33,270 research outputs found
Removal and Contraction Operations in D Generalized Maps for Efficient Homology Computation
In this paper, we show that contraction operations preserve the homology of
D generalized maps, under some conditions. Removal and contraction
operations are used to propose an efficient algorithm that compute homology
generators of D generalized maps. Its principle consists in simplifying a
generalized map as much as possible by using removal and contraction
operations. We obtain a generalized map having the same homology than the
initial one, while the number of cells decreased significantly.
Keywords: D Generalized Maps; Cellular Homology; Homology Generators;
Contraction and Removal Operations.Comment: Research repor
Information hiding through variance of the parametric orientation underlying a B-rep face
Watermarking technologies have been proposed for many different,types of digital media. However, to this date, no viable watermarking techniques have yet emerged for the high value B-rep (i.e. Boundary Representation) models used in 3D mechanical CAD systems. In this paper, the authors propose a new approach (PO-Watermarking) that subtly changes a model's geometric representation to incorporate a 'transparent' signature. This scheme enables software applications to create fragile, or robust watermarks without changing the size of the file, or shape of the CAD model. Also discussed is the amount of information the proposed method could transparently embed into a B-rep model. The results presented demonstrate the embedding and retrieval of text strings and investigate the robustness of the approach after a variety of transformation and modifications have been carried out on the data
Sources of variability in cartographers' deconstruction of fractals : paper presented at the 18 November 1998 meeting of the British Cartographic Society's Design Group at the University of Glasgow
CISRG discussion paper ; 1
Geodesic-Preserving Polygon Simplification
Polygons are a paramount data structure in computational geometry. While the
complexity of many algorithms on simple polygons or polygons with holes depends
on the size of the input polygon, the intrinsic complexity of the problems
these algorithms solve is often related to the reflex vertices of the polygon.
In this paper, we give an easy-to-describe linear-time method to replace an
input polygon by a polygon such that (1)
contains , (2) has its reflex
vertices at the same positions as , and (3) the number of vertices
of is linear in the number of reflex vertices. Since the
solutions of numerous problems on polygons (including shortest paths, geodesic
hulls, separating point sets, and Voronoi diagrams) are equivalent for both
and , our algorithm can be used as a preprocessing
step for several algorithms and makes their running time dependent on the
number of reflex vertices rather than on the size of
On Khovanov's cobordism theory for su(3) knot homology
We reconsider the su(3) link homology theory defined by Khovanov in
math.QA/0304375 and generalized by Mackaay and Vaz in math.GT/0603307. With
some slight modifications, we describe the theory as a map from the planar
algebra of tangles to a planar algebra of (complexes of) `cobordisms with
seams' (actually, a `canopolis'), making it local in the sense of Bar-Natan's
local su(2) theory of math.GT/0410495.
We show that this `seamed cobordism canopolis' decategorifies to give
precisely what you'd both hope for and expect: Kuperberg's su(3) spider defined
in q-alg/9712003. We conjecture an answer to an even more interesting question
about the decategorification of the Karoubi envelope of our cobordism theory.
Finally, we describe how the theory is actually completely computable, and
give a detailed calculation of the su(3) homology of the (2,n) torus knots.Comment: 49 page
A Review of State-of-the-Art Large Sized Foam Cutting Rapid Prototyping and Manufacturing Technologies.
Purpose – Current additive rapid prototyping (RP) technologies fail to efficiently produce objects greater than 0.5?m3 due to restrictions in build size, build time and cost. A need exists to develop RP and manufacturing technologies capable of producing large objects in a rapid manner directly from computer-aided design data. Foam cutting RP is a relatively new technology capable of producing large complex objects using inexpensive materials. The purpose of this paper is to describe nine such technologies that have been developed or are currently being developed at institutions around the world. The relative merits of each system are discussed. Recommendations are given with the aim of enhancing the performance of existing and future foam cutting RP systems.
Design/methodology/approach – The review is based on an extensive literature review covering academic publications, company documents and web site information.
Findings – The paper provides insights into the different machine configurations and cutting strategies. The most successful machines and cutting strategies are identified.
Research limitations/implications – Most of the foam cutting RP systems described have not been developed to the commercial level, thus a benchmark study directly comparing the nine systems was not possible.
Originality/value – This paper provides the first overview of foam cutting RP technology, a field which is over a decade old. The information contained in this paper will help improve future developments in foam cutting RP systems
Steinitz Theorems for Orthogonal Polyhedra
We define a simple orthogonal polyhedron to be a three-dimensional polyhedron
with the topology of a sphere in which three mutually-perpendicular edges meet
at each vertex. By analogy to Steinitz's theorem characterizing the graphs of
convex polyhedra, we find graph-theoretic characterizations of three classes of
simple orthogonal polyhedra: corner polyhedra, which can be drawn by isometric
projection in the plane with only one hidden vertex, xyz polyhedra, in which
each axis-parallel line through a vertex contains exactly one other vertex, and
arbitrary simple orthogonal polyhedra. In particular, the graphs of xyz
polyhedra are exactly the bipartite cubic polyhedral graphs, and every
bipartite cubic polyhedral graph with a 4-connected dual graph is the graph of
a corner polyhedron. Based on our characterizations we find efficient
algorithms for constructing orthogonal polyhedra from their graphs.Comment: 48 pages, 31 figure
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