74 research outputs found
An Upper Bound on the Average Size of Silhouettes
It is a widely observed phenomenon in computer graphics that the size of the
silhouette of a polyhedron is much smaller than the size of the whole
polyhedron. This paper provides, for the first time, theoretical evidence
supporting this for a large class of objects, namely for polyhedra that
approximate surfaces in some reasonable way; the surfaces may be non-convex and
non-differentiable and they may have boundaries. We prove that such polyhedra
have silhouettes of expected size where the average is taken over
all points of view and n is the complexity of the polyhedron
Triangulating the Real Projective Plane
We consider the problem of computing a triangulation of the real projective
plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a
triangulation of P2 always exists if at least six points in S are in general
position, i.e., no three of them are collinear. We also design an algorithm for
triangulating P2 if this necessary condition holds. As far as we know, this is
the first computational result on the real projective plane
Experiments in Model-Checking Optimistic Replication Algorithms
This paper describes a series of model-checking experiments to verify
optimistic replication algorithms based on Operational Transformation (OT)
approach used for supporting collaborative edition. We formally define, using
tool UPPAAL, the behavior and the main consistency requirement (i.e.
convergence property) of the collaborative editing systems, as well as the
abstract behavior of the environment where these systems are supposed to
operate. Due to data replication and the unpredictable nature of user
interactions, such systems have infinitely many states. So, we show how to
exploit some features of the UPPAAL specification language to attenuate the
severe state explosion problem. Two models are proposed. The first one, called
concrete model, is very close to the system implementation but runs up against
a severe explosion of states. The second model, called symbolic model, aims to
overcome the limitation of the concrete model by delaying the effective
selection and execution of editing operations until the construction of
symbolic execution traces of all sites is completed. Experimental results have
shown that the symbolic model allows a significant gain in both space and time.
Using the symbolic model, we have been able to show that if the number of sites
exceeds 2 then the convergence property is not satisfied for all OT algorithms
considered here. A counterexample is provided for every algorithm
Time- and Space-Efficient Evaluation of Some Hypergeometric Constants
The currently best known algorithms for the numerical evaluation of
hypergeometric constants such as to decimal digits have time
complexity and space complexity of or .
Following work from Cheng, Gergel, Kim and Zima, we present a new algorithm
with the same asymptotic complexity, but more efficient in practice. Our
implementation of this algorithm improves slightly over existing programs for
the computation of , and we announce a new record of 2 billion digits for
Interaction Grammars
Interaction Grammar (IG) is a grammatical formalism based on the notion of
polarity. Polarities express the resource sensitivity of natural languages by
modelling the distinction between saturated and unsaturated syntactic
structures. Syntactic composition is represented as a chemical reaction guided
by the saturation of polarities. It is expressed in a model-theoretic framework
where grammars are constraint systems using the notion of tree description and
parsing appears as a process of building tree description models satisfying
criteria of saturation and minimality
On the expected size of the 2d visibility complex
We study the expected size of the 2D visibility complex of randomly distributed objects in the plane. We prove that the asymptotic expected number of free bitangents (which correspond to 0-faces of the visibility complex) among unit discs (or polygons of bounded aspect ratio and similar size) is linear and exhibit bounds in terms of the density of the objects. We also make an experimental assessment of the size of the visibility complex for disjoint random unit discs. We provide experimental estimates of the onset of the linear behavior and of the asymptotic slope and y-intercept of the number of free bitangents in terms of the density of discs. Finally, we analyze the quality of our estimates in terms of the density of discs.
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