Affine invariant triangulations

We study affine invariant 2D triangulation methods. That is, methods that produce the same for a point set S any (unknown) transformation of S. Our work is based on method by Nielson (1993) uses inverse covariance matrix to define an norm, denoted AS, and triangulation, DTAS[S]. revisit AS-norm from geometric perspective, show DTAS[S] can be seen as standard Delaunay transformed prove it retains all its well-known properties such being 1-tough, containing perfect matching, constant spanner complete graph extends hierarchy related structures minimum spanning tree, nearest neighbor graph, Gabriel relative neighborhood higher order versions these graphs. In addition, we provide different sorting vertices polygon P combined with known algorithms obtain other P. novel alternative computing are computationally simpler than using AS-norm. this focus theoretical part do not experimental results.