Connectivity of Graphs Induced by Directional Antennas

This paper addresses the problem of finding an orientation and a minimum radius for directional antennas of a fixed angle placed at the points of a planar set S, that induce a strongly connected communication graph. We consider problem instances in which antenna angles are fixed at 90 and 180 degrees, and establish upper and lower bounds for the minimum radius necessary to guarantee strong connectivity. In the case of 90-degree angles, we establish a lower bound of 2 and an upper bound of 7. In the case of 180-degree angles, we establish a lower bound of sqrt(3) and an upper bound of 1+sqrt(3). Underlying our results is the assumption that the unit disk graph for S is connected.Comment: 8 pages, 10 figure

Collective Construction of 2D Block Structures with Holes

In this paper we present algorithms for collective construction systems in which a large number of autonomous mobile robots trans- port modular building elements to construct a desired structure. We focus on building block structures subject to some physical constraints that restrict the order in which the blocks may be attached to the structure. Specifically, we determine a partial ordering on the blocks such that if they are attached in accordance with this ordering, then (i) the structure is a single, connected piece at all intermediate stages of construction, and (ii) no block is attached between two other previously attached blocks, since such a space is too narrow for a robot to maneuver a block into it. Previous work has consider this problem for building 2D structures without holes. Here we extend this work to 2D structures with holes. We accomplish this by modeling the problem as a graph orientation problem and describe an O(n^2) algorithm for solving it. We also describe how this partial ordering may be used in a distributed fashion by the robots to coordinate their actions during the building process.Comment: 13 pages, 3 figure

Unfolding Orthogrids with Constant Refinement

We define a new class of orthogonal polyhedra, called orthogrids, that can be unfolded without overlap with constant refinement of the gridded surface.Comment: 19 pages, 12 figure

Epsilon-Unfolding Orthogonal Polyhedra

An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connected, planar piece without overlap (except possibly at boundary points). It is a long unsolved problem to determine whether every polyhedron may be unfolded. Here we prove, via an algorithm, that every orthogonal polyhedron (one whose faces meet at right angles) of genus zero may be unfolded. Our cuts are not necessarily along edges of the polyhedron, but they are always parallel to polyhedron edges. For a polyhedron of n vertices, portions of the unfolding will be rectangular strips which, in the worst case, may need to be as thin as epsilon = 1/2^{Omega(n)}.Comment: 23 pages, 20 figures, 7 references. Revised version improves language and figures, updates references, and sharpens the conclusio

Unfolding Manhattan Towers

We provide an algorithm for unfolding the surface of any orthogonal polyhedron that falls into a particular shape class we call Manhattan Towers, to a nonoverlapping planar orthogonal polygon. The algorithm cuts along edges of a 4x5x1 refinement of the vertex grid.Comment: Full version of abstract that appeared in: Proc. 17th Canad. Conf. Comput. Geom., 2005, pp. 204--20

Grid Vertex-Unfolding Orthogonal Polyhedra

An edge-unfolding of a polyhedron is produced by cutting along edges and flattening the faces to a *net*, a connected planar piece with no overlaps. A *grid unfolding* allows additional cuts along grid edges induced by coordinate planes passing through every vertex. A vertex-unfolding permits faces in the net to be connected at single vertices, not necessarily along edges. We show that any orthogonal polyhedron of genus zero has a grid vertex-unfolding. (There are orthogonal polyhedra that cannot be vertex-unfolded, so some type of "gridding" of the faces is necessary.) For any orthogonal polyhedron P with n vertices, we describe an algorithm that vertex-unfolds P in O(n^2) time. Enroute to explaining this algorithm, we present a simpler vertex-unfolding algorithm that requires a 3 x 1 refinement of the vertex grid.Comment: Original: 12 pages, 8 figures, 11 references. Revised: 22 pages, 16 figures, 12 references. New version is a substantial revision superceding the preliminary extended abstract that appeared in Lecture Notes in Computer Science, Volume 3884, Springer, Berlin/Heidelberg, Feb. 2006, pp. 264-27

Mapping Historic Open Canopy Habitat using USGS Surface Soil Data

While open canopy habitat such as pine barrens, sand plains and coastal dune ecosystems were ONCE prevalent across the Northeastern United States, today this habitat is RARE. Open canopy habitat should receive high conservation priority due to the extensive range of species it supports. To understand the progression of habitat loss, and to better direct restoration efforts, estimates of the historic extent of open canopy habitat is useful. Because historical records are spotty, this study mapped an approximation of pine barrens, sand plains and coastal dune ecosystems in New York State based on present day surficial geology. We used ArcMap, a geographic information system (GIS) application, to create a predictive habitat model using data from the United States Geologic Survey and the North American Land Change Monitoring System. Even though, today, New York open canopy habitat is recognized in only 34,158 hectares, our model indicates that there are 1.5 million hectares of deep, sandy soils that could support this type of ecosystem. Therefore, about 12% of the total area of New York State contains sandy soils identified by our model, yet open canopy habitat is only recognized in about 2.28% of the sandy soils identified by our model. The wide spread nature of these soils, and the small area of open canopy habitat currently located on these soils, suggests that there are large areas of land where future restoration efforts could focus on to increase the area of present-day open canopy habitat and protect the vast number of species this habitat hosts

SAE Baja Dynamic Loading

Cal Poly’s SAE Baja team undertook a project to measure the loads applied to an offroad buggy via the ground, including any obstacles. Originally, the ground loads pertaining to suspension, drivetrain, and chassis were based on rough estimates and historical part failures. This led to large safety factors, overbuilt parts, unknown part life, and improperly designed points of failure. In order for the team’s designs to advance to the next level of competition, an accurate set of loading cases were required. The main focus of the project was the suspension loads measured with strain gauges and a shock potentiometer, however loading the chassis was also analyzed