Stretch-Energy-Minimizing B-Spline Interpolation Curves and Their Applications

Qian Ni () and Chen Xie
Additional contact information
Qian Ni: School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing 211816, China
Chen Xie: School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing 211816, China

Mathematics, 2023, vol. 11, issue 21, 1-9

Abstract: In this paper, we propose a new method to construct energy-minimizing cubic B-spline interpolation curves by minimizing the approximated stretch energy. The construction of a B-spline interpolation curve with a minimal approximated stretch energy can be addressed by solving a sparse linear system. The proof of both the existence and uniqueness of the solution for the linear system is provided. In addition, we analyze the computational cost of cubic B-spline curves with an approximated stretch energy, which is close to that of the ordinary interpolation method with cubic B-splines without the requirement of stretch energy.

Keywords: interpolation curves; minimal stretch energy; B-spline curves; sparse linear system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/21/4534/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/21/4534/ (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:11:y:2023:i:21:p:4534-:d:1273757

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 ().