incenter

Class: triangulation

Incenter of triangle or tetrahedron

Syntax

IC = incenter(TR,ti)
[IC,r] = incenter(TR,ti)

Description

IC = incenter(TR,ti) returns the coordinates of the incenter of each triangle or tetrahedron specified by ti.

[IC,r] = incenter(TR,ti) also returns the radii of the inscribed circles or spheres.

Input Arguments

TR

Triangulation representation, see triangulation or delaunayTriangulation.

ti

Triangle or tetrahedron IDs, specified as a column vector.

Output Arguments

IC

Incenters, returned as a matrix. Each row of IC contains the coordinates of an incenter. For example, IC(j,:) is the incenter of ti(j).

r

Radii of the inscribed circles or spheres, returned as a vector. r(j) is the radius of the inscribed circle or sphere whose center is IC(j,:).

Definitions

Triangle or Tetrahedron ID

A row number of the matrix, TR.ConnectivityList. Use this ID to refer a specific triangle or tetrahedron.

Examples

expand all

Find Incenters in 3-D Triangulation

Load a 3-D triangulation.

load tetmesh

Calculate the incenters of the first five tetrahedra.

TR = triangulation(tet,X);
IC = incenter(TR,[1:5]')
IC =

   -6.1083  -31.0234    8.1439
   -2.1439  -31.0283    5.8742
   -1.9555  -31.9463    7.4112
   -4.3019  -30.8460   10.5169
   -3.1596  -29.3642    6.1851

Find Incenters in 2-D Delaunay Triangulation

Create the Delaunay triangulation.

x = [0 1 1 0 0.5]';
y = [0 0 1 1 0.5]';
DT = delaunayTriangulation(x,y);

Calculate incenters of the triangles

IC = incenter(DT)
IC =

    0.2071    0.5000
    0.5000    0.7929
    0.7929    0.5000
    0.5000    0.2071

Plot the triangles and incenters.

figure
triplot(DT)
axis equal
axis([-0.2 1.2 -0.2 1.2])
hold on
plot(IC(:,1),IC(:,2),'*r')
hold off

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