A family of quasi-cubic blended splines and applications

Su, Benyue; Tan, Jieqing

doi:10.1631/jzus.2006.a1550

Cited by 13 publications

(13 citation statements)

References 8 publications

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“…Let = 1 , and (1-)= 2 , and substituting them into the above formula, and then we can get the same results in [8]. As a fact, the state S 3 and S 4 may be combined into a state under the condition of the above parameters given.…”

Section: Theoremmentioning

confidence: 75%

Reliability and Security Characteristic Analysis on Complicated Equipment Operation

Su¹

2013

IJCA

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Section: Theoremmentioning

confidence: 75%

Reliability and Security Characteristic Analysis on Complicated Equipment Operation

Su¹

2013

IJCA

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“…Besides this property, the quasi-cubic piecewise interpolation spline curves also possess symmetry, geometric invariability and other properties, the details of these properties can be found in our another paper ( [11]). …”

Section: -Continuous Generalized Quasi-cubic Interpolation Splinementioning

confidence: 96%

Sweeping Surface Generated by a Class of Generalized Quasi-cubic Interpolation Spline

Tan

2007

Computational Science – ICCS 2007

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Abstract. In this paper we present a new method for the model of interpolation sweep surfaces by the C 2 -continuous generalized quasicubic interpolation spline. Once given some key position, orientation and some points which are passed through by the spine and initial cross-section curves, the corresponding sweep surface can be constructed by the introduced spline function without calculating control points inversely as in the cases of B-spline and Bézier methods or solving equation system as in the case of cubic polynomial interpolation spline. A local control technique is also proposed for sweep surfaces using scaling function, which allows the user to change the shape of an object intuitively and effectively. On the basis of these results, some examples are given to show how the method is used to model some interesting surfaces.

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“…In order to construct interpolation curves, Su [13] and Yan [14] constructed the trigonometric curves over the spaces {1, t, sint, cost, sin2t, cos2t} and {1, t, sint, cost, sin 2 t, sin 3 t, cos 3 t}. The two trigonometric curves presented in [13,14] can automatically interpolate the given data points without solving equation systems, which provides a simple and efficient way to construct interpolation curves. However, although the quasi-cubic blended interpolation curves defined by Su [13] could interpolate the given data points automatically, their shapes cannot be adjusted when the data points are fixed.…”

Section: Introductionmentioning

confidence: 99%

A Class of Cubic Trigonometric Automatic Interpolation Curves and Surfaces with Parameters

2016

MCA

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This paper presents the cubic trigonometric interpolation curves with two parameters generated over the space {1, sint, cost, sin 2 t, sin 3 t, cos 3 t}. The new curves can not only automatically interpolate the given data points without solving equation systems, but are also C 2 and adjust their shape by altering values of the two parameters. The optimal interpolation curves can be determined by an energy optimization model. The corresponding interpolation surfaces have characteristics similar to the new curves.The rest of this paper is organized as follows. In Section 2, the cubic trigonometric interpolation basis functions with two parameters generated over the space {1, sint, cost, sin 2 t, sin 3 t, cos 3 t} are presented, and some properties of the basis functions are given. In Section 3, the interpolation curves are defined on the base of the basis functions and some properties of the curves are given. Then, determining the optimal interpolation curves is discussed. In Section 4, the corresponding interpolation surfaces are presented. A short conclusion is given in Section 5. The CTI-Basis FunctionsThe cubic trigonometric interpolation basis functions with two parameters are defined as follows.Definition 1. For 0 ď t ď 1, α, β P R, the following four functions about t are called cubic trigonometric interpolation basis functions with parameters α and β (CTI-basis functions for short),

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A family of quasi-cubic blended splines and applications

Cited by 13 publications

References 8 publications

Reliability and Security Characteristic Analysis on Complicated Equipment Operation

Reliability and Security Characteristic Analysis on Complicated Equipment Operation

Sweeping Surface Generated by a Class of Generalized Quasi-cubic Interpolation Spline

A Class of Cubic Trigonometric Automatic Interpolation Curves and Surfaces with Parameters

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