Work

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

Year: 2025

Type: article

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.

Source: Mathematics

DOI: 10.3390/math13172862

Authors: Baoxing Zhang, Hongchan Zheng, Huanxin Cao

Institutions: Hebei University of Economics and Business, Northwestern Polytechnical University, Xi'an University of Technology

Language: English

Topic: Advanced Numerical Analysis Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Natural Science Basic Research Program of Shaanxi Province