A cell subdivision strategy for r-nearest neighbors computation

Due to the popularity of optical digitizing devices which can digitize an object easily and densely, the processing of a huge amount of data points has become important. Searching is one of the fundamental computational tasks in data analysis algorithms as it often dominates the computational efficiency significantly. The purpose of this study is to provide algorithms based on cell subdivision to search for the nearest neighbors adjacent to a given entity, where the given entity can be a point, a line segment or a triangle. The nearest-points search is used to find a set of points closest to a given point; the nearest-edges search is to find the edges that intersect the given edge; the nearest-triangles search is to find the mapping triangles of a given point or a given triangle. A detailed discussion for each of the above algorithms is described. Several examples are provided also to demonstrate the feasibility of the proposed algorithms.