An Efficient and Regularized Modeling Method for Massive Scattered Data Combining Triangulated Irregular Network and Multiquadric Function

Haifei Liu, Yuhao Zhang, Xin Liu (), Ijaz Ahmed and Jianxin Liu
Additional contact information
Haifei Liu: School of Geosciences and Info-Physics, Central South University, Changsha 410083, China
Yuhao Zhang: School of Geosciences and Info-Physics, Central South University, Changsha 410083, China
Xin Liu: Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen 518055, China
Ijaz Ahmed: School of Geosciences and Info-Physics, Central South University, Changsha 410083, China
Jianxin Liu: School of Geosciences and Info-Physics, Central South University, Changsha 410083, China

Mathematics, 2025, vol. 13, issue 6, 1-16

Abstract: Spatial discrete data modeling plays a crucial role in geoscientific data analysis, with accuracy and efficiency being significant factors to consider in the modeling of massive discrete datasets. In this paper, an efficient and regularized modeling method, TIN-MQ, which integrates a triangulated irregular network (TIN) and a multiquadric (MQ) function, is proposed. Initially, a constrained residual MQ function and a damped least squares linear equation are constructed, and the conjugate gradient method is employed to solve this equation to enhance the modeling precision and stability. Subsequently, the divide-and-conquer algorithm is used to build the TIN, and, based on this TIN, the concave hull boundary of the discrete point set is constructed. The connectivity relationships between adjacent triangles in the TIN are then utilized to build modeling subdomains within the concave hull boundary. By integrating the OpenMP multithreading programming technology, the modeling tasks for all subdomains are dynamically distributed to all threads, allowing each thread to independently execute the assigned tasks, thereby rapidly enhancing the modeling efficiency. Finally, the TIN-MQ method is applied to model synthetic Gaussian model data, the submarine terrain of the Norwegian fjords, and elevation data from Hunan Province, demonstrating the method’s good fidelity, stability, and high efficiency.

Keywords: triangulated irregular network; multiquadric function; massive scattered data; stable modeling (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/2227-7390/13/6/978/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/6/978/ (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:6:p:978-:d:1613514

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 ().