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circumcenters

(Not recommended) Circumcenters of specified simplices

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circumcenters(TriRep) is not recommended. Use circumcenter(triangulation) instead.

TriRep is not recommended. Use triangulation instead.

Syntax

CC = circumcenters(TR)
CC = circumcenters(TR,SI)
[CC,RCC] = circumcenters(TR,SI)

Description

CC = circumcenters(TR) returns the coordinates of the circumcenter of each simplex in the triangulation. The circumcenter associated with simplex i is the i'th row of CC.

CC = circumcenters(TR,SI) returns the coordinates of the circumcenter of each specified simplex SI. CC is an m-by-n matrix, where m is of length length(SI), the number of specified simplices, and n is the dimension of the space where the triangulation resides.

example

[CC,RCC] = circumcenters(TR,SI) also returns the corresponding radii of the circumscribed circles or spheres.

example

Examples

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Open Live Script

Load a 2-D triangulation and create a TriRep object.

load trimesh2d
trep = TriRep(tri,x,y)
trep = 
  TriRep with properties:

                X: [180x2 double]
    Triangulation: [182x3 double]

Compute the circumcenters and plot them with the triangulation.

cc = circumcenters(trep);
triplot(trep)
axis equal
hold on
plot(cc(:,1),cc(:,2),'*r')
hold off

Figure contains an axes object. The axes object contains 2 objects of type line. One or more of the lines displays its values using only markers

The circumcenters represent points on the medial axis of the polygon.

Open Live Script

Create a 3-D triangulation with DelaunayTri. Compute the circumcenters and radii of the first five tetrahedra.

 X = rand(10,3);
 dt = DelaunayTri(X);
 [cc,rcc] = circumcenters(dt,[1:5]')
cc = 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


rcc = 5×1

    0.6129
    1.5666
    1.1135
    0.4706
    0.3670

Input Arguments

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Triangulation representation, specified as a TriRep or DelaunayTri object.

Simplex indices, specified as a column vector. SI contains simplex indices that index into the triangulation matrix TR.Triangulation.

Output Arguments

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Circumcenter coordinates, returned as an m-by-n matrix. m is the number of specified simplices and n is the dimension of the space where the triangulation resides. Each row CC(i,:) represents the coordinates of the circumcenter of simplex SI(i).

Radii of circumscribed circles or spheres, returned as a vector of length length(SI), the number of specified simplices.

More About

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Simplex

A simplex is a triangle/tetrahedron or higher-dimensional equivalent.

Version History

Introduced in R2009a

See Also

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