4,171 research outputs found
Configurations of infinitely near points
We present a survey of some aspects and new results on configurations, i.e.
disjoint unions of constellations of infinitely near points, local and global
theory, with some applications and results on generalized Enriques diagrams,
singular foliations, and linear systems defined by clusters
Towards an Iterative Algorithm for the Optimal Boundary Coverage of a 3D Environment
This paper presents a new optimal algorithm for locating a set of sensors in 3D able to see the boundaries of a polyhedral environment. Our approach is iterative and is based on a lower bound on the sensors' number and on a restriction of the original problem requiring each face to be observed in its entirety by at least one sensor. The lower bound allows evaluating the quality of the solution obtained at each step, and halting the algorithm if the solution is satisfactory. The algorithm asymptotically converges to the optimal solution of the unrestricted problem if the faces are subdivided into smaller part
PENCIL: Towards a Platform-Neutral Compute Intermediate Language for DSLs
We motivate the design and implementation of a platform-neutral compute
intermediate language (PENCIL) for productive and performance-portable
accelerator programming
Algorithmic Perception of Vertices in Sketched Drawings of Polyhedral Shapes
In this article, visual perception principles were used to build an artificial perception model aimed at developing an algorithm for detecting junctions in line drawings of polyhedral objects that are vectorized from hand-drawn sketches. The detection is performed in two dimensions (2D), before any 3D model is available and minimal information about the shape depicted by the sketch is used. The goal of this approach is to not only detect junctions in careful sketches created by skilled engineers and designers but also detect junctions when skilled people draw casually to quickly convey rough ideas. Current approaches for extracting junctions from digital images are mostly incomplete, as they simply merge endpoints that are near each other, thus ignoring the fact that different vertices may be represented by different (but close) junctions and that the endpoints of lines that depict edges that share a common vertex may not necessarily be close to each other, particularly in quickly sketched drawings. We describe and validate a new algorithm that uses these perceptual findings to merge tips of line segments into 2D junctions that are assumed to depict 3D vertices
Tropical polar cones, hypergraph transversals, and mean payoff games
We discuss the tropical analogues of several basic questions of convex
duality. In particular, the polar of a tropical polyhedral cone represents the
set of linear inequalities that its elements satisfy. We characterize the
extreme rays of the polar in terms of certain minimal set covers which may be
thought of as weighted generalizations of minimal transversals in hypergraphs.
We also give a tropical analogue of Farkas lemma, which allows one to check
whether a linear inequality is implied by a finite family of linear
inequalities. Here, the certificate is a strategy of a mean payoff game. We
discuss examples, showing that the number of extreme rays of the polar of the
tropical cyclic polyhedral cone is polynomially bounded, and that there is no
unique minimal system of inequalities defining a given tropical polyhedral
cone.Comment: 27 pages, 6 figures, revised versio
Beltrami vector fields with an icosahedral symmetry
A vector field is called a Beltrami vector field, if . In this paper we construct two unique Beltrami vector fields
and , such that
,
, and such that both have an
orientation-preserving icosahedral symmetry. Both of them have an additional
symmetry with respect to a non-trivial automorphism of the number field
.Comment: 22 pages, 9 figure
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