circumcenters - Class: TriRep

Circumcenters of specified simplices

Syntax

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

Description

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.

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

Inputs

`TR`	Triangulation object.
`SI`	Column vector of simplex indices that index into the triangulation matrix `TR.Triangulation`. If `SI` is not specified the circumcenter information for the entire triangulation is returned, where the circumcenter associated with simplex `i` is the `i`'th row of `CC`.

Outputs

`CC`	`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)`.
`RCC`	Vector of length `length(SI)`, the number of specified simplices containing radii of the circumscribed circles or spheres.

Definitions

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

Examples

Example 1

Load a 2-D triangulation.

load trimesh2d
trep = TriRep(tri, x,y)

Compute the circumcenters.

cc = circumcenters(trep);
triplot(trep);
axis([-50 350 -50 350]);
axis equal;
hold on; 
plot(cc(:,1),cc(:,2),'*r'); 
hold off;

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

Example 2

Query a 3-D triangulation created with DelaunayTri. Compute the circumcenters of the first five tetrahedra.

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