This paper describes a new technique for dynamic binary space partitioning with applications to the dynamic hidden surface removal problem of polygons. The dynamic hidden surface removal problem is to determine and maintain visible surfaces in 3-D set of polygons from a given viewpoint under changes to the scene and it allows for eecient insertions and deletions of polygons in a 3-D scene. The ...

Two vertex-labelled polygons are compatible if they have the same clockwise cyclic ordering of vertices. The definition extends to polygonal regions (polygons with holes) and to triangulations—for every face, the clockwise cyclic order of vertices on the boundary must be the same. It is known that every pair of compatible n-vertex polygonal regions can be extended to compatible triangulations b...

We are interested in the problem of covering simple orthogonal polygons with the minimum number of r-stars; an orthogonal polygon is an r-star if it is orthogonally convex and star-shaped. The problem has been considered by Worman and Keil who described an algorithm running in O(n 17 poly-log n) time where n is the size of the input polygon. In this paper, we consider the above problem on simpl...

Belleville, P. and T.C. Shermer, Probing polygons minimally is hard, Computational Geometry: Theory and Applications 2 (1993) 255-265. Let r be a set of convex unimodal polygons in fixed position and orientation. We prove that the problem of determining whether k finger probes are sufficient to distinguish among the polygons in f is NP-complete for two types of finger probes. This implies that ...

A total of 21 gauges across the mountainous leeward portion of the island of Oʻahu, Hawaiʻi, were used to compare rainfall interpolation methods and assess rainfall spatial variability over a 34-month monitoring period from 2005 to 2008. Traditional and geostatistical interpolation methods, including Thiessen polygon, inverse distance weighting (IDW), linear regression, ordinary kriging (OK), a...

This paper presents three multivariate geostatistical algorithms for incorporating a digital elevation model into the spatial prediction of rainfall: simple kriging with varying local means; kriging with an external drift; and colocated cokriging. The techniques are illustrated using annual and monthly rainfall observations measured at 36 climatic stations in a 5000 km region of Portugal. Cross...

We consider combinatorial problems motivated by sensor networks for beacon-based point-to-point routing and covering. A beacon b is a point that can be activated to effect a ‘magnetic pull’ toward itself everywhere in a polygonal domain P . The routing problem asks how many beacons are required to route between any pair of points in a polygonal domain P . In simple polygons with n vertices we s...

Current interactive hybrid (combined volume and surface) rendering techniques are only able to embed opaque polygonal objects and therefore cannot provide accurate depth perception of semi-transparent surfaces. This paper proposes a volume rendering approach based on a Multi-Layer Depth Map (MDM) that enables multiple translucent polygons to be embedded. This novel approach generates multiple d...

We describe an algorithm for computing the separating common tangents of two simple polygons using linear time and only constant workspace. A tangent of a polygon is a line touching the polygon such that all of the polygon lies to the same side of the line. A separating common tangent of two polygons is a tangent of both polygons where the polygons are lying on different sides of the tangent. E...

Let n be a positive integer, not a power of two. A Reinhardt polygon is a convex n-gon that is optimal in three different geometric optimization problems: it has maximal perimeter relative to its diameter, maximal width relative to its diameter, and maximal width relative to its perimeter. For almost all n, there are many Reinhardt polygons with n sides, and many of them exhibit a particular pe...