# Triangular Meshes Delaunay Conforming Filter

Gelas, Arnaud, Gouaillard, Alexandre, Megason, Sean
Harvard Medical School

###### Published in The Insight Journal - 2008 July - December.
Submitted by null null on 2008-08-05T16:40:20Z.

The \emph{Delaunay triangulation} is the triangulation of a set of points which maximizes the minimum angle of all angles of the triangles, and thus triangle aspect ratios. So converting a non Delaunay triangulation into a Delaunay triangulation, \emph{Delaunay conforming}, improves the all triangle aspect ratios and avoid elongated triangles. Note that combining this filter with usual operations like smoothing will provide a better approximation and a better distribution a triangle aspect ratios. Here this document describes a new filter based on the $n$D $2$-manifold mesh data structure available in itk: \code{itk::QuadEdgeMesh}~\cite{itkQE} to produce (planar or surfacic) Delaunay triangulation from any non-Delaunay triangulation by edge flipping, by implementing the edge flipping method decribed in~\cite{Dyer2007sgp}.