The Crust Algorithm is an algorithm for the surface reconstruction from unorganized cloud points in 3D. This is the first algorithm which is developed for this problem. For a given point cloud from a smooth surface, the output guarantees to be topologically correct and as the sampling density increases it moves towards a common point to the original surface. According to the definition of a good sample the sampling density varies locally, strictly captures the intuitive notion so that the featureless areas can be reconstructed from fewer clouds. The algorithm is based on the three-dimensional Voronoi diagrams.