ON GOOD TRIANGULATIONS IN THREE DIMENSIONS

Good Triangulations in Plane

Good triangulations yield good tours

Consider the following heuristic for planar Euclidean instances of the traveling salesman problem (TSP): select a subset of the edges which induces a planar graph, and solve either the TSP or its graphical relaxation on that graph. In this paper, we give several motivations for considering this heuristic, along with extensive computational results. It turns out that the Delaunay and greedy tria...

Three Dimensional Triangulations in Cgal

This paper describes the design and the implementation of the three-dimensional trian-gulation package 1 of the Computational Geometric Algorithms Library Cgal 2. We focus on representation issues and especially insist on how the cases of degenerate dimensions are treated. The algorithmic issues are not examined in this short paper.

Geometric and combinatorial properties of well-centered triangulations in three and higher dimensions

An n-simplex is said to be n-well-centered if its circumcenter lies in its interior. We introduce several other geometric conditions and an algebraic condition that can be used to determine whether a simplex is n-well-centered. These conditions, together with some other observations, are used to describe restrictions on the local combinatorial structure of simplicial meshes in which every simpl...

Dimensions of Spline Spaces over Unconstricted Triangulations

One of the puzzlingly hard problems in Computer Aided Geometric Design and Approximation Theory is that of finding the dimension of the spline space of C piecewise degree n polynomials over a 2D triangulation Ω. We denote such spaces by Sr n(Ω). In this note, we restrict Ω to have a special structure, namely to be unconstricted. This will allow for several exact dimension formulas.