IsoGeometric Smoothing: A new approach for smoothing on surfaces

We propose a new approach for smoothing on surfaces. More precisely, we aim at estimating functions lying on a surface represented by NURBS, which are geometrical representations commonly used in industrial applications. The estimation is based on the minimization of a penalized least-square functional which is equivalent to solve a 4th-order Partial Differential Equation (PDE). We use Isogeometric Analysis (IGA), which is a method for numerically solve PDE, for the numerical approximation of such surface PDE, leading to an IsoGeometric Smoothing (IGS) method. IGA has the great advantage to use the exact geometrical representation of the surface in the analysis, thus avoiding complex meshing procedures. IGA also provides at least globally $C^1-$continuous basis functions with compact support. We show the performance of the proposed IGS method by means of numerical simulations and we apply it to the estimation of the pressure coefficient, and associated aerodynamic force on a winglet of the SOAR space shuttle.

, 8th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2015), London, UK