Calculation of 3D Scattered Point Cloud Curvature with Code Implementation

Several computational methods are available for calculating curvature properties of three-dimensional scattered point clouds, including principal curvatures, Gaussian curvature, and mean curvature. The Principal Component Analysis (PCA) method is widely adopted in computer vision applications, where eigenvalue decomposition of the covariance matrix from local point neighborhoods determines curvature directions and magnitudes. Alternatively, surface fitting approaches involve constructing mathematical surfaces (such as quadric or polynomial surfaces) to approximate the point cloud geometry. These fitting methods can be categorized into local and global techniques. Local methods compute curvature at each point by fitting surfaces to neighboring points using k-nearest neighbors or radius-based neighborhood search algorithms, while global methods fit a single surface to the entire point cloud dataset before curvature extraction.

The accompanying package provides comprehensive implementation details through readme documentation and demonstration files. The readme file contains technical specifications for curvature calculation algorithms, parameter configuration guidelines, and API references for key functions including neighborhood selection and curvature tensor computation. Demo files include sample point cloud datasets (in PLY or PCD formats) with complete MATLAB/Python code examples demonstrating curvature calculation workflows, visualization techniques, and result validation methods. This resource enables efficient curvature analysis for various 3D scattered point cloud applications in computer vision and geometric processing.