{'fraction_non_alphanumeric': 0.02, 'fraction_numerical': 0.0005405405405405405, 'mean_word_length': 5.634408602150538, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Novel geometric methods in multiscale analysis: curvature and slope

The aim of this paper is to demonstrate the use of novel geometric multiscale methods in the characterization of surface topographies with a view to establishing functional relations between formation processes and resulted topography or between topography and its performance during interaction with the environment (e.g. friction, fatigue or gloss reflectance). Geometric properties of rough surfaces change with the scale of observation, i.e., measurement or calculation. In this paper, I focus on two novel method, which analyse slope and curvature in multiple scales. The digital nature of measured surfaces is recognized and is not smoothed to fit a continuous function to the measured heights. Curvature is represented as a second order tensor, which components describe maximal and minimal curvatures and their directions. In order to describe curvature distributions for analyzed regions, statistical parameters, such as: mean and standard deviation, are used. Those measures are utilized to find correlations between them and certain formation or performance parameters. The other method described here bases on slope. In this work, two calculation techniques are presented using orientation normal vectors estimated through covariance matrix method or cross product. As a result of further processing, 3D distributions of direction cosines are obtained, based on which multivariate statistical parameters are calculated (incl. measures of dispersion and higher statistical moments). This paper also presents the sample strong correlations between slope or curvature, for actual measured textures, and manufacturing or performance parameters. This indicates a great potential of those two methods in the development of multiscale characterization of surface topographies.