The idea of triangulation arises in two contexts in Davidson’s work. In the first, triangulation is used as an analogy to help explain the central idea of a transcendental argument designed to show that we can have the concept of objective truth only in the context of communication. In the second, the triangulation of two speakers responding to each other and to a common cause of similar respon...

Given a set S of points in the plane, a triangulation of S is a partition of the convex hull of S into triangles whose vertices are the points of S. A triangulation of S is said to be Delaunay if no point of S lies inside the triangles’ circumcircles. In this thesis, we study a generalization of these notions to a set S of disjoint segments in the plane. At first, we define a new family of diag...

We show that the length of the minimum weight Steiner triangulation (MWST) of a point set can be approximated within a constant factor by a triangulation algorithm based on quadtrees. In O(n log n) time we can compute a triangulation with O(n) new points, and no obtuse triangles, that approximates the MWST. We can also approximate the MWST with triangulations having no sharp angles. We generali...

We study the problem of acute triangulations of convex polyhedra and the space Rn. Here an acute triangulation is a triangulation into simplices whose dihedral angles are acute. We prove that acute triangulations of the n–cube do not exist for n ≥ 4. Further, we prove that acute triangulations of the space Rn do not exist for n ≥ 5. In the opposite direction, in R3, we present a construction of...

We describe a method to triangulate P × Q which is very useful to obtain triangulations of the d-cube I of good asymptotic efficiency. The main idea is to triangulate P × Q from a triangulation of Q and another of P ×∆, where ∆ is a simplex of dimension m− 1, which is supposed to be smaller than dim(Q) = n− 1. Last triangulation will induce a triangulation of P ×∆. Thus, considering P := I and ...

A view-dependent multiresolution triangulation algorithm is presented for a real-time flythrough. The triangulation of the terrain is generated incrementally onthe-fly during the rendering time. We show that since the view changes smoothly only a few incremental modifications are required to update the triangulation to a new view. The resulting triangles form a multiresolution Delaunay triangul...

Considering the problem of the minimal triangulation for a given polyhedra (dividing polyhedra into tetrahedra) it is known that the cone triangulation provides the number of tetrahedra which is the smallest, or the closest to it. It is also shown that when we want to know whether the cone triangulation is the minimal one, it is necessary to find the order of all vertices, as well as the order ...

We introduce the notion of generalized Delaunay triangulation of a planar straight-line graph G = (V, E) in the Euclidean plane and present some characterizations of the triangulation. It is shown that the generalized Delaunay triangulation has the property that the minimum angle of the triangles in the triangulation is maximum among all possible triangulations of the graph. A general algorithm...

It is shown that there exists a dihedral acute triangulation of the three-dimensional cube. The method of constructing the acute triangulation is described, and symmetries of the triangulation are discussed.