Open AccessQuasi-Newtonian methods for modeling of plan curve
Author(s) -
Alla Nesterenko,
Oleksandr Duchenko
Publication year - 2021
Publication title -
fìziko-matematične modelûvannâ ta ìnformacìjnì tehnologìï/fìzìko-matematične modelûvannâ ta ìnformacìjnì tehnologìï
Language(s) - English
Resource type - Journals
eISSN - 2617-5258
pISSN - 1816-1545
DOI - 10.15407/fmmit2021.33.062
Subject(s) - curvature , torsion of a curve , tangent , mathematics , curvilinear coordinates , quadratic equation , curve fitting , nonlinear system , mathematical analysis , osculating circle , total curvature , center of curvature , geometry , mean curvature , mean curvature flow , physics , statistics , quantum mechanics
The paper is devoted to the methods of geometric modeling of plane curves given in the natural parameterization. The paper considers numerical modeling methods that make it possible to find the equation of curvature of the desired curve for different cases of the input data. The unknown curvature distribution coefficients of the required curve are determined by solving a system of nonlinear integral equations. Various numerical methods are considered to solve this nonlinear system. The results of computer implementation of the proposed methods for modeling two curvilinear contours with different initial data are presented. For the first curve, the input data are the coordinates of three points, the angles of inclination of the tangents at the extreme points and the linear law of curvature distribution. The second example considers an S-shaped curve with a quadratic law of curvature distributi.