Thin-Plate Splines Generalized Interpolation Based on Duchon’s Semi-Norm Minimization Extended to CAD-Compliant Surface Mesh Deformation

The Thin-Plate Splines (TPS) technique, using Kybic et al.’s generalized interpolation approach, is extended to differentiable manifolds. The initial application to surface mesh deformation resulting from parameterized Computer Aided Design (CAD) used in the framework of shape optimization is given. Coming to RSM (Response Surface Model), we give a comparison with Kriging and RBF (Radial Basis Functions), and an enrichment methodology is proposed. The new approach proposed is a breakthrough for UAV shape design of high-curvature areas.