Construction of curves and surfaces by means of parametric polynomials

摘要

A method for constructing surfaces is proposed for an approximate parametric description of three-dimensional domains using a given set of points located at domain boundaries. The method is based on a two-dimensional polynomial approximation with a special choice of conjugation boundaries of portions of a composite surface and allows one to avoid oscillations without decreasing order of the approximating polynomials. It is shown that the approximating polynomial for all variables possesses guaranteed properties of smoothness and monotonicity. The algorithm implementing this method can be also used to approximate and smooth experimental data, to solve equations in partial derivatives by finite-difference methods, and to solve variational problems with controlled free boundaries.