# nearestNeighbor

Vertex closest to specified point

## Description

example

ID = nearestNeighbor(TR,P) returns the IDs of the vertices closest to the query points in P. Each row in the matrix P contains the coordinates of a query point.

ID = nearestNeighbor(TR,x,y) specifies the x-coordinates and y-coordinates of 2-D query points as separate column vectors.

example

ID = nearestNeighbor(TR,x,y,z) specifies the x-coordinates, y-coordinates, and z-coordinates of 3-D query points as separate column vectors.

example

[ID,d] = nearestNeighbor(___) also returns the Euclidean distance between each query point and its nearest neighbor for any of the previous syntaxes.

## Examples

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Compute the nearest neighbors in a 3-D triangulation.

Create a 3-D Delaunay triangulation.

P = [1 1 0; -1 1 0; -1 -1 0; 1 -1 0; 0 0 2; 0 0 0];
TR = delaunayTriangulation(P);

Plot the triangulation and a query point.

tri = TR(:,:);
trisurf(tri,P(:,1),P(:,2),P(:,3),'FaceAlpha',0.5)
hold on
x = 0;
y = -0.5;
z = 2;
plot3(x,y,z,'k*')

Find the coordinates of the nearest neighbor to the query point.

ID = nearestNeighbor(TR,x,y,z);
C = TR.Points(ID,:)
C = 1×3

0     0     2

Compute the nearest neighbors in a 2-D triangulation.

Create a 2-D triangulation.

C = [5 3 1; 3 2 1; 3 4 2; 4 6 2];
TP = [2.5 8.0; 6.5 8.0; 2.5 5.0; 6.5 5.0; 1.0 6.5; 8.0 6.5];
TR = triangulation(C,TP);

Define two query points.

P = [2 4; 6 6.5];

Plot the triangulation and the query points.

triplot(TR)
hold on
plot(P(:,1),P(:,2),'k*')
ylim([1.5 8.5])
xlim([0.5 8.5])

Find the nearest neighbors to the query points and the distances between them.

[ID,d] = nearestNeighbor(TR,P);

Highlight in red the points in the triangulation that are the nearest neighbors to the query points.

N = TP(ID,:);
plot(N(:,1),N(:,2),'*r')

Display the distance between each query point and its nearest neighbor.

d
d = 2×1

1.1180
1.5811

## Input Arguments

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Triangulation representation, specified as a scalar triangulation or delaunayTriangulation object. nearestNeighbor does not support delaunayTriangulation objects with constrained edges.

Data Types: triangulation | delaunayTriangulation

Query points, specified as a matrix with 2 or 3 columns. P contains the x-coordinates, y-coordinates, and (possibly) z-coordinates of the query points.

Data Types: double

x-coordinates of query points, specified as a column vector.

Data Types: double

y-coordinates of query points, specified as a column vector.

Data Types: double

z-coordinates of query points, specified as a column vector.

Data Types: double

## Output Arguments

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Vertex IDs of the nearest neighbors to the query points, returned as a column vector. A vertex ID is the row number of the corresponding vertex in the Points property.

Data Types: double

Euclidean distances from the query points to their nearest neighbors, returned as a column vector the same length as ID.

Data Types: double

## Version History

Introduced in R2013a