IMPROVEMENT OF THE ALGORITHM FOR SETTING THE CHARACTERISTICS OF INTERPOLATION MONOTONE CURVE

Abstract

Interpolation of a point series is a necessary step in solving such problems as building graphs de-scribing phenomena or processes, as well as modelling based on a set of reference points of the line frames defining the surface. To obtain an adequate model, the following conditions are imposed upon the interpolating curve: a minimum number of singular points (kinking points, inflection points or points of extreme curvature) and a regular curvature change along the curve. The aim of the work is to develop the algorithm for assigning characteristics (position of normals and curvature value) to the interpolating curve at reference points, at which the curve complies with the specified conditions. The characteristics of the curve are assigned within the area of their possible location. The possibilities of the proposed algorithm are investigated by interpolating the point series assigned to the branches of the parabola. In solving the test example, deviations of the normals and curvature radii from the corresponding characteristics of the original curve have been determined. The values obtained confirm the correctness of the solutions proposed in the paper.

Keywords

• interpolation
• monotone curve
• singular points
• normal
• centre of curvature
• evolute