Application of piecewise­cubic functions for constructing a Bezier type curve of C1 smoothness

Stelia, Oleg; Potapenko, Leonid; Sirenko, I. G.

doi:10.15587/1729-4061.2018.128284

Cited by 2 publications

(2 citation statements)

References 13 publications

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“…These systems of equations have three-diagonal matrices. It was shown in [20] that matrices of the equation systems (6), (7), (12) have a diagonal superiority under conditions 1 2 3 3…”

Section: Methods Of Curve Designmentioning

confidence: 99%

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Computer Realizations of the Cubic Parametric Spline Curve of Bèzier Type

Stelia¹,

Potapenko²,

Sirenko³

2019

IJC

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This paper presents a new method for constructing a third degree parametric spline curve of C1 continuity. Like the Bèzier curve, the proposed curve is constructed and operated by control points. The peculiarity of the proposed algorithm is the assignment of some unknown values of the spline in the control points abscissas, which are based on the conditions of the first derivative continuity of the curve at these points. The position of the touch points, as well as the control points, can be set interactively. Changing of these points positions leads to a change in the curve shape. This allows the user to flexibly adjust the shape of the curve. Systems of algebraic equations with tridiagonal matrix for calculating the coefficients of a spline curve are constructed. Conditions for the existence and uniqueness of such a curve are presented. Examples of the use of the proposed curve, in particular, for monotone data sets, approximation the ellipse and constructing the letter "S" are given.

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“…These systems of equations have three-diagonal matrices. It was shown in [20] that matrices of the equation systems (6), (7), (12) have a diagonal superiority under conditions 1 2 3 3…”

Section: Methods Of Curve Designmentioning

confidence: 99%

“…In all calculations, all = 1 / 2 i  was put. The local behavior of the spline curve, depending on the i  parameter values, is considered in [20].…”

Section: Numerical Examplesmentioning

confidence: 99%

Computer Realizations of the Cubic Parametric Spline Curve of Bèzier Type

Stelia¹,

Potapenko²,

Sirenko³

2019

IJC

Self Cite

View full text Add to dashboard Cite

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Geometric Piecewise Cubic Bézier Interpolating Polynomial with C2 Continuity

Fadhel

Omar

2021

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Bézier curve is a parametric polynomial that is applied to produce good piecewise interpolation methods with more advantage over the other piecewise polynomials. It is, therefore, crucial to construct Bézier curves that are smooth and able to increase the accuracy of the solutions. Most of the known strategies for determining internal control points for piecewise Bezier curves achieve only partial smoothness, satisfying the first order of continuity. Some solutions allow you to construct interpolation polynomials with smoothness in width along the approximating curve. However, they are still unable to handle the locations of the inner control points. The partial smoothness and non-controlling locations of inner control points may affect the accuracy of the approximate curve of the dataset. In order to improve the smoothness and accuracy of the previous strategies, а new piecewise cubic Bézier polynomial with second-order of continuity C2 is proposed in this study to estimate missing values. The proposed method employs geometric construction to find the inner control points for each adjacent subinterval of the given dataset. Not only the proposed method preserves stability and smoothness, the error analysis of numerical results also indicates that the resultant interpolating polynomial is more accurate than the ones produced by the existing methods.

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Application of piecewisecubic functions for constructing a Bezier type curve of C1 smoothness

Cited by 2 publications

References 13 publications

Computer Realizations of the Cubic Parametric Spline Curve of Bèzier Type

Computer Realizations of the Cubic Parametric Spline Curve of Bèzier Type

Geometric Piecewise Cubic Bézier Interpolating Polynomial with C2 Continuity

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Application of piecewise­cubic functions for constructing a Bezier type curve of C1 smoothness

Cited by 2 publications

References 13 publications

Computer Realizations of the Cubic Parametric Spline Curve of Bèzier Type

Computer Realizations of the Cubic Parametric Spline Curve of Bèzier Type

Geometric Piecewise Cubic Bézier Interpolating Polynomial with C2 Continuity

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Product

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Application of piecewisecubic functions for constructing a Bezier type curve of C1 smoothness