Abstract
This paper proposes a method which smoothly approximates mesh data for measured points by iterative local procedures. The method calculates fourth divided differences along u and υ parametric lines at each mesh point as a local fairness criterion from the regular mesh of measured data, and modifies the central 9 points using 16 points from 5×5 mesh points around the point with the maximum local fairness criterion so as to make the criterion zero iteratively. It repeats these procedures until the global fairness criterion, which is the sum of the local fairness criteria, does not decrease. For treating boundaries or incomplete mesh points, it modifies several candidate points and selects the mesh point with the minimum global fairness criterion among them. Further, it obtains a smooth mesh when a parametric line is given across which the continuity between mesh points is C 1 Some examples demonstrate effectiveness of the method for the data with random errors and a few extraordinary large errors.
