Design of Engineering Surfaces Using Quartic Parabolas

Chekalin, A A; Решетников, М. К.; Shpilev, V. V.; Borodulina, Svetlana

doi:10.1088/1757-899x/221/1/012015

Cited by 5 publications

(7 citation statements)

References 2 publications

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Interpolation with Specified Error of a Point Series Belonging to a Monotone Curve

Havrylenko

Kholodniak

Halko

et al. 2021

Entropy

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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.

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Section: Introductionmentioning

confidence: 99%

Interpolation with Specified Error of a Point Series Belonging to a Monotone Curve

Havrylenko

Kholodniak

Halko

et al. 2021

Entropy

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“…The problem of interpolating a point series specifying a monotone curve is solved by forming a contour—a curve consisting of sections of analytically determined curves joined at the reference points. At present, the most developed methods of forming contours are second-order curves, Bézier curves and B-splines [ 7 , 8 , 9 , 10 , 11 ].…”

Section: Introductionmentioning

confidence: 99%

Representation of a Monotone Curve by a Contour with Regular Change in Curvature

Havrylenko

Kholodniak

Halko

et al. 2021

Entropy

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The problem of modelling a smooth contour with a regular change in curvature representing a monotone curve with specified accuracy is solved in this article. The contour was formed within the area of the possible location of a convex curve, which can interpolate a point series. The assumption that if a sequence of points can be interpolated by a monotone curve, then the reference curve on which these points have been assigned is monotone, provides the opportunity to implement the proposed approach to estimate the interpolation error of a point series of arbitrary configuration. The proposed methods for forming a convex regular contour by arcs of ellipses and B-spline ensure the interpolation of any point series in parts that can be interpolated by a monotone curve. At the same time, the deflection of the contour from the boundaries of the area of the possible location of the monotone curve can be controlled. The possibilities of the developed methods are tested while solving problems of the interpolation of a point series belonging to monotone curves. The problems are solved in the CAD system of SolidWorks with the use of software application created based on the methods developed in the research work.

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“…Common methods of forming contour (interpolation by second-order curves, by the curves of Bézier, В-spline) [16][17][18][19] do not allow to control accuracy of interpolation. An error with which the contour presents initial geometric image can be calculated only after modelling the contour and providing that the initial geometric image is known.…”

Section: Discussion Of Resultsmentioning

confidence: 99%

“…The method of contours design via pieces of secondorder curves ensures absence of oscillation at interpolating any quantity of initial nodes. This method is suggested in the works [16]. It provides for single position of the tangent line to contour in the connection points of its pieces.…”

Section: Analysis Of Recent Studies and Publicationsmentioning

confidence: 99%

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Modelling of Surfaces of Engineering Products on the Basis of Array of Points

2020

Teh. vjesn.

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Design of Engineering Surfaces Using Quartic Parabolas

Cited by 5 publications

References 2 publications

Interpolation with Specified Error of a Point Series Belonging to a Monotone Curve

Interpolation with Specified Error of a Point Series Belonging to a Monotone Curve

Representation of a Monotone Curve by a Contour with Regular Change in Curvature

Modelling of Surfaces of Engineering Products on the Basis of Array of Points

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