A simple proof for visibility paths in simple polygons

The purpose of this note is to give a simple proof for a necessary and sufficient condition for visibility paths in simple polygons. A visibility path is a curve such that every point inside a simple polygon is visible from at least one point on the path. This result is essential for finding the shortest watchman route inside a simple polygon specially when the route is restricted to curved paths

A linear time algorithm to remove winding of a simple polygon

AbstractIn this paper, we present a linear time algorithm to remove winding of a simple polygon P with respect to a given point q inside P. The algorithm removes winding by locating a subset of Jordan sequence that is in the proper order and uses only one stack

Negative Externalities on Property Values Resulting from Water Impairment: The Case of the Pigeon River Watershed

The following hypothesis was tested: Willingness to bear a negative water impairment externality differs between those who do and those who do not receive economic benefit from the impairment source, e.g., a paper mill. The hypothesis was tested using a hedonic analysis of ambient water quality in two discrete housing markets in the Pigeon River Watershed, which have been polluted by the operation of a paper mill. The results suggest that North Carolina residents of the subwatersheds with impaired river, who experience economic benefits from the paper mill in addition to harmful effects, do perceive the pollution as a negative externality, whereas they may have a willingness to bear a similar type of negative externality associated with impaired streams. In contrast, the effects of both degraded river and streams on property values is perceived as a negative externality by residents in the Tennessee side, who experience only harmful effects from the pollution. North Carolina residents may hold greater willingness to bear the harmful effects of pollution as a given condition in their decision-making process because they receive economic benefits from the paper mill, while this internalization of the negative externality is weaker for residents in the Tennessee side.negative Externalities, water quality, spatial hedonic model, Environmental Economics and Policy,

Partially Walking a Polygon

Deciding two-guard walkability of an n-sided polygon is a well-understood problem. We study the following more general question: How far can two guards reach from a given source vertex while staying mutually visible, in the (more realistic) case that the polygon is not entirely walkable? There can be Theta(n) such maximal walks, and we show how to find all of them in O(n log n) time