Variationally Improved Bézier Surfaces with Shifted Knots

Daud Ahmad, Kanwal Hassan, M. Khalid Mahmood, Javaid Ali, Ilyas Khan and M. Fayz-Al-Asad

Advances in Mathematical Physics, 2021, vol. 2021, issue 1

Abstract: The Plateau‐Bézier problem with shifted knots is to find the surface of minimal area amongst all the Bézier surfaces with shifted knots spanned by the admitted boundary. Instead of variational minimization of usual area functional, the quasi‐minimal Bézier surface with shifted knots is obtained as the solution of variational minimization of Dirichlet functional that turns up as the sum of two integrals and the vanishing condition gives us the system of linear algebraic constraints on the control points. The coefficients of these control points bear symmetry for the pair of summation indices as well as for the pair of free indices. These linear constraints are then solved for unknown interior control points in terms of given boundary control points to get quasi‐minimal Bézier surface with shifted knots. The functional gradient of the surface gives possible candidate functions as the minimizers of the aforementioned Dirichlet functional; when solved for unknown interior control points, it results in a surface of minimal area called quasi‐minimal Bézier surface. In particular, it is implemented on a biquadratic Bézier surface by expressing the unknown control point P11 as the linear combination of the known control points in this case. This can be implemented to Bézier surfaces with shifted knots of higher degree, as well if desired.

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2021/9978633

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:9978633

Access Statistics for this article

More articles in Advances in Mathematical Physics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().