This paper presents a novel method for smoothing irregularly triangulated data to remove noise and uneven edges while preserving desirable geometric features. The approach includes three key features: implicit integration for efficiency and stability, a scale-dependent Laplacian operator to improve diffusion, and a robust curvature flow operator for shape smoothing. The method also supports automatic volume preservation and constraints on mesh point positions. The authors compare their method to previous operators and algorithms, demonstrating its mathematical advantages and practical effectiveness. They provide examples to illustrate the quality of the results, showing that their method offers better smoothing and stability compared to existing techniques. The paper discusses the implementation details, including the use of preconditioned bi-conjugate gradient (PBCG) for solving linear systems and the derivation of a scale-dependent Laplacian operator. The authors conclude by highlighting the advantages of their implicit fairing method and suggesting potential improvements, such as multigrid preconditioning and subdivision techniques.This paper presents a novel method for smoothing irregularly triangulated data to remove noise and uneven edges while preserving desirable geometric features. The approach includes three key features: implicit integration for efficiency and stability, a scale-dependent Laplacian operator to improve diffusion, and a robust curvature flow operator for shape smoothing. The method also supports automatic volume preservation and constraints on mesh point positions. The authors compare their method to previous operators and algorithms, demonstrating its mathematical advantages and practical effectiveness. They provide examples to illustrate the quality of the results, showing that their method offers better smoothing and stability compared to existing techniques. The paper discusses the implementation details, including the use of preconditioned bi-conjugate gradient (PBCG) for solving linear systems and the derivation of a scale-dependent Laplacian operator. The authors conclude by highlighting the advantages of their implicit fairing method and suggesting potential improvements, such as multigrid preconditioning and subdivision techniques.