2011
DOI: 10.9735/0975-2927.3.1.18-24
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Quadratic Nuat B‐spline Curves With Multiple Shape Parameters

Abstract: 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 q… Show more

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Cited by 9 publications
(6 citation statements)
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“…Authors of [12] employ a trigonometric basis that contains parameters of the shape to represent an ellipse. Article [13] reported building a new type of splines, which are called quadratic irregular algebraic trigonometric B-splines with several shape parameters, and which make it possible to globally or locally adjust the shape of the curves. Paper [14] studied the dependence of geometrical properties of the proposed cubic trigonometric curves and the Bezier surfaces on the shape parameters.…”
Section: Smoothness O S T E L I Amentioning
confidence: 99%
See 1 more Smart Citation
“…Authors of [12] employ a trigonometric basis that contains parameters of the shape to represent an ellipse. Article [13] reported building a new type of splines, which are called quadratic irregular algebraic trigonometric B-splines with several shape parameters, and which make it possible to globally or locally adjust the shape of the curves. Paper [14] studied the dependence of geometrical properties of the proposed cubic trigonometric curves and the Bezier surfaces on the shape parameters.…”
Section: Smoothness O S T E L I Amentioning
confidence: 99%
“…Equating expressions (13) and (14) and substituting values Q 1 and Q 2 , we obtain a system of linear algebraic equations with a three-diagonal matrix for determining ϕ i : )( ) …”
Section: We Introduce Notationmentioning
confidence: 99%
“…Quadratic and cubic trigonometric B-spline curves with shape parameters are proposed by Han (2002Han ( , 2004. Quadratic NUAT-B-spline curves with multiple shape parameters are developed by Dube and Sharma (2011).…”
Section: Introductionmentioning
confidence: 99%
“…The trigonometric B-splines were first introduced by Schoenberg [13] . A study of trigonometric splines has been made by a number of authors, [1,4,5,7,10] . It was found that problems of scattered data interpolation over spherical surfaces can be better handled in terms of accuracy, computational convenience and smoothness of the resulting surface using trigonometric splines.…”
Section: Introductionmentioning
confidence: 99%