NUAT B-spline curves

Wang, Guozhao; Chen, Qinyu; Zhou, Mi

doi:10.1016/j.cagd.2003.10.002

Cited by 84 publications

(51 citation statements)

References 12 publications

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“…If τ 2 − τ 1 ∈] 3π 4 , π[, then we have to require τ 0 to be sufficiently close to τ 1 . For instance, if τ 2 − τ 1 = 3, then condition (38) implies that τ 1 − τ 0 must be less than 0.15. On such a small interval, we could as well replace V 0 by the restriction to [τ 0 , τ 1 ] of the polynomial space of degree 1.…”

Section: This Is Possible If and Only Ifmentioning

confidence: 98%

“…, x n−2 , cos x, sin x, which in general are not Chebyshevian splines in the sense of Chapter 9 of [35]. The integral construction of the corresponding B-spline basis under the condition t k+1 − t k < π for all k was addressed in [38]. We now know that it is the optimal NTP basis.…”

Section: Remark 513mentioning

confidence: 99%

“…... So far, the latter questions have been solved only for a few special cases and only partially (see, for instance, [38,39]). In the present work we will definitely give complete affirmative answers to all of them.…”

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confidence: 99%

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On a general new class of quasi Chebyshevian splines

Mazure

2011

Numer Algor

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International audienceWe prove that a general class of splines with sections in different Extended Chebyshev spaces or in different quasi Extended Chebyshev spaces can be viewed as quasi Chebyshevian splines, that is, as splines with all sections in a single convenient quasi Extended Chebyshev space. As a result, we can affirm the presence of blossoms in the corresponding spline spaces, with all the important consequences inherent in blossoms, namely, the possibility of developing all design algorithms for splines, the existence of B-splines bases, along with their optimality

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Section: This Is Possible If and Only Ifmentioning

confidence: 98%

Section: Remark 513mentioning

confidence: 99%

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On a general new class of quasi Chebyshevian splines

Mazure

2011

Numer Algor

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“…In [1] C-Bézier curves are constructed in the space spanned by . Non-uniform algebraic trigonometric B-splines (NUAT B-splines), are generated in [14] over the space spanned by in which k is an arbitrary integer larger than or equal to 3. But all these curves do not have any shape parameter.…”

Section: Introductionmentioning

confidence: 99%

Quadratic Nuat B‐spline Curves With Multiple Shape Parameters

Dube¹,

Sharma²

2011

Int J Mach Intell

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Abstract-In this paper a new kind of splines, called quadratic non-uniform algebraic trigonometric B-splines (quadratic NUAT Bsplines) with multiple shape parameters are constructed over the space spanned by { } . As each piece of the curves is generated by three consecutive control points, they possess many properties of the quadratic B-spline curves and quadratic trigonometric B-spline curves. These curves have continuity with non-uniform knot vector. These curves are closer to the control polygon than the quadratic B-spline curves and quadratic trigonometric B-spline curves when choosing special shape parameters. The shape parameters serve to local control in the curves. The changes of one shape parameter will only affect two curve segments. Taking different values of the shape parameters, one can globally or locally adjust the shapes of the curves. The generation of tensor product surfaces by these new splines is straightforward. Keywords-Quadratic NUAT B-spline; shape parameter; continuity; spline surface. IntroductionThe trigonometric B-splines were presented in [12]. The recurrence relation for the trigonometric B-splines of arbitrary order was established in [8]. The construction of exponential tension B-splines of arbitrary order was given in [7]. It was further shown in [13] that the trigonometric Bsplines of odd order form a partition of a constant in the case of equidistant knots. In recent years, several bases in new spaces other than the polynomial space have been proposed for geometric modeling in CAGD. For instance, in [10] a basis is constructed for Cm=span { }. In [11] a basis for the space of trigonometric polynomials { } is constructed. Some bases are constructed in [9] for the spaces { }, { } and { }. In [1] C-Bézier curves are constructed in the space spanned by . Non-uniform algebraic trigonometric B-splines (NUAT B-splines), are generated in [14] over the space spanned by in which k is an arbitrary integer larger than or equal to 3. But all these curves do not have any shape parameter. In [15,16] C-B-splines are presented in the space spanned by { } with parameter .

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“…In order to improve the shape of a curve and to overcome the shortcomings of B-splines many bases with shape parameters are presented using trigonometric functions or the blending of polynomial and trigonometric functions in [1][2][3][4][5]. Han presented quadratic trigonometric polynomial curves with one shape parameter [6].…”

Section: Introductionmentioning

confidence: 99%

Extension of ?-? B-Spline Curves and Its Application in Surface Modelling

2015

IJSR

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An extension of λ-μ B-spline curves with a shape parameter is presented in this paper. Each curve segmet is generated by four consecutive control points. These curves possess most optimal properties of B-spline basis. We can easily obtain different shapes by altering the value of shape parameter. The lower degree of the basis functions provides less computational complexity. The associated λ-μ B-spline surfaces can exactly represent the surfaces of revolution.

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NUAT B-spline curves

Cited by 84 publications

References 12 publications

On a general new class of quasi Chebyshevian splines

On a general new class of quasi Chebyshevian splines

Quadratic Nuat B‐spline Curves With Multiple Shape Parameters

Extension of ?-? B-Spline Curves and Its Application in Surface Modelling

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