Properties of the Delaunay Triangulation

Details Properties of the Delaunay Triangulation Properties of the Delaunay Triangulation

2003-12-02

arxiv.org/abs/math/0312050v1

Proc. 13th annu. ACM Sympos. Comput. Geom. ACM Press, 1997, p. 424-426

Mathematics

Metric Geometry

Scientific paper

We defined several functionals on the set of all triangulations of the finite system of points in d-space achieving global minimum on the Delaunay triangulation (DT). We consider a so called "parabolic" functional and prove it attains its minimum on DT in all dimensions. As the second example we treat "mean radius" functional (mean of circumcircle radii of triangles) for planar triangulations. As the third example we treat a so called "harmonic" functional. For a triangle this functional equals the sum of squares of sides over area. Finally, we consider a discrete analog of the Dirichlet functional. DT is optimal for these functionals only in dimension two.

Affiliated with

Also associated with

No associations

Rating

Properties of the Delaunay Triangulation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Properties of the Delaunay Triangulation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Properties of the Delaunay Triangulation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-688168