The Quadratic Trigonometric B-Spline Curve with a Shape Parameter

Li, Jun Cheng; Chen, Guo Hua; Yang, Liang

doi:10.4028/www.scientific.net/amr.468-471.2463

Cited by 2 publications

(2 citation statements)

References 8 publications

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“…Furthermore, Misro, et al (2017b) presented a Quintic trigonometric Bézier curve with two shape parameters. Liu, et al (2012) defined a cubic trigonometric polynomial B-spline C 3 curves with a shape parameter and became closer to control points when value of shape parameter was increased. Li, (2018a,2018b and 2018c) defined α-Bézier curves of degree n with shape parameter α by extending definition of Bézier curve, planar T-Bézier curve with approximate minimum curvature variation and curvature variation minimizing cardianl spline curve with different shape parameters, respectively.…”

Section: Some Engineering Applications Of New Trigonometric Cubicmentioning

confidence: 99%

Some engineering applications of new trigonometric cubic Bézier-like curves to free-form complex curve modeling

Usman

Abbas

Miura

2020

JAMDSM

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The construction of free-form complex curves is very hot topic in engineering and computer aided design/computer aided manufacturing (CAD/CAM). The trigonometric Bézier-like curves got more attention in the fields of mathematics and engineering in recent years because of their useful geometric properties as compared to classical Bézier curves as well as ordinary Bernstein basis functions. The new trigonometric cubic Bézier-like (or TC Bézier-like, for short) curves along with new trigonometric cubic Bernstein-like (or TC Bernstein-like, for short) basis functions with single shape parameter with continuity conditions are presented in this paper. The necessary and sufficient constraints for C 2 and G 2 between two contiguous TC Bézier-like curves are constructed in order to remove the difficulty to composite curves which they cannot often be constructed by means of single curve. The role of shape parameter on connected curves with detailed smooth continuity steps is also part of this study. The ellipses and parabolas can also be represented exactly by using the TC Bézier-like curves. Some important applications of TC Bézier-like curves as: approximate some conic curves, font designing and free form complex curves are discussed. Some modelling examples show that the proposed TC Bézier-like curve technique is time saving, very effective and efficient which they can easily be modelled and give a powerful tool to design engineering complex curves.

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Section: Some Engineering Applications Of New Trigonometric Cubicmentioning

confidence: 99%

Some engineering applications of new trigonometric cubic Bézier-like curves to free-form complex curve modeling

Usman

Abbas

Miura

2020

JAMDSM

View full text Add to dashboard Cite

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“…They also analyzed the effect of taking different values of shape parameters on the curve. Recently, some more trigonometric curves with shape parameters were constructed [20,21,22,23]. In these curves, the shape parameter lies in the range [0,1], [0,1], [-1,1], [-1, 1.5] respectively.…”

Section: T (U )mentioning

confidence: 99%

Cubic TP B-Spline Curves with a Shape Parameter

Dube

Sharma

2013

JERA

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In this paper a new kind of splines, called cubic trigonometric polynomial B-spline (cubic TP B-spline) curves with a shape parameter, are constructed over the space spanned by As each piece of the curve is generated by three consecutive control points, they posses many properties of the quadratic B-spline curves. These trigonometric curves with a non-uniform knot vector are C1 and G2 continuous. They are C2 continuous when choosing special shape parameter for non-uniform knot vector. These curves are closer to the control polygon than the quadratic B-spline curves when choosing special shape parameters. With the increase of the shape parameter, the trigonometric spline curves approximate to the control polygon. The given curves posses many properties of the quadratic B-spline curves. The generation of tensor product surfaces by these new splines is straightforward.

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The Quadratic Trigonometric B-Spline Curve with a Shape Parameter

Cited by 2 publications

References 8 publications

Some engineering applications of new trigonometric cubic Bézier-like curves to free-form complex curve modeling

Some engineering applications of new trigonometric cubic Bézier-like curves to free-form complex curve modeling

Cubic TP B-Spline Curves with a Shape Parameter

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