Curve construction based on quartic Bernstein-like basis

Kai Wang; Guicang Zhang; Kai Wang; Guicang Zhang

doi:10.3934/math.2020343

AIMS Mathematics

2020, Volume 5, Issue 5: 5344-5363. doi: 10.3934/math.2020343

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Research article

Curve construction based on quartic Bernstein-like basis

Kai Wang ^,,
Guicang Zhang

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, China

Received: 22 April 2020 Accepted: 08 June 2020 Published: 22 June 2020
MSC : 65D07, 65D17

A new quartic Bernstein-like basis possessing two exponential shape parameters is developed and the condition of C² ∩ FC^2l+3 continuity and the definition of such continuity-related curves are discussed. Based on this new basis, a new cubic B-spline-like basis possessing two global and three local shape parameters is presented and the related cubic B-spline-like curves have C² ∩ FC^2l+3 continuity at each point and include the classical cubic uniform curves as a special case. Representative properties regarding connecting, interpolation and local adjustment of the cubic Bspline-like curves are also discussed.
- exponential shape parameters,
- B-spline-like basis,
- continuity,
- connecting,
- interpolation
Citation: Kai Wang, Guicang Zhang. Curve construction based on quartic Bernstein-like basis[J]. AIMS Mathematics, 2020, 5(5): 5344-5363. doi: 10.3934/math.2020343

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Abstract

A new quartic Bernstein-like basis possessing two exponential shape parameters is developed and the condition of C² ∩ FC^2l+3 continuity and the definition of such continuity-related curves are discussed. Based on this new basis, a new cubic B-spline-like basis possessing two global and three local shape parameters is presented and the related cubic B-spline-like curves have C² ∩ FC^2l+3 continuity at each point and include the classical cubic uniform curves as a special case. Representative properties regarding connecting, interpolation and local adjustment of the cubic Bspline-like curves are also discussed.

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