Algorithm for finding all k -nearest neighbours in three-dimensional scattered points and its application in reverse engineering
X Li, Robert J. Cripps · Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture · 2007
A fast and exact algorithm for computing the k-nearest neighbours, or k-closest points in terms of Euclidean distance, for all data in three-dimensional point clouds is presented that avoids using complicated Voronoi diagrams or Dirichlet tessellations. Experimental evidence suggests that the algorithm has a timing of O(n) for most practical values of k under the condition: k < 0.05 n, where n is the number of three-dimensional points in the cloud. Case studies are presented to illustrate the robustness and efficiency of the method and a comparison is made to an existing exact method.