3D Point Cloud Surface Reconstruction Program Based on Crust Algorithm

The Crust algorithm is a widely-used 3D point cloud surface reconstruction method in computational geometry. Its core concept involves reconstructing object surfaces from point cloud geometric properties to obtain continuous triangular mesh models. This algorithm is particularly suitable for processing scattered point cloud data acquired from devices like 3D scanners.

The algorithm begins by performing Delaunay triangulation on the input point cloud, establishing topological connections between points. During implementation, computational geometry libraries typically provide functions like delaunay_triangulation() to create initial tetrahedral structures. The Crust algorithm then eliminates triangles that don't correspond to the actual object surface while retaining mesh structures that reflect geometric features. This critical step utilizes point cloud normal vectors or curvature information through functions such as calculate_normals() or estimate_curvature() to guide mesh generation, ensuring smooth and accurate surface reconstruction.

Compared to traditional methods like Poisson reconstruction or ball-pivoting algorithms, the Crust algorithm demonstrates superior performance when handling sharp edges and complex topological structures. It's particularly effective for objects with distinct geometric features such as mechanical components or architectural structures, rather than just smooth organic shapes. However, the algorithm shows sensitivity to point cloud density and noise, requiring preprocessing steps like point_cloud_filtering() and noise_reduction() functions for optimal results.

In practical applications, the Crust algorithm combined with efficient numerical computation libraries (such as CGAL) enables rapid meshing. The implementation typically involves calling library functions like crust_reconstruction() that handle the complex geometric computations internally. The final output produces triangular mesh models suitable for 3D printing, reverse engineering, or visualization analysis, often exported in standard formats like STL or OBJ through export_mesh() functions.