# All nearest neighbors query¶

Some applications need to work with the interaction of points that are close to each other. For example, in one technique used for additive manufacturing, the particles in a powder bed are melted using a laser. Particle behavior against nearby particles determines droplet formation. The all-nearest-neighbors query takes as input a list of point positions and regions and a maximum radius. For each point, using the L2 norm as the distance measure, the query calculates the nearest neighbor point not in the same region, as shown in the figure.

Here is an example of query usage, from <axom>/src/axom/quest/tests/quest_all_nearest_neighbors.cpp.

#include "axom/quest/AllNearestNeighbors.hpp"


Query input consists of the points’ x, y, and z positions and region IDs, the point count, and the search radius.

  double x[] = {-1.2, -1.0, -0.8, -1.0, 0.8, 1.0, 1.2, 1.0};
double y[] = {0.0, -0.2, 0.0, 0.2, 0.0, -0.2, 0.0, 0.2};
double z[] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
int region[] = {0, 0, 0, 0, 1, 1, 1, 1};
int n = 8;
double limit = 1.9;


For each input point, the output arrays give the point’s neighbor index and squared distance from the point to that neighbor.

    axom::quest::all_nearest_neighbors(x, y, z, region, n, limit, neighbor, dsq);