PECULIARITIES OF LOCATION OF BASIC NODES OF HOUSE-FUNCTION ON THE EXAMPLE OF SPIRAL-CURVED CURVES

Abstract

In the article   the interpolation errors of spiral curves were analyzed on the example of a Litus spiral using developed software product. There is a problem of large error with a sharp change in distances between nodes when interpolating using Gaussian function method. This problem was solved by changing the standard calculation of the coefficient α, and by introducing a "fake" interpolation node.

The article considers the basis points location influence on the relative interpolation error by the Gaussian interpolation function. There are several examples of favorable and unfavorable basis points location to minimize interpolation error in interpolation methods based on Gaussian functions. The research was carried out on the example of spiral curves. The results of interpolation by Gaussian methods are compared with the Lagrange method using the Litus spiral as example.

Spiral curves interpolation problems are important for the design of outdoor and car routes, planning for robots, planning a route for drones and low-power industrial devices. In addition, it is important that an interpolation method is stable to the inhomogeneous basis points location, which are the input parameters for interpolation.

The shape of the Gaussian interpolation curve is influenced by the coefficient a. The conventional ratio can be changed if the results exceed the specified accuracy. To avoid a large error, it is recommended to make additional "false" basis points.

To automate the process of selecting the coefficient a and using a "fake" node to reduce the interpolation error was a reason of creating a system for studying spiral functions interpolation.

The research was conducted together with a software application development using C# programming language with the .Net Core 3.1 framework involved. The application displays the results of experiments in real time and has a graphical interface required for research.

Key words: interpolation, Gaussian interpolation, interpolation error, Litus spiral.