Concept

Skew polygon

Publications associées (12)

Perimeter Modes of Nanomechanical Resonators Exhibit Quality Factors Exceeding 10(9) at Room Temperature

Tobias Kippenberg, Guanhao Huang, Alberto Beccari, Amirali Arabmoheghi, Nils Johan Engelsen, Sergey Fedorov

Systems with low mechanical dissipation are extensively used in precision measurements such as gravitational wave detection, atomic force microscopy, and quantum control of mechanical oscillators via optomechanics and electromechanics. The mechanical quali ...

AMER PHYSICAL SOC2022

Almost impossible E_8 and Leech lattices

Maryna Viazovska

We start this short note by introducing two remarkable mathematical objects: the E8E8 root lattice Lambda8Lambda8 in 8-dimensional Euclidean space and the Leech lattice Lambda24Lambda24 in 24-dimensional space. These two lattices stand out among their lat ...

2021

Squall

Aleksandar Vitorovic

Squall is a scalable online query engine that runs complex analytics in a cluster using skew-resilient, adaptive operators. Online processing implies that results are incrementally built as the input arrives, and it is ubiquitous for many applications such ...

EPFL2016

On Polygons Excluding Point Sets

Radoslav Fulek, Balázs Keszegh, Filip Moric

By a polygonization of a finite point set S in the plane we understand a simple polygon having S as the set of its vertices. Let B and R be sets of blue and red points, respectively, in the plane such that is in general position, and the convex hull of B c ...

Springer Japan2013

Fast continuous Fourier and Haar transforms of rectilinear polygons from very-large-scale integration layouts

Paul Hurley, Robin Scheibler, Amina Chebira

We propose two new fast algorithms for the computation of the continuous Fourier series and the continuous Haar transform of rectilinear polygons such as those of mask layouts in optical lithography. These algorithms outperform their discrete counterparts ...

2013

Fourier Approximation Of Symmetric Ideal Knots

Henryk Gerlach, Mathias Carlen

Enforcing a specific symmetry group on a curve, knotted or not, is not trivial using standard interpolations such as polygons or splines. For a prescribed symmetry group we present a symmetrization process based on a Fourier description of a knot. The pres ...

2012

Indecomposable Coverings with Concave Polygons

We show that for any concave polygon that has no parallel sides and for any k, there is a k-fold covering of some point set by the translates of this polygon that cannot be decomposed into two coverings. Moreover, we give a complete classification of open ...

Springer-Verlag2010

Algorithms for the Computation of Continuous Transforms of Rectilinear Polygons from IC Layouts

Robin Scheibler

In this work, we present a novel way of computing the continuous Haar, Fourier and cosine series coefficients of rectilinear polygons. We derive algorithms to compute the inner products with the continuous basis functions directly from the vertices of the ...

2009

Application of 3D range camera in virtual human-computer interfaces

Huan Du

In this work, we propose new ways to employ 3D-ranging systems in advanced human-computer interfaces and show that they can be used for precise hand-tracking systems aiming at virtual keyboard or mouse applications. We first implement a Structured Light (S ...

EPFL2008

An Exact Method for Computing the Area Moments of Wavelet and Spline Curves

Michaël Unser, Thierry Blu, Mathews Jacob

We present a method for the exact computation of the moments of a region bounded by a curve represented by a scaling function or wavelet basis. Using Green's Theorem, we show that the computation of the area moments is equivalent to applying a suitable mul ...

IEEE2001

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