. Although truncated hierarchical B-splines enable localized refinement, classical hierarchical fitting frequently applies refinement even when errors are predominantly caused by distorted parameterization rather than insufficient geometric resolution. This work presents a hybrid fitting framework that integrates local parametric optimization with adaptive truncated hierarchical refinement to achieve high accuracy while maintaining a compact surface representation. A global least-squares B-spline approximation establishes the baseline geometry, and an error-driven analysis identifies regions requiring improvement. Each region is first corrected through local optimization of parametric values to reduce mapping distortion, while refinement is introduced only when optimization alone provides insufficient error reduction. Truncation confines refinement to the selected region, limiting the recomputation to the associated control points. The framework is evaluated on several engineering geometries and consistently reduces refinement depth and degrees of freedom while achieving accuracy comparable to or better than classical hierarchical fitting. The results indicate that coupling parametric optimization with localized hierarchical refinement provides a computationally efficient and robust strategy for engineering-oriented freeform surface reconstruction.