Abstract
The paper addresses the problem of modeling a smooth contour interpolating a point series belonging to a curve containing no special points, which represents the original curve with specified accuracy. The contour is formed within the area of possible location of the parts of the interpolated curve along which the curvature values are monotonously increased or decreased. The absolute interpolation error of the point series is estimated by the width of the area of possible location of the curve. As a result of assigning each intermediate point, the location of two new sections of the curve that lie within the area of the corresponding output section is obtained. When the interpolation error becomes less than the given value, the area of location of the curve is considered to be formed, and the resulting point series is interpolated by a contour that lies within the area. The possibility to shape the contours with arcs of circles specified by characteristics is investigated.
Highlights
Published: 21 April 2021Modeling is an effective tool for investigating objects, phenomena, and processes.Geometric modeling of an object often determines its functional properties
The analysis of the output point series is based on determination of the radii of adjacent circles (AC), each of which passes through three consecutive points in the series
The position of the specified points was determined based on the condition of a monotonous increase in the AC radii along the point series
Summary
Modeling is an effective tool for investigating objects, phenomena, and processes. Geometric modeling of an object often determines its functional properties. Such objects are, first of all, items bounded by functional surfaces which ensure the laminar nature of the item’s flow around by the environment–gas, liquid, or loose materials [1,2,3]. Examples of items limited by functional surfaces are automobile and aircraft hulls, working bodies of agricultural machinery, impeller blades of turbines, and compressors. Complex surfaces are typically modeled based on linear frameworks whose elements are formed by interpolation of point series. The operating performance of the item is ensured by the geometric characteristics of the interpolated curves
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