GRAPHIC-ANALYTICAL METHOD FOR LOCATING WITH A PRELIMINARY DEFINED ACCURACY OF INFLECTION POINTS FOR FLAT SEGMENTS OF A SINGLE-PARAMETRIC POINT POLYNOMA

Abstract

The general form of the equation of a one-parameter point polynomial, which is determined by the geometric parameters of the original plane discretely represented curve.

It is indicated that the graphical-analytical method for finding inflection points provides for discretization of a one-parameter point polynomial and its repetition with decreasing step and narrowing the section of its segment on which the inflection point is located.

The inflection point is located on the link of the accompanying broken line, built according to the results of the sign of the determinants. Determinants consist of three points of the accompanying polyline, which define its adjacent three vertices.

A formalized feature of the link of the accompanying broken line, on which the inflection point is located, is the presence of identical lines in adjacent determinants with positive and negative values.

Graphical interpolation is provided, which explains the existing difference in signs in adjacent identifiers, for a section of an accompanying polyline with an inflection point.

An algorithm for finding the inflection is shown, with a predetermined accuracy, the inflection points are perceived as a reduced link of the accompanying broken line.

Several examples of finding the links of an accompanying broken line with an existing inflection point in the middle of the convex and concave curves of a one-parameter point polynomial, as well as on its initial and final links are given.

For the proposed method of finding the inflection points on the continuous curves do not need to differentiate them, ie the algorithm is universal. This allows you to create its software implementations by a single method for both discrete and continuous curves. This same approach will reduce the cost of creating software products, reduce costs during its operation, which will increase efficiency, creating with its use, geometric models.

Keywords. A flat curve is discretely represented by a one-parameter point polynomial, an inflection point.