How to Draw a Planarization

How to Draw a Planarization

In this thesis we study the problem of computing a straight-line representation of a planarization with a fixed combinatorial structure. By the results of Mnëv [Mnë88] and Shor [Sho91] this problem is as hard as the Existential Theory of the Reals (∃R-Complete). We present a heuristic called Geometric Planarization Drawing to compute a straight-line representation of a planarization. We take an...

How to draw a group?

A map is at the same time a group. To represent a map (that is, a graph drawn on the sphere or on another surface) we usually use a pair of permutations on the set of the \ends" of edges. These permutations generate a group which we call a cartographic group. The main motivation for the study of the cartographic group is the so-called theory of \dessins d'enfants" of Grothendieck, which relates...

How to draw a hexagon

Pictures of the G2(2) hexagon and its dual are presented. A way to obtain these pictures is discussed. 1. Introduction This paper presents pictures of the two classical generalised hexagons over the eld with two elements. Information on these generalised hexagons is employed so that the pictures make some properties of these hexagons obvious. Familiarity with the theory of generalised polygons ...

How to Draw the Minimum

How to Draw a Sequence Diagram

In this paper, we consider the aesthetic criteria and constraints related to the layouts of UML sequence diagrams. We consider the applicability of the traditional graph drawing aesthetics in drawing sequence diagrams. Because of the special nature of sequence diagrams, many of these aesthetics are not applicable. Based on our view on how these diagrams are read or viewed, we propose some new a...