Interpolating Triangular Meshes Using a Non-Uniform, Non-Stationary Loop Subdivision

Baoxing Zhang (), Hongchan Zheng and Huanxin Cao
Additional contact information
Baoxing Zhang: College of Statistics and Mathematics, Hebei University of Economics and Business, Shijiazhuang 050061, China
Hongchan Zheng: School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China
Huanxin Cao: School of Economics and Administration, Xi’an University of Technology, Xi’an 710054, China

Mathematics, 2025, vol. 13, issue 17, 1-15

Abstract: This paper presents a novel non-uniform, non-stationary Loop subdivision that directly interpolates arbitrary initial triangular meshes. This subdivision is derived by assigning distinct parameters for “vertex-point” and “edge-point” generation within the stencils of a uniform, non-stationary Loop subdivision. This underlying uniform, non-stationary scheme is obtained based on a suitably chosen iterative process. Crucially, we derive the limit positions of the initial points under this non-uniform scheme and decrease the assigned parameters to a single shape parameter when interpolating the initial mesh. Compared with the existing methods interpolating the initial mesh using approximating subdivision, this new one achieves interpolation in finite steps and without any additional adjustment to the initial mesh or subdivision rules. Several numerical examples are given to show the scheme’s interpolation accuracy and shape control capabilities.

Keywords: Loop subdivision; non-stationary; non-uniform; limit position; triangular mesh interpolation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/17/2862/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/17/2862/ (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:13:y:2025:i:17:p:2862-:d:1742338

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 ().