# pointLocation

Triangle or tetrahedron enclosing point

## Description

example

ID = pointLocation(TR,P) returns the IDs of the triangles or tetrahedra enclosing the query points in P. Each row in the matrix P contains the coordinates of a query point.

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

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

example

[ID,B] = pointLocation(___) also returns the barycentric coordinates of each query point with respect to its enclosing triangle or tetrahedron for any of the previous syntaxes.

## Examples

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Find the triangles of a triangulation that enclose a set of query points.

Define the points and connectivity of a triangulation.

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];
C = [5 3 1; 3 2 1; 3 4 2; 4 6 2];
TR = triangulation(C,TP);

Define two query points.

P = [2.25 7; 6 6.5];

Plot the triangulation and the query points.

triplot(TR)
hold on
plot(P(:,1),P(:,2),'k*')
ylim([4 9])
xlim([0 9])

Determine the IDs of the triangles that enclose each query point.

ID = pointLocation(TR,P)
ID = 2×1

1
3

Highlight the triangles that enclose the query points in red.

triplot(TR.ConnectivityList(ID,:),TP(:,1),TP(:,2),'r')

Find the tetrahedra of a 3-D triangulation that enclose a set of query points.

Create a Delaunay triangulation from a set of 3-D points.

rng('default')
x = rand([20 1]);
y = rand([20 1]);
z = rand([20 1]);
TR = delaunayTriangulation(x,y,z);

Find the IDs of the tetrahedra that enclose the query points, and compute the barycentric coordinates of the query points.

P = [0.7 0.6 0.3; 0.5 0.5 0.5];
[ID,B] = pointLocation(TR,P)
ID = 2×1

9
8

B = 2×4

0.2046    0.0893    0.5721    0.1340
0.1900    0.1495    0.6422    0.0183

## Input Arguments

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Triangulation representation, specified as a scalar triangulation or delaunayTriangulation object.

Data Types: triangulation | delaunayTriangulation

Query points, specified as a 2-column matrix (2-D) or a 3-column matrix (3-D). 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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Triangle or tetrahedra IDs of the triangles or tetrahedra enclosing the query points, returned as a column vector. A triangle or tetrahedron ID is the row number of the corresponding triangle or tetrahedron in the ConnectivityList property.

If a query point lies on the boundary of two or more triangles or tetrahedra, then the largest ID is returned.

ID contains NaN values for points that are not located in a triangle or tetrahedron of the triangulation.

Data Types: double

Barycentric coordinates of each query point with respect to its enclosing triangle or tetrahedron, returned as a 3-column matrix (2-D) or a 4-column matrix (3-D).

Data Types: double

## Version History

Introduced in R2013a