An Efficient and Regularized Modeling Method for Massive Scattered Data Combining Triangulated Irregular Network and Multiquadric Function
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 ir...
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MDPI AG
2025-03-01
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| Series: | Mathematics |
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| author | Haifei Liu Yuhao Zhang Xin Liu Ijaz Ahmed Jianxin Liu |
| author_facet | Haifei Liu Yuhao Zhang Xin Liu Ijaz Ahmed Jianxin Liu |
| author_sort | Haifei Liu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d4a344094a614f4b8c06ed6640ccd2b6 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-d4a344094a614f4b8c06ed6640ccd2b62025-08-20T01:49:04ZengMDPI AGMathematics2227-73902025-03-0113697810.3390/math13060978An Efficient and Regularized Modeling Method for Massive Scattered Data Combining Triangulated Irregular Network and Multiquadric FunctionHaifei Liu0Yuhao Zhang1Xin Liu2Ijaz Ahmed3Jianxin Liu4School of Geosciences and Info-Physics, Central South University, Changsha 410083, ChinaSchool of Geosciences and Info-Physics, Central South University, Changsha 410083, ChinaDepartment of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen 518055, ChinaSchool of Geosciences and Info-Physics, Central South University, Changsha 410083, ChinaSchool of Geosciences and Info-Physics, Central South University, Changsha 410083, ChinaSpatial 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.https://www.mdpi.com/2227-7390/13/6/978triangulated irregular networkmultiquadric functionmassive scattered datastable modeling |
| spellingShingle | Haifei Liu Yuhao Zhang Xin Liu Ijaz Ahmed Jianxin Liu An Efficient and Regularized Modeling Method for Massive Scattered Data Combining Triangulated Irregular Network and Multiquadric Function Mathematics triangulated irregular network multiquadric function massive scattered data stable modeling |
| title | An Efficient and Regularized Modeling Method for Massive Scattered Data Combining Triangulated Irregular Network and Multiquadric Function |
| title_full | An Efficient and Regularized Modeling Method for Massive Scattered Data Combining Triangulated Irregular Network and Multiquadric Function |
| title_fullStr | An Efficient and Regularized Modeling Method for Massive Scattered Data Combining Triangulated Irregular Network and Multiquadric Function |
| title_full_unstemmed | An Efficient and Regularized Modeling Method for Massive Scattered Data Combining Triangulated Irregular Network and Multiquadric Function |
| title_short | An Efficient and Regularized Modeling Method for Massive Scattered Data Combining Triangulated Irregular Network and Multiquadric Function |
| title_sort | efficient and regularized modeling method for massive scattered data combining triangulated irregular network and multiquadric function |
| topic | triangulated irregular network multiquadric function massive scattered data stable modeling |
| url | https://www.mdpi.com/2227-7390/13/6/978 |
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