The cubic trigonometric automatic interpolation spline

Li, Juncheng; Song, Laizhong; Liu, Chengzhi

doi:10.1109/jas.2017.7510442

Cited by 12 publications

(8 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 1 . The spline defined in the cubic trigonometric polynomial space { 1 , sin t , cos t , sin 2 t , sin 3 t , cos 3 t } 17,18 has global adjustability but not local adjustability. To construct a spline that has local and global adjustability, we consider expanding the cubic trigonometric polynomial space to be quartic.…”

Section: The Basismentioning

confidence: 99%

A quartic trigonometric interpolatory spline with local free parameters

Liu

2023

Advances in Mechanical Engineering

Self Cite

View full text Add to dashboard Cite

The construction of trigonometric interpolatory splines plays a very important role in geometric modeling. This paper presents a quartic trigonometric interpolatory spline with local free parameters. The new spline not only automatically interpolates the given points and achieves C2 continuity, but also owns shape adjustability when the points remain fixed. Some examples show that the shape of the new spline can easily realize local and global adjustment by changing the free parameters.

show abstract

Section: The Basismentioning

confidence: 99%

A quartic trigonometric interpolatory spline with local free parameters

Liu

2023

Advances in Mechanical Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Note that M has twenty-four undetermined numbers, it is necessary to set two free parameters in these undetermined numbers because Equations ( 17) and ( 18) only have twenty-two equations in total. If we set a 61 = α and a 63 = β as free parameters, α, β ∈ R, then from Equations ( 17) and (18) we could obtain…”

Section: Construction Of Cubic Trigonometric Hermite Interpolation Curvementioning

confidence: 99%

“…In the recent years, trigonometric polynomials have received much attention within geometric modeling. Such as the trigonometric Bézier curves [11][12][13][14], the trigonometric B-spline curves [15][16][17], the trigonometric interpolation curves [18,19], etc. The curves constructed in trigonometric polynomial space have broad application prospects in engineering.…”

Section: Introductionmentioning

confidence: 99%

Cubic Trigonometric Hermite Interpolation Curve: Construction, Properties, and Shape Optimization

Liu

2022

Journal of Function Spaces

Self Cite

View full text Add to dashboard Cite

Cubic Hermite interpolation curve plays a very important role in interpolation curves modeling, but it has three shortcomings including low continuity, difficult shape adjustment, and the inability to accurately represent some common engineering curves. We construct a cubic trigonometric Hermite interpolation curve to make up the three shortcomings of cubic Hermite interpolation curve once and for all. The cubic trigonometric Hermite interpolation curve not only inherits the features of cubic Hermite interpolation curve but also achieves C2 continuity, has local and global adjustability, and can accurately represent elliptical arc, circular arc, quadratic parabolic arc, cubic parabolic arc, and astroid arc that often appear in engineering. In addition, we give the schemes for optimizing the shape of the cubic trigonometric Hermite interpolation curve based on internal energy minimization. The schemes include optimizing the shape of planar curve and spatial curve. Some modeling examples show that the proposed schemes are effective and the cubic trigonometric Hermite interpolation curve is more practical than cubic Hermite interpolation curve.

show abstract

“…Yan and Liang, 2011 presented xy-Bézier curves with two shape parameters x and y and they constructed most of the conics, transcendental curves, helix, cycloid and asteroid. Li, et al (2017) presented a class of cubic trigonometric interpolation spline curves having shape parameters. Furthermore, Li, 2016 presented a cubic trigonometric interpolation curves with two shape parameters.…”

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

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.

show abstract

The cubic trigonometric automatic interpolation spline

Cited by 12 publications

References 10 publications

A quartic trigonometric interpolatory spline with local free parameters

A quartic trigonometric interpolatory spline with local free parameters

Cubic Trigonometric Hermite Interpolation Curve: Construction, Properties, and Shape Optimization

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

Contact Info

Product

Resources

About