Delaunay tessellation field estimator

This is a volume-covering division of space into triangles (tetrahedra in three dimensions), whose vertices are formed by the point distribution (see figure, upper right-hand frame).

This property of the Delaunay tessellation is exploited in step 2 of the DTFE, in which the local density is estimated at the locations of the sampling points.

For this purpose the density is defined at the location of each sampling point as the inverse of the area of its surrounding Delaunay triangles (times a normalization constant, see figure, lower right-hand frame).

Below the DTFE reconstruction of the 2dF Galaxy Redshift Survey is shown, revealing an impressive view on the cosmic structures in the nearby universe.

The fields are reconstructed locally without the application of an artificial or user-dependent smoothing procedure, resulting in an optimal resolution and the suppression of shot noise effects.