Documentation

This is machine translation

Translated by
Mouse over text to see original. Click the button below to return to the English verison of the page.

circumcenters

Class: TriRep

(Not recommended) Circumcenters of specified simplices

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

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.

Input Arguments

 `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`.

Output Arguments

 `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 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]') ```