Accuracy of C1 natural neighbors interpolation of feature tracking data and vorticity measurements

The Feature Tracking (FT) and the C1 Natural Neighbours (NN) interpolation techniques are implemented in the lagrangian-eulerian PTV-PIV system YATS (Yet Another Tracking Software 3.01, Miozzi 2004). This work describes the theoretical approach to the use of Bezier-Berenstain patches, weighted with NN coordinates on a NN support, as a C1 interpolation method (Farin, 1990). Results on synthetic and real data are reported and compared with available PIV literature. In relatively recent works on interpolation theory, meshless methods have been proposed in the context of solid mechanics. Among those algorithms, Natural Element Method uses the Natural Neighbours interpolant to calculate its weight functions (NN coordinates). In NN interpolation, the support for data gridding is not defined by the same measure in all directions, but is allowed to be non isotropic. The support size in any direction r is not given by an L2 metric but is a consequence of the geometric construction which defines the region of interaction between features. NN interpolation represents a meshfree method. By embedding NN coordinates in the Bernstein- Bezier representation of a cubic simplex, a C1 interpolant is obtained (Sukumar and Moran 1999). The C1 property optimization effect on the gradients evaluation over the remapped velocity surfaces is a crucial aspect of this algorithm.