Robust and physically-constrained interpolation of fluid flow fields

The authors investigate the problem of interpolating, under physical constraints, 3-D vector fields from sample vectors at random positions. This problem arises from analysis of fluid motion, but the results can also be applied to such areas as geometric modeling, approximation theory, and other types of nonrigid motion. The algorithm proposed combines the generalized multivariable quadratic interpolation and physical constraints into one step to form an overdetermined linear equation system whose solution gives the coefficients of interpolation, which are much less sensitive to noise compared to other interpolation methods. The authors utilized methods in robust statistics to detect outliers in the sample data so that the results are more stable in the presence of gross errors. The algorithm is applied to both synthesized velocity fields of fluid and empirically measured 3-D velocity fields