(Not recommended) Facets referenced by only one simplex
FF = freeBoundary(TR)
[FF XF] = freeBoundary(TR)
FF = freeBoundary(TR) returns a matrix
represents the free boundary facets of the triangulation. A facet
is on the free boundary if it is referenced by only one simplex (triangle/tetrahedron,
FF is of size
where m is the number of boundary facets and n is the number of vertices
per facet. The vertices of the facets index into the array of points
representing the vertex coordinates
TR.X. The array
be empty as in the case of a triangular mesh representing the surface
of a sphere.
[FF XF] = freeBoundary(TR) returns a matrix
of free boundary facets
TriRep to compute the boundary triangulation
of an imported triangulation.
Load a 3-D triangulation:
load tetmesh; trep = TriRep(tet, X);
Compute the boundary triangulation:
[tri xf] = freeBoundary(trep);
Plot the boundary triangulation:
trisurf(tri, xf(:,1),xf(:,2),xf(:,3), ... 'FaceColor','cyan', 'FaceAlpha', 0.8);
Perform a direct query of a 2-D triangulation created with
Plot the mesh:
x = rand(20,1); y = rand(20,1); dt = DelaunayTri(x,y); fe = freeBoundary(dt)'; triplot(dt); hold on;
Display the free boundary edges in red:
plot(x(fe), y(fe), '-r', 'LineWidth',2) ; hold off;
In this instance the free edges correspond to the convex hull
A simplex is a triangle/tetrahedron or higher-dimensional equivalent.
A facet is an edge of a triangle or a face of a tetrahedron.