Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
A Delaunay based numerical method for three dimensions: generation, formulation, and partition
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Umbrellas and polytopal approximation of the Euclidean ball
Journal of Approximation Theory
Optimal coarsening of unstructured meshes
Journal of Algorithms
Journal of Approximation Theory
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Hi-index | 0.01 |
In this paper, we show that both sphere covering problems and optimal polytope approximation of convex bodies are related to optimal Delaunay triangulations, which are the triangulations minimizing the interpolation error between function ||x||2 and its linear interpolant based on the underline triangulations. We then develop a new analysis based on the estimate of the interpolation error to get the Coxeter-Few-Rogers lower bound for the thickness in the sphere covering problem and a new estimate of the constant deln appeared in the optimal polytope approximation of convex bodies.