Kremetz T. Conformal mapping of drawings on an isometric grids in morphogenetic design processes

Dissertation on competition of scientific degree of the candidate of engineering science by speciality 05.01.03 – Technical aesthetics. – Kyiv National University of Building and Architecture, Kyiv, Ukraine, 2016. Dissertation it is devoted working out of a mode of formation of flat images from segments of straight lines and arcs of curves, their conformal transformation and drawing on a surface. The mode is justified on isometric grid to which the plane or a surface are referred. The infinitesimal element of such grid is quadrate. Analytical indication of the specified grid is the equality of extreme factors of the first quadratic form and lack of average factor. There are different isometric grids on a plane – Cartesian, polar, elliptic, parabolic and others. If to set a line the interior equation at the Cartesian isometric grid its substitution at parametric equations of other isometric grids it is possible to gain the converted lines which conformally will be mapped on these grids. Flat lines on surface which are referred to isometric grids are analogously mapped. Formation of flat drawing is carried out from segments of straight lines and arcs of rounds in the environment of system "AutoCad", whence we obtain all necessary data for analytical exposition of these elements the interior equations. Drawing conformal mapping on an isometric grids is carried out by the program a recurring of equal operations on initial co-ordinates of each element. Isometric grids on known surface of revolutions are in-process built and discovered new which suppose such parameterization.