7,243 research outputs found
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
The Complexity of Finding Small Triangulations of Convex 3-Polytopes
The problem of finding a triangulation of a convex three-dimensional polytope
with few tetrahedra is proved to be NP-hard. We discuss other related
complexity results.Comment: 37 pages. An earlier version containing the sketch of the proof
appeared at the proceedings of SODA 200
Memory-Constrained Algorithms for Simple Polygons
A constant-workspace algorithm has read-only access to an input array and may
use only O(1) additional words of bits, where is the size of
the input. We assume that a simple -gon is given by the ordered sequence of
its vertices. We show that we can find a triangulation of a plane straight-line
graph in time. We also consider preprocessing a simple polygon for
shortest path queries when the space constraint is relaxed to allow words
of working space. After a preprocessing of time, we are able to solve
shortest path queries between any two points inside the polygon in
time.Comment: Preprint appeared in EuroCG 201
Triangulating stable laminations
We study the asymptotic behavior of random simply generated noncrossing
planar trees in the space of compact subsets of the unit disk, equipped with
the Hausdorff distance. Their distributional limits are obtained by
triangulating at random the faces of stable laminations, which are random
compact subsets of the unit disk made of non-intersecting chords coded by
stable L\'evy processes. We also study other ways to "fill-in" the faces of
stable laminations, which leads us to introduce the iteration of laminations
and of trees.Comment: 34 pages, 5 figure
TRIANGULAR MATRIX REPRESENTATIONS OF SKEW MONOID RINGS
Let R be a ring and S a u.p.-monoid. Assume that there is a monoid homomorphism α : S → Aut (R). Suppose that α is weakly rigid and lR(Ra) is pure as a left ideal of R for every element a ∈ R. Then the skew monoid ring R*S induced by α has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is R*S.</p
3D Reconstruction with Low Resolution, Small Baseline and High Radial Distortion Stereo Images
In this paper we analyze and compare approaches for 3D reconstruction from
low-resolution (250x250), high radial distortion stereo images, which are
acquired with small baseline (approximately 1mm). These images are acquired
with the system NanEye Stereo manufactured by CMOSIS/AWAIBA. These stereo
cameras have also small apertures, which means that high levels of illumination
are required. The goal was to develop an approach yielding accurate
reconstructions, with a low computational cost, i.e., avoiding non-linear
numerical optimization algorithms. In particular we focused on the analysis and
comparison of radial distortion models. To perform the analysis and comparison,
we defined a baseline method based on available software and methods, such as
the Bouguet toolbox [2] or the Computer Vision Toolbox from Matlab. The
approaches tested were based on the use of the polynomial model of radial
distortion, and on the application of the division model. The issue of the
center of distortion was also addressed within the framework of the application
of the division model. We concluded that the division model with a single
radial distortion parameter has limitations
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