Review of Three-Dimensional Model Simplification Algorithms Based on Quadric Error Metrics and Bibliometric Analysis by Knowledge Map

With the rapid advancement of computer graphics and three-dimensional modeling technology, the processing and optimization of three-dimensional (3D) models have become contentious research topics. In the context of mobile devices or web applications, situations may arise where it becomes necessary to load a 3D model with a substantial memory footprint in real-time or dynamically adjust the level of detail of a model based on the scene’s proximity. In such cases, it is imperative to optimize the original model to ensure smoothness and responsiveness. Due to the simplicity of their algorithm, quadric error metrics (QEMs) can deliver excellent results in simplifying 3D models while maintaining high efficiency. Therefore, QEM is widely employed in engineering applications within the realm of computer graphics development. Moreover, in the pursuit of enhanced quality and efficiency, numerous scholars have improved it based on QEM algorithms. This study aims to provide a systematic review and summary of the principles and applications of current research on QEM algorithms. First, we conducted a bibliometric analysis of 128 studies in related fields spanning from 1998 to 2022 using CiteSpace. This allowed us to sort QEM algorithms and gain insights into their development status and emerging trends. Second, we delve into the fundamental principles and optimizations of the QEM algorithms to provide a deeper understanding of their implementation process. Following that, we explore the advantages and limitations of the QEM algorithms in practical applications and analyze their potential in various domains, including virtual reality and game development. Finally, this study outlines future research directions, which encompass the development of more efficient error metric calculation methods, the exploration of adaptive simplification strategies, and the investigation of potential synergies with deep learning technologies. Current research primarily centers on enhancing QEM algorithms by incorporating additional geometric constraints to better differentiate between flat and irregular areas. This enables a more accurate determination of the areas that should be prioritized for folding. Nevertheless, it is important to note that these improvements may come at the cost of reduced computational efficiency. Therefore, future research directions could involve exploring parallel computing techniques and utilizing GPUs to enhance computational efficiency.