Triangulations and Applications


Book Description

This book will serve as a valuable source of information about triangulations for the graduate student and researcher. With emphasis on computational issues, it presents the basic theory necessary to construct and manipulate triangulations. In particular, the book gives a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. It also discusses various data structures used for the representation of triangulations.













Triangulation of the circle


Book Description

This book reveals the experiences and coexistence of the members of an atypical and cosmopolitan family, founded on a love triangle and trapped in a vicious circle of deception, terrorism and persecution. Over two generations, we will accompany them on their journey and desperate flight forward, showing us a cruel and changing world of false expectations, hypocrisy and mixed feelings of all kinds. We will dive into the psychological depths of the human being and his turbulent personal and family relationships.










An Upper Bound for Conforming Delaunay Triangulations


Book Description

Abstract: "A plane geometric graph C in R℗ conforms to another such graph G if each edge of G is the union of some edges of C. It is provedthat for every G with n vertices and m edges, there is a completion of a Delaunay triangulation of O(m℗N) points that conforms to G. The algorithm that constructs the points is also described."




Dynamic Constrained Delaunay Triangulation and Application to Multichip Module Layout


Book Description

Abstract: "The Voronoi diagram is a partition of a set S of N points in a plane, such that each region is the locus of the points (x, y) closer to a point of S than to any other point of S. If no four points are co-circular, the Delaunay triangulation is the straight-line dual of the Voronoi diagram. The triangulation may be constrained, that is, a set of straight-line segments may be prespecified. This thesis presents some characteristics of constrained Delaunay triangulation and introduces a set of numerically stable algorithms for incremently constructing and updating constrained Delaunay triangulation. The dynamic constrained Delaunay triangulation algorithms have been implemented in a layout system for multichip modules. It has been used as the underlying data representation for rubber-band sketch, a topological routing for one layer. We have proved the O(n log n) expected running time for the Delaunay triangulation algorithm."