Optimized M-Hermite Interpolation for Geometrically and Physically Consistent Airfoil Reconstruction

Accurate airfoil reconstruction is crucial for aerodynamic analysis, geometric modeling, and computational design applications. This study proposes an optimized M-Hermite interpolation framework for high-accuracy airfoil reconstruction and geometric preservation. Unlike classical Hermite interpolation, the proposed framework integrates a truncated M-derivative formulation through M-inspired parameter-dependent scaling into the interpolation structure, enabling adaptive local geometric control via fractional parameters α and β. Additionally, a tangential scaling coefficient is incorporated to improve curvature adaptation and reconstruction stability in critical geometric regions. The proposed framework is evaluated using 11 reference airfoil geometries and compared with widely used interpolation methods, including Cubic Spline, B-Spline, Bézier, Catmull-Rom, Classical Hermite, and unoptimized M-Hermite interpolation. Reconstruction performance was assessed using both global and local geometric validation metrics, including RMSE, MAE, maximum error, Hausdorff distance, leading-edge RMSE, trailing-edge RMSE, thickness retention error, and curvature retention error. Experimental results demonstrated that the optimized M-Hermite framework achieved the best overall reconstruction performance and geometric consistency across the evaluated airfoil families. The proposed framework improved reconstruction accuracy, particularly in high-curvature leading-edge regions, while preserving geometrically relevant shape descriptors known to influence aerodynamic behavior, including thickness distribution, camber-line consistency, and curvature structure. Optimization analyses further revealed that reconstruction performance is strongly dependent on geometry-adaptive parameter configurations, particularly the β parameter, which governs local geometric behavior. These findings demonstrate that the proposed optimized M-Hermite framework provides an adaptive and computationally efficient interpolation strategy for accurate airfoil reconstruction and geometric shape preservation applications.