circumcenter

Circumcenter of triangle or tetrahedron

Syntax

C = circumcenter(TR)

C = circumcenter(TR,ID)

[C,r] = circumcenter(___)

Description

C = circumcenter(TR) returns the coordinates of the circumcenters for each triangle or tetrahedron in the triangulation TR.

C = circumcenter(TR,ID) returns the coordinates of the circumcenters for the triangles or tetrahedra indexed by ID. The identification numbers of the triangles or tetrahedra in TR are the corresponding row numbers of the property TR.ConnectivityList.

[C,r] = circumcenter(___) also returns the radii of the circumscribed circles or spheres in TR for either of the previous syntaxes.

Examples

Compute Circumcenters of 2-D Triangulation

Load 2-D triangulation data and create a triangulation representation.

load trimesh2d
TR = triangulation(tri,x,y);

Compute the circumcenters of each triangle in TR.

C = circumcenter(TR);

Plot the triangulation along with the circumcenters in red. The $x$-coordinates of the circumcenters are contained in the first column of C and the corresponding $y$-coordinates are contained in the second column.

triplot(TR)
axis([-100 400 -50 350])
hold on 
plot(C(:,1),C(:,2),'r.')
hold off

Radii of Circumscribed Spheres

Create a Delaunay triangulation for a set of points.

rng default;
P = rand(10,3);
TR = delaunayTriangulation(P);

Compute the circumcenters of the first five tetrahedra in TR, and the radii of their circumscribed spheres.

[C,r] = circumcenter(TR,[1:5]')

C = 5×3

    0.5265    0.0860    1.1919
    0.1626    0.3794    2.3048
    0.3089    0.1067   -0.3349
    0.5708    0.4461    0.3751
    0.2805    0.7532    0.5855

r = 5×1

    0.6129
    1.5666
    1.1135
    0.4706
    0.3670

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 identification

scalar | column vector

Triangle or tetrahedron identification, 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 — Circumcenters

matrix

Circumcenters of triangles or tetrahedra, returned as a two-column matrix for 2-D coordinates or a three-column matrix for 3-D coordinates.

Data Types: double

r — Radii

scalar | vector

Radii of the circumscribed circles or spheres, returned as a scalar or 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