Equiareal Parameterization of Triangular Bézier Surfaces

Jun Chen (), Xiang Kong and Huixia Xu
Additional contact information
Jun Chen: Faculty of Science, Ningbo University of Technology, Ningbo 315211, China
Xiang Kong: Faculty of Science, Ningbo University of Technology, Ningbo 315211, China
Huixia Xu: Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, China

Mathematics, 2022, vol. 10, issue 23, 1-11

Abstract: Parameterization is the key property of a parametric surface and significantly affects many kinds of applications. To improve the quality of parameterization, equiareal parameterization minimizes the equiareal energy, which is presented as a measure to describe the uniformity of iso-parametric curves. With the help of the binary Möbius transformation, the equiareal parameterization is extended to the triangular Bézier surface on the triangular domain for the first time. The solution of the corresponding nonlinear minimization problem can be equivalently converted into solving a system of bivariate polynomial equations with an order of three. All the exact solutions of the equations can be obtained, and one of them is chosen as the global optimal solution of the minimization problem. Particularly, the coefficients in the system of equations can be explicitly formulated from the control points. Equiareal parameterization keeps the degree, control points, and shape of the triangular Bézier surface unchanged. It improves the distribution of iso-parametric curves only. The iso-parametric curves from the new expression are more uniform than the original one, which is displayed by numerical examples.

Keywords: equiareal parameterization; equiareal energy; binary Möbius transformation; triangular Bézier surface; computer-aided geometric design (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/23/4620/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/23/4620/ (text/html)

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:gam:jmathe:v:10:y:2022:i:23:p:4620-:d:994839

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().