Straight-Line Drawing of Quadrangulations

نویسنده

  • Éric Fusy
چکیده

This article introduces a straight-line drawing algorithm for quadrangulations, in the family of the face-counting algorithms. It outputs in linear time a drawing on a regular W×H grid such that W+H = n − 1 −∆, where n is the number of vertices and ∆ is an explicit combinatorial parameter of the quadrangulation.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

4-Labelings and Grid Embeddings of Plane Quadrangulations

We show that each quadrangulation on n vertices has a closed rectangle of influence drawing on the (n − 2) × (n − 2) grid. Further, we present a simple algorithm to obtain a straight-line drawing of a quadrangulation on the ⌈ n 2 ⌉ × ⌈ 3n 4 ⌉ grid. This is not optimal but has the advantage over other existing algorithms that it is not needed to add edges to the quadrangulation to make it 4-conn...

متن کامل

Lix, ´ Ecole Polytechnique Et Projet Algo, Inria Rocquencourt Combinatoire Des Cartes Planaires Et Applications Algorithmiques

This thesis describes algorithms on planar maps (graphs embedded in the plane without edge-crossings) based on their combinatorial properties. For several important families of planar maps (3-connected, triangulations, quadrangulations), efficient procedures of random generation, encoding, and straight-line drawing are described. In particular, the first optimal encoder for the combinatorial in...

متن کامل

Quadrangulations and 2-colorations

Any metric quadrangulation (made by segments of straight line) of a point set in the plane determines a 2-coloration of the set, such that edges of the quadrangulation can only join points with different colors. In this work we focus in 2-colorations and study whether they admit a quadrangulation or not, and whether, given two quadrangulations of the same 2-coloration, it is possible to carry o...

متن کامل

A Note on Minimum-Segment Drawings of Planar Graphs

A straight-line drawing of a planar graph G is a planar drawing of G, where each vertex is mapped to a point on the Euclidean plane and each edge is drawn as a straight line segment. A segment in a straight-line drawing is a maximal set of edges that form a straight line segment. A minimum-segment drawing of G is a straightline drawing of G, where the number of segments is the minimum among all...

متن کامل

Straight-Line Drawability of a Planar Graph Plus an Edge

We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The characterization enables a linear-time testing algorithm to determine whether an almostplanar graph admits a straight-line drawing, and a linear-time drawing algorithm that...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006