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freeBoundary

Free boundary facets

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Syntax

F = freeBoundary(TR)
[F,P] = freeBoundary(TR)

Description

F = freeBoundary(TR) returns the free boundary facets of the triangles or tetrahedra in TR. A facet in TR is on the free boundary if it is referenced by only one triangle or tetrahedron.

example

[F,P] = freeBoundary(TR) also returns a matrix containing the vertices of the free boundary facets.

example

Examples

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Open Live Script

You can use the freeBoundary function to highlight the outer edges of a 2-D Delaunay triangulation.

Create a triangulation from a 2-D set of points. 

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

Find the free boundary edges. 

F = freeBoundary(TR);

Plot the triangulation and highlight the free boundary edges in red. 

triplot(TR)
hold on
plot(x(F),y(F),'-r','LineWidth',2)

Figure contains an axes object. The axes object contains 3 objects of type line.

Open Live Script

You can use the freeBoundary function to extract the facets of a 3-D triangulation that cover the surface of an object.

Load a 3-D triangulation. 

load tetmesh
TR = triangulation(tet,X);

Compute the boundary triangulation. 

[F,P] = freeBoundary(TR);

Plot the boundary triangulation. 

trisurf(F,P(:,1),P(:,2),P(:,3), ...
       'FaceColor','cyan','FaceAlpha',0.8);

Figure contains an axes object. The axes object contains an object of type patch.

Input Arguments

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

Data Types: triangulation | delaunayTriangulation

Output Arguments

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Triangulation connectivity list, returned as a matrix.

If you call freeBoundary with one output argument, then the elements of F are row numbers in the Points property of the input triangulation. If you call freeBoundary with two output arguments, then the elements of F are row numbers in P.

Data Types: double

Free boundary points, returned as a matrix containing the coordinates of the vertices of the free boundary facets. Each row of P contains the coordinates of a vertex.

Data Types: double

Extended Capabilities

Thread-Based Environment
Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

Version History

Introduced in R2013a

See Also

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