4階差分商を用いたメッシュデータの平滑化

抄録

This paper proposes a method which approximates mesh data for measured points smoothly by iterative and local procedures. The method calculates fourth divided differences for u and v directions at each mesh point as a local fairness criterion, and modifies the central 9 points using 16 points from 5 × 5 mesh points for the point with the maximum local fairness so as to make their fourth divided differences zero iteratively. It repeats these procedures until the global fairness, which is the sum of the local fairness criteria, does not decrease. Then it fits the mesh curves locally with parametric cubic polynomials and obtains fifth-degree C² parametric patches. Several examples demonstrate effectiveness of the method for the data with random errors and a few extraordinarily large errors.