CURVATURE PROJECT

This project advances multiscale curvature analysis to characterize surface topographies. Importantly this project will furnish open-source code for multiscale analysis for interlaboratory comparisons and developing national and international standards. Multiscale curvatures characterizations have been used in multiscale regression and discrimination analyses to find functional correlations and differences of both kinds (ASME B46.1 2019 appendix k).

Algorithms are being developed in MATLAB and Python to curvatures as functions of position and scale from profiles (z=z(x)). It uses discrete measurement data and several different methods, including Heron, finite difference calculus, change in slope, Lagrange, and parabolic fits.

These methods are tested on smooth shapes with known regular curvatures, such as semicircles and sine waves. Situational accuracies with percent errors are calculated at each scale to understand when each is best. Then, by combining methods, curvature values of the best, known accuracies can be used for actual, irregular profile data.

Future plans include extending the code to calculate multiscale curvature tensors from areal measurements (z=z(x,y)), extending the capabilities of the program to 3D surfaces rather than just 2D profiles.