Plane geometry drawing tutorial

Drawing Plane Graphs

Automatic aesthetic drawing of plane graphs has recently created intense interest due to its broad applications, and as a consequence, a number of drawing methods, such as the straight line drawing, convex drawing, orthogonal drawing, rectangular drawing and box-rectangular drawing, have come out [8,9,3,4,5,6,7, 10,11,14,16,23,29,33]. In this talk we survey the recent results on these drawings ...

Algorithms for Drawing Plane Graphs

Graph drawing addresses the problem of constructing geometric representation of information and finds applications in almost every branch of science and technology. Efficient algorithms are essential for automatic drawings of graphs, and hence a lot of research has been carried out in the last decade by many researchers over the world to develop efficient algorithms for drawing graphs. In this ...

Model Theory and Geometry ( Tutorial )

Fuzzy plane geometry: triangles

A fuzzy triangle T (with a discrete-valued membership function) can be regarded as a nest of parallel-sided triangles T i with successively higher membership values. Such a nest is determined by its max projections on any two of its \sides". The area (perimeter) of T is a weighted sum of the areas (perimeters) of the T i 's. The side lengths and altitudes of T can also be deened as weighted sum...

Drawing Plane Triangulations with Few Segments

Dujmović, Eppstein, Suderman, and Wood showed that every 3-connected plane graph G with n vertices admits a straight-line drawing with at most 2.5n− 3 segments, which is also the best known upper bound when restricted to plane triangulations. On the other hand, they showed that there exist triangulations requiring 2n − 6 segments. In this paper we show that every plane triangulation admits a st...