1,479 research outputs found
Extending the Calculus of Constructions with Tarski's fix-point theorem
We propose to use Tarski's least fixpoint theorem as a basis to define
recursive functions in the calculus of inductive constructions. This widens the
class of functions that can be modeled in type-theory based theorem proving
tool to potentially non-terminating functions. This is only possible if we
extend the logical framework by adding the axioms that correspond to classical
logic. We claim that the extended framework makes it possible to reason about
terminating and non-terminating computations and we show that common facilities
of the calculus of inductive construction, like program extraction can be
extended to also handle the new functions
Inductive and Coinductive Components of Corecursive Functions in Coq
In Constructive Type Theory, recursive and corecursive definitions are
subject to syntactic restrictions which guarantee termination for recursive
functions and productivity for corecursive functions. However, many terminating
and productive functions do not pass the syntactic tests. Bove proposed in her
thesis an elegant reformulation of the method of accessibility predicates that
widens the range of terminative recursive functions formalisable in
Constructive Type Theory. In this paper, we pursue the same goal for productive
corecursive functions. Notably, our method of formalisation of coinductive
definitions of productive functions in Coq requires not only the use of ad-hoc
predicates, but also a systematic algorithm that separates the inductive and
coinductive parts of functions.Comment: Dans Coalgebraic Methods in Computer Science (2008
The union of unit balls has quadratic complexity, even if they all contain the origin
We provide a lower bound construction showing that the union of unit balls in
three-dimensional space has quadratic complexity, even if they all contain the
origin. This settles a conjecture of Sharir.Comment: 5 pages, 5 figure
Improved Incremental Randomized Delaunay Triangulation
We propose a new data structure to compute the Delaunay triangulation of a
set of points in the plane. It combines good worst case complexity, fast
behavior on real data, and small memory occupation.
The location structure is organized into several levels. The lowest level
just consists of the triangulation, then each level contains the triangulation
of a small sample of the levels below. Point location is done by marching in a
triangulation to determine the nearest neighbor of the query at that level,
then the march restarts from that neighbor at the level below. Using a small
sample (3%) allows a small memory occupation; the march and the use of the
nearest neighbor to change levels quickly locate the query.Comment: 19 pages, 7 figures Proc. 14th Annu. ACM Sympos. Comput. Geom.,
106--115, 199
Continued Fraction Expansion of Real Roots of Polynomial Systems
We present a new algorithm for isolating the real roots of a system of
multivariate polynomials, given in the monomial basis. It is inspired by
existing subdivision methods in the Bernstein basis; it can be seen as
generalization of the univariate continued fraction algorithm or alternatively
as a fully analog of Bernstein subdivision in the monomial basis. The
representation of the subdivided domains is done through homographies, which
allows us to use only integer arithmetic and to treat efficiently unbounded
regions. We use univariate bounding functions, projection and preconditionning
techniques to reduce the domain of search. The resulting boxes have optimized
rational coordinates, corresponding to the first terms of the continued
fraction expansion of the real roots. An extension of Vincent's theorem to
multivariate polynomials is proved and used for the termination of the
algorithm. New complexity bounds are provided for a simplified version of the
algorithm. Examples computed with a preliminary C++ implementation illustrate
the approach.Comment: 10 page
Concrete Domains
This paper introduces the theory of a particular kind of computation domains
called concrete domains. The purpose of this theory is to find a satisfactory
framework for the notions of coroutine computation and sequentiality of evaluation
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
Gloss Perception in Painterly and Cartoon Rendering
International audienceDepictions with traditional media such as painting and drawing represent scene content in a stylized manner. It is unclear however how well stylized images depict scene properties like shape, material and lighting. In this paper, we describe the first study of material perception in stylized images (specifically painting and cartoon) and use non photorealistic rendering algorithms to evaluate how such stylization alters the perception of gloss. Our study reveals a compression of the range of representable gloss in stylized images so that shiny materials appear more diffuse in painterly rendering, while diffuse materials appear shinier in cartoon images. From our measurements we estimate the function that maps realistic gloss parameters to their perception in a stylized rendering. This mapping allows users of NPR algorithms to predict the perception of gloss in their images. The inverse of this function exaggerates gloss properties to make the contrast between materials in a stylized image more faithful. We have conducted our experiment both in a lab and on a crowdsourcing website. While crowdsourcing allows us to quickly design our pilot study, a lab experiment provides more control on how subjects perform the task. We provide a detailed comparison of the results obtained with the two approaches and discuss their advantages and drawbacks for studies like ours
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