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 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.