{'fraction_non_alphanumeric': 0.014492753623188406, 'fraction_numerical': 0.001932367149758454, 'mean_word_length': 5.240963855421687, '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}}
A Method for the 2-D Quasi-isometric Regular

A method for the generation of quasi-isometric boundarytted curvilinear coordinate systems for arbitrary domains is developed on the basis of the theory of conformal, quasi-conformal and quasi-isometric mappings and results from the non-Euclidean geometry concerning surfaces of constant curvature. The method as it is proposed has an advantage of similar methods developed earlier that number of unknown parameters to be found is decreased, strict boundaries for parameters are found and a simple and e cient process of identi cation of an unknown parameter is given. The reliability of the method is assured by an existence and uniqueness theorem for quasi-isometric maps between physical regions and geodesic quadrangles on surfaces of constant curvature which are used to constrict quasi-isometric grids in physical domains. We formulate the Riemannian metric consistent with this theorem which is available analytically. Illustrations of this technique is given for various domains. 2