Socioscientific controversies are “extended argumentative engagements over socially significant issues ... comprising communicative events and practices in and from both scientific and nonscientific spheres” (Stewart, 2009, p. 125). While global warming is not controversial among the vast majority of climate scientists, socioscientific controversies over global warming abound in various media, ...

In Chapter 1 it was shown that Fisk's proof of the art gallery theorem can be converted into an algorithm that covers a polygon of n vertices with [n/3\ guards in O{n logn) time. Although [n/3\ is necessary in some cases, often this is far more guards than are needed to cover a particular polygon. For example, convex polygons only require one guard, but Avis and Toussaint's algorithm would stil...

Let Fq be a finite field of cardinality q and characteristic p. Let P (x) be any one-variable Laurent polynomial over Fq of degree (d1, d2) respectively and p d1d2. For any fixed s ≥ 1 coprime to p, we prove that the q-adic Newton polygon of the L-functions of exponential sums of P (xs) has a tight lower bound which we call Hodge-Stickelberger polygon, depending only on the d1, d2, s and the re...

How many different classes of partially distinguishable landmarks are needed to ensure that a robot can always see a landmark without simultaneously seeing two of the same class? To study this, we introduce the chromatic art gallery problem. A guard set S ⊂ P is a set of points in a polygon P such that for all p ∈ P , there exists an s ∈ S such that s and p are mutually visible. Suppose that tw...

The art gallery problem asks for the smallest number of guards required to see every point of the interior of a polygon P . We introduce and study a similar problem called the chromatic art gallery problem. Suppose that two members of a finite point guard set S ⊂ P must be given different colors if their visible regions overlap. What is the minimum number of colors required to color any guard s...

In 1973, Victor Klee posed the problem of determining the minimum number of guards sufficient to cover the interior of an n-wall art gallery room (Honsberger 1976). He posed this question extemporaneously in response to a request from Vasek Chvatal (at a conference at Stanford in August) for an interesting geometric problem, and Chvatal soon established what has become known as "Chvatal's Art G...

Consider a set of circles of the same length and r irregular polygons with vertices on a circle of this length. Each of the polygons has to be arranged on a given subset of all circles and the positions of the polygon on the different circles are depending on each other. How should the polygons be arranged relative to each other to minimize some criterion function depending on the distances bet...

The straight skeleton of a simple polygon is defined as the trace of the vertices when the initial polygon is shrunken in self-parallel manner [2]. In this paper, we propose a simple algorithm for drawing the straight skeleton of a monotone polygon. The time and space complexities of our algorithm are O(nlogn) and O(n) respectively.

The article provides a set of algorithms for performing set operations on polygonal regions in the plane using standard oating point arithmetic. The algorithms are robust, guaranteeing both topological consistency and numerical accuracy. Each polygon edge is modeled as an implicit or explicit polygonal curve which stays within some distance of the original line segment. If the curve is implicit...

Graphs have enormous usage in software engineering, network and electrical engineering. In fact graphs drawing is a geometrically representation of information. Among graphs, trees are concentrated because of their ability in hierarchical extension as well as processing VLSI circuit. Many algorithms have been proposed for drawing binary trees within polygons. However these algorithms generate b...