incenter

Incenter of triangulation elements

Syntax

C = incenter(TR)

C = incenter(TR,ID)

[C,r] = incenter(___)

Description

C = incenter(TR) returns the coordinates of the incenters of each triangle or tetrahedron in the triangulation TR.

C = incenter(TR,ID) returns the coordinates of the incenter of each triangle or tetrahedron specified by ID. The identification numbers of the triangles or tetrahedra in TR are the corresponding row numbers of the property TR.ConnectivityList.

[C,r] = incenter(___) also returns the radii of the inscribed circles or spheres.

Examples

Compute Incenters of 2-D Delaunay Triangulation

Create a 2-D Delaunay triangulation.

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

Compute the incenters of the triangles.

C = incenter(TR);

Plot the triangles and incenters.

triplot(TR)
axis equal
axis([-0.2 1.2 -0.2 1.2])
hold on 
plot(C(:,1),C(:,2),'*r') 

3-D Triangulation

Load a 3-D triangulation.

load tetmesh

Calculate the incenter coordinates of the first five tetrahedra in the triangulation, in addition to the radii of their inscribed spheres.

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

C = 5×3

   -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

r = 5×1

    0.7528
    0.9125
    0.8430
    0.6997
    0.7558

Input Arguments

TR — Triangulation representation

scalar triangulation object

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

Data Types: triangulation | delaunayTriangulation

ID — Triangle or tetrahedron IDs

scalar | column vector

Triangle or tetrahedron IDs, specified as a scalar or a column vector whose elements each correspond to a single triangle or tetrahedron in the triangulation object. The identification number of each triangle or tetrahedron is the corresponding row number of the ConnectivityList property.

Data Types: double

Output Arguments

C — Incenters

matrix

Incenters, returned as a matrix whose rows contain the coordinates of an incenter.

Data Types: double

r — Radii

vector

Radii of the inscribed circles or spheres, returned as a vector.

Data Types: double

Extended Capabilities

Thread-Based Environment

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

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced in R2013a