G² Optimization of Complex Surfaces Based on a Variable-Scale Chaotic Algorithm

In reverse engineering, the reconstruction of point cloud data typically results in complex surfaces composed of multiple "piecewise smooth" surface patches. Therefore, achieving high-quality stitching between such surfaces requires at least G² continuity across adjacent patches. To address the limitations of conventional surface stitching methods and optimization algorithms, this study proposes a novel approach that combines adjacent surface interval recursion with a variable-scale chaotic search algorithm to determine the control points and weights necessary for G²-continuous stitching of NURBS surfaces. Continuity between adjacent intervals is maintained through recursive computation driven by the transfer of key equation coefficients. Meanwhile, the chaotic characteristics of variables, together with the adaptive scale strategy, enable dynamic adjustment of the search interval and precision control. The results demonstrate that the proposed method provides an effective strategy for G² fitting and optimization in surface reconstruction for reverse engineering.