This paper introduces, analyzes, and compares various surface simplification methods for point-sampled geometry. The methods include incremental and hierarchical clustering, iterative simplification, and particle simulation, all of which work directly on point clouds without requiring intermediate tessellation. These methods aim to reduce the sampling density of point-based models while minimizing approximation error, especially in regions of high curvature. The paper presents a new method for computing numerical and visual error estimates for point-sampled surfaces, demonstrating the effectiveness of point-based surface simplification. The goal of point-based surface simplification is to find a point cloud with a target sampling rate that minimizes the distance between the simplified surface and the original surface. The paper discusses different simplification techniques, including clustering, iterative simplification, and particle simulation, and evaluates their performance in terms of surface quality, computational efficiency, and memory usage. Clustering methods are fast and memory-efficient, while iterative simplification focuses on high surface quality. Particle simulation allows intuitive control over the sampling distribution. The paper also introduces a method for measuring the distance between two point-sampled surfaces using an upsampled point cloud and the MLS projection operator. This method provides both numerical and visual error estimates, which are crucial for evaluating the quality of simplified surfaces. The results show that iterative simplification using quadric error metrics produces the lowest average surface error. The paper compares different simplification methods, including clustering, iterative simplification, and particle simulation, and discusses their advantages and disadvantages. Clustering methods are suitable for applications where the sampling distribution is important, while iterative simplification and particle simulation are more effective for achieving uniform sampling distributions. The paper also highlights the computational efficiency of the proposed methods, which are particularly useful for large point clouds. The paper concludes that the proposed methods are fast, robust, and produce high-quality surfaces without requiring tessellation of the underlying surface. The methods are applicable to a wide range of applications, including multiresolution modeling, compression, and efficient level-of-detail rendering. Future work includes out-of-core implementations, appearance-preserving simplification, and progressive schemes for representing point-based surfaces.This paper introduces, analyzes, and compares various surface simplification methods for point-sampled geometry. The methods include incremental and hierarchical clustering, iterative simplification, and particle simulation, all of which work directly on point clouds without requiring intermediate tessellation. These methods aim to reduce the sampling density of point-based models while minimizing approximation error, especially in regions of high curvature. The paper presents a new method for computing numerical and visual error estimates for point-sampled surfaces, demonstrating the effectiveness of point-based surface simplification. The goal of point-based surface simplification is to find a point cloud with a target sampling rate that minimizes the distance between the simplified surface and the original surface. The paper discusses different simplification techniques, including clustering, iterative simplification, and particle simulation, and evaluates their performance in terms of surface quality, computational efficiency, and memory usage. Clustering methods are fast and memory-efficient, while iterative simplification focuses on high surface quality. Particle simulation allows intuitive control over the sampling distribution. The paper also introduces a method for measuring the distance between two point-sampled surfaces using an upsampled point cloud and the MLS projection operator. This method provides both numerical and visual error estimates, which are crucial for evaluating the quality of simplified surfaces. The results show that iterative simplification using quadric error metrics produces the lowest average surface error. The paper compares different simplification methods, including clustering, iterative simplification, and particle simulation, and discusses their advantages and disadvantages. Clustering methods are suitable for applications where the sampling distribution is important, while iterative simplification and particle simulation are more effective for achieving uniform sampling distributions. The paper also highlights the computational efficiency of the proposed methods, which are particularly useful for large point clouds. The paper concludes that the proposed methods are fast, robust, and produce high-quality surfaces without requiring tessellation of the underlying surface. The methods are applicable to a wide range of applications, including multiresolution modeling, compression, and efficient level-of-detail rendering. Future work includes out-of-core implementations, appearance-preserving simplification, and progressive schemes for representing point-based surfaces.