Abstract
The problem of building a smooth surface containing given points or curves is actual due to development of industry and computer technology. Previously used for those purposes, shells of zero Gaussian curvature and minimal surfaces based on isotropic analytic curves are restricted in their consumer properties. To expand the possibilities regarding the shaping of surfaces we propose the method of constructing surfaces based on isotropic fractional-rational curves. The surfaces are built using flat isothermal and orthogonal grids and on the basis of the Weierstrass method. In the latter case, the surfaces are minimal. Examples of surfaces that were built according to the proposed method are given.
Highlights
The intensive development of mechanical engineering, the construction industry, and computer technology brings to the fore the problem of building a smooth surface containing given points or curves [1, 2]
Shells of zero Gaussian curvature were used [3, 4], which are simple in design and manufacture
It did not always give the best result when covering complex structures, since the carrying capacity of such shells significantly depends on small deviations of their overall contour from the ideal shape [5]. The elimination of these drawbacks in the most natural way is possible using minimal surfaces [6], whose theory has been successfully developed for a long time
Summary
The intensive development of mechanical engineering, the construction industry, and computer technology brings to the fore the problem of building a smooth surface containing given points or curves [1, 2] To solve this problem, shells of zero Gaussian curvature were used [3, 4], which are simple in design and manufacture. Shells of zero Gaussian curvature were used [3, 4], which are simple in design and manufacture It did not always give the best result when covering complex structures, since the carrying capacity of such shells significantly depends on small deviations of their overall contour from the ideal shape [5]. The purpose of this work is to create mathematical models of surfaces with specific differential properties based on isotropic fractional-rational curves. It is necessary to construct isotropic fractional-rational curves in the plane and in space, to use flat isotropic fractional-rational curves to construct a network and use curves and grids to construct surfaces
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