Direction monotonicity for a rational Bézier curve

Shen, Wanqiang; Wang, Guozhao; Huang, Fang

doi:10.1007/s11766-016-3399-7

Cited by 4 publications

(9 citation statements)

References 12 publications

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“…The methods of piece-smooth approximations form a contour of sections of analytically given curves, which link up at output points. Sections of curves of the second order form a contour in a work [5], Beziers curves -in work [6], B-splines -in paper [7].…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…The method developed in paper [6] makes possible to ensure regularity of values of the curvature along the contour. The method involves a use of Bezier curves of the third or higher order.…”

Section: Fig 1 Investigation Of the Convergence Of Interpolationmentioning

confidence: 99%

“…The estimation of the accuracy of interpolation through determination of a height of the base triangles is possible at formation of contours by methods that provide the control of the occurrence of oscillations. This is a method of curves of the second order [5], Bezier curves [6], B-splines [7] and methods of discrete interpolation [11][12][13].…”

Section: H Imentioning

confidence: 99%

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Development of the method for the formation of one-dimensional contours by the assigned interpolation accuracy

Havrylenko

Kholodniak

Vershkov

et al. 2018

EEJET

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Fig 1 Investigation Of the Convergence Of Interpolationmentioning

confidence: 99%

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Development of the method for the formation of one-dimensional contours by the assigned interpolation accuracy

Havrylenko

Kholodniak

Vershkov

et al. 2018

EEJET

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“…The method that was developed in the work [17] allows ensuring regularity of curvature values lengthwise the contour. This method provides for using Bézier Curves of the third or high orders.…”

Section: Analysis Of Recent Studies and Publicationsmentioning

confidence: 99%

“…Control of the error with which generated contour presents the set curve is a feature and advantage of our method. In case of interpolation of initial set of points by the analytically set curves [16][17][18][19], the error of interpolation is not controlled.…”

Section: Figure 4 Estimation Of the Position Of The Tangent Straight mentioning

confidence: 99%

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

2020

Teh. vjesn.

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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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Direction monotonicity for a rational Bézier curve

Cited by 4 publications

References 12 publications

Development of the method for the formation of one-dimensional contours by the assigned interpolation accuracy

Development of the method for the formation of one-dimensional contours by the assigned interpolation accuracy

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

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

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