436 research outputs found
Unfolding Orthogonal Terrains
It is shown that every orthogonal terrain, i.e., an orthogonal (right-angled)
polyhedron based on a rectangle that meets every vertical line in a segment,
has a grid unfolding: its surface may be unfolded to a single non-overlapping
piece by cutting along grid edges defined by coordinate planes through every
vertex.Comment: 7 pages, 7 figures, 5 references. First revision adds Figure 7, and
improves Figure 6. Second revision further improves Figure 7, and adds one
clarifying sentence. Third corrects label in Figure 7. Fourth revision
corrects a sentence in the conclusion about the class of shapes now known to
be grid-unfoldabl
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
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
Bio-inspired Tensegrity Soft Modular Robots
In this paper, we introduce a design principle to develop novel soft modular
robots based on tensegrity structures and inspired by the cytoskeleton of
living cells. We describe a novel strategy to realize tensegrity structures
using planar manufacturing techniques, such as 3D printing. We use this
strategy to develop icosahedron tensegrity structures with programmable
variable stiffness that can deform in a three-dimensional space. We also
describe a tendon-driven contraction mechanism to actively control the
deformation of the tensegrity mod-ules. Finally, we validate the approach in a
modular locomotory worm as a proof of concept.Comment: 12 pages, 7 figures, submitted to Living Machine conference 201
Ethnographic Advocacy Against the Death Penalty
This article develops the concept of âethnographic advocacyâ to make sense of the humanizing, openâended knowledge practices involved in the defense of criminal defendants charged with capital murder. Drawing from anthropological fieldwork with wellârespected figures in the American capital defense bar, as well as my own professional experience as an investigator specializing in death penalty sentencing mitigation, I argue that effective advocacy for life occurs through qualitative knowledge practices that share notable methodological affinities with contemporary anthropological ethnography. The article concludes with a preliminary exploration of what the concept of ethnographic advocacy might reveal about academic anthropology\u27s own advocative engagements
'Chariots of Fire': The Evolution of Tank Technology, 1915-1945
We revisit the notion of technological trajectories by means of a detailed case-study of the evolution of tank technology between 1915 and 1945. We use principal component analysis to analyze the distribution of technological characteristics and how they map into specific service characteristics. We find that, despite the existence of differences in technical leadership, tank designs of different countries show a high degree of overlap and closeness along a common technological trajectory. In the conclusions, we speculate on whether this pattern can be explained by common heuristics that influenced the rate and direction of design activities or by doctrinal viewpoints influencing the development and use of tanks on the battlefield.Technological trajectories, Technological paradigms, Tanks.
Constrained Shortest Paths in Terrains and Graphs
Finding a shortest path is one of the most well-studied optimization problems. In this thesis we focus on shortest paths in geometric and graph theoretic settings subject to different feasibility constraints that arise in practical applications of such paths.
One of the most fundamental problems in computational geometry is finding shortest paths in terrains, which has many applications in robotics, computer graphics and Geographic Information Systems (GISs). There are many variants of the problem in which the feasibility of a path is determined by some geometric property of the terrain. One such variant is the shortest descending path (SDP) problem, where the feasible paths are those that always go downhill. We need to compute an SDP, for example, for laying a canal of minimum length from the source of water at the top of a mountain to fields for irrigation purpose, and for skiing down a mountain along a shortest route. The complexity of finding SDPs is open. We give a full characterization of the bend angles of an SDP, showing that they follow a generalized form of Snell's law of refraction of light. We also reduce the SDP problem to the problem of finding an SDP through a given sequence of faces, by adapting the sequence tree approach of Chen and Han for our problem. Our results have two implications. First, we isolate the difficult aspect of SDPs. The difficulty is not in deciding which face sequence to use, but in finding the SDP through a given face sequence. Secondly, our results help us identify some classes of terrains for which the SDP problem is solvable in polynomial time. We give algorithms for two such classes.
The difficulty of finding an exact SDP motivates the study of approximation algorithms for the problem. We devise two approximation algorithms for SDPs in general terrains---these are the first two algorithms to handle the SDP problem in such terrains. The algorithms are robust and easy-to-implement. We also give two approximation algorithms for the case when a face sequence is given. The first one solves the problem by formulating it as a convex optimization problem. The second one uses binary search together with our characterization of the bend angles of an SDP to locate an approximate path.
We introduce a generalization of the SDP problem, called the shortest gently descending path (SGDP) problem, where a path descends but not too steeply. The additional constraint to disallow a very steep descent makes the paths more realistic in practice. For example, a vehicle cannot follow a too steep descent---this is why a mountain road has hairpin bends. We give two easy-to-implement approximation algorithms for SGDPs, both using the Steiner point approach. Between a pair of points there can be many SGDPs with different number of bends. In practice an SGDP with fewer bends or smaller total turn-angle is preferred. We show using a reduction from 3-SAT that finding an SGDP with a limited number of bends or a limited total turn-angle is hard. The hardness result applies to a generalization of the SGDP problem called the shortest anisotropic path problem, which is a well-studied computational geometry problem with many practical applications (e.g., robot motion planning), yet of unknown complexity.
Besides geometric shortest paths, we also study a variant of the shortest path problem in graphs: given a weighted graph G and vertices s and t, and given a set X of forbidden paths in G, find a shortest s-t path P such that no path in X is a subpath of P. Path P is allowed to repeat vertices and edges. We call each path in X an exception, and our desired path a shortest exception avoiding path. We formulate a new version of the problem where the algorithm has no a priori knowledge of X, and finds out about an exception x in X only when a path containing x fails. This situation arises in computing shortest paths in optical networks. We give an easy-to-implement algorithm that finds a shortest exception avoiding path in time polynomial in |G| and |X|. The algorithm handles a forbidden path using vertex replication, i.e., replicating vertices and judiciously deleting edges so as to remove the forbidden path but keep all of its subpaths. The main challenge is that vertex replication can result in an exponential number of copies of any forbidden path that overlaps the current one. The algorithm couples vertex replication with the "growth" of a shortest path tree in such a way that the extra copies of forbidden paths produced during vertex replication are immaterial
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