`circumcenter`

Circumcenters (and circumradii) of the triangles or tetrahedra in a triangulation.

Category: Mathematics > Computational Geometry

Syntax

C = circumcenter(TR)

Circumcenter of every simplex, one row each.

C = circumcenter(TR, T)

Only for the simplices whose indices are in T.

[C, r] = circumcenter(___)

Also returns the circumradii.

Description

The circumcenter is the point equidistant from all vertices of a simplex; the common distance is the circumradius. In a Delaunay triangulation the circumcircle of each triangle contains no other point, which is the defining property of that triangulation. The circumcenters are also the vertices of the Voronoi diagram.

Input arguments

TR: A triangulation or delaunayTriangulation: 2-D, 3-D tetrahedral or a 3-D surface of triangles.
T: Optional column vector of simplex indices.

Output arguments

C: Circumcenter coordinates, one row per simplex.
r: Column vector of circumradii.

Example

Circumcenters of a square mesh

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

Output

C = 4×2

    1.0000    0.5000
    0.5000         0
         0    0.5000
    0.5000    1.0000
r = 4×1

    0.5000
    0.5000
    0.5000
    0.5000

circumcenter