Chernyak V. Discrete approximation of disordered sets of points

Thesis for the Candidate's Degree in engineering science in speciality 05.01.01 - Applied geometry, engineering graphics. - Kyiv national university of construction and architecture, Kyiv, 2011. Thesis is devoted to discrete approximation of disordered sets of points by the geometric objects of different type (curves, surfaces, m-surfaces and hypersurfaces) in spaces of any measurableness. The geometrical methods of arrangement and analysis of sets are developed: determination and removal of extrass from sets of points; estimations of expedience of approximation of set by its research on a compactness; determination of type of approximation object, proceeding from descriptions of set. Ordered set of points transforms into geometric object (curve, surface, m-surface and hypersurface) discretely presented in approximation, the topology of which corresponds to the structure of initial set of points. Obtained approximation object is checked up in the presence of oscillations, after which a smoothing approximation of oscillation points by this or other method is taking place. The methods of estimation of exactness of approximation of sets of points are in-process developed by significant geometric objects, methods of determination of geometrical area of placing of not oscillating point of approximate object (accompanying tetrahedron, simplex, polyhedron), method of construction of the triangulated significant surface in three-dimensional space and m-surface in n-dimensional space. The results of researches are inculcated in practice of processing of data.