GPU‐Accelerated Optimization of Discrete Ricci Flow for High‐Resolution Triangular Meshes

ABSTRACT The discrete Ricci flow is a powerful tool for designing Riemannian metrics on surfaces by user‐defined Gaussian curvatures, which has been widely applied in computer graphics, medical image processing, and computer vision. The discrete Ricci flow algorithm performs surface parameterization by dynamically adjusting edge lengths to conform to a prescribed target curvature. During execution, it requires frequent updates of mesh edge lengths, repeated construction of Hessian matrices, and solving systems of equations, resulting in substantial computational overhead. Classical methods typically employ half‐edge data structures to traverse mesh edges, vertices, and faces for geometric computations. However, as model scale increases, their computational complexity grows exponentially, making large‐scale model processing impractical within acceptable timeframes. To address this computational bottleneck, this paper proposes a GPU‐accelerated Ricci flow computation framework. By reformulating the original iterative process into parallelizable matrix operations, this framework leverages GPU hardware advantages in parallel computing, significantly improving algorithm efficiency. Experimental results demonstrate that the GPU implementation reduces computation time substantially compared to traditional methods, with acceleration effects becoming more pronounced as model resolution increases. This approach not only provides a viable pathway for handling high‐resolution mesh parameterization but also offers new insights for real‐time geometric processing and interactive applications.