Publications related to Star polygon

Discontinuous Galerkin methods for Fisher-Kolmogorov equation with application to a-synuclein spreading in Parkinson's disease

This spreading of prion proteins is at the basis of brain neurodegeneration. This paper deals with the numerical modelling of the misfolding process of a-synuclein in Parkinson's disease. We introduce and analyse a discontinuous Galerkin method for the sem ...

Elsevier Science Sa2023

Quadratic serendipity element shape functions on general planar polygons

Xiaodong Wei, Juan Cao

This paper proposes a method for the construction of quadratic serendipity element (QSE) shape functions on planar convex and concave polygons. Existing approaches for constructing QSE shape functions are linear combinations of the pair-wise products of ge ...

ELSEVIER SCIENCE SA2022

HybridSDF: Combining Deep Implicit Shapes and Geometric Primitives for 3D Shape Representation and Manipulation

Pascal Fua, Pierre Bruno Baqué, Nicolas Talabot, Subeesh Vasu, Artem Lukoianov

Deep implicit surfaces excel at modeling generic shapes but do not always capture the regularities present in manufactured objects, which is something simple geometric primitives are particularly good at. In this paper, we propose a representation combinin ...

2022

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

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

American Physical Society2022

Smooth Shapes with Spherical Topology: Beyond Traditional Modeling, Efficient Deformation, and Interaction

Michaël Unser, Pablo Garcia-Amorena Garcia, Daniel Andreas Schmitter

Existing shape models with spherical topology are typically designed either in the discrete domain using interpolating polygon meshes or in the continuous domain using smooth but non-interpolating schemes such as subdivision or NURBS. Both polygon models a ...

2017

Smoothly Deformable Spheres: Modeling, Deformation, and Interaction

Michaël Unser, Pablo Garcia-Amorena Garcia, Daniel Andreas Schmitter

Existing shape models with spherical topology are typically designed either in the discrete domain using interpolating polygon meshes or in the continuous domain using smooth but non-interpolating schemes such as NURBS. Polygon models and subdivision metho ...

ACM2016

Protrusion-retraction switches and traction forces in spontaneous cell polarization

Alicia Carine Bornert

Cell migration is a fundamental property of all animal cells which is involved in processes such as embryogenesis, immune response, tissue regeneration and cancer metastasis. Directional migration requires cell polarization which could happen in response t ...

EPFL2016

From Compact Semi-Toric Systems To Hamiltonian S-1-Spaces

Silvia Sabatini

We show how any labeled convex polygon associated to a compact semi-toric system, as de fined by V (u) over tilde Ngoc, determines Karshon's labeled directed graph which classifies the underlying Hamiltonian S-1-space up to isomorphism. Then we characteriz ...

Amer Inst Mathematical Sciences2015

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

Small distances in convex polygons

Filip Moric

Let d(1) < d(2) < ... denote the set of all distances between two vertices of a convex n-gon. We show that the number of pairs of vertices at distance d(2) from one another is at most n + O(1). (C) 2013 Elsevier B.V. All rights reserved. ...

Elsevier2013

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

Can One Hear the Shape of a Room: The 2–D Polygonal Case

Martin Vetterli, Yue Lu, Ivan Dokmanic

We consider the problem of estimating room geometry from the acoustic room impulse response (RIR). Existing approaches addressing this problem exploit the knowledge of multiple RIRs. In contrast, we are interested in reconstructing the room geometry from a ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Indecomposable Coverings with Concave Polygons

Doemoetoer Palvoelgyi

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

Convex polygons are cover-decomposable

Doemoetoer Palvoelgyi

We show that for any open convex polygon P, there is a constant k(P) such that any k(P)-fold covering of the plane with translates of P can be decomposed into two coverings. ...

2010

Origami - Folded Plate Structures

Hans Ulrich Buri

This research investigates new methods of designing folded plate structures that can be built with cross-laminated timber panels. Folded plate structures are attractive to both architects and engineers for their structural, spatial, and plastic qualities. ...

EPFL2010

Decomposition of Geometric Set Systems and Graphs

Doemoetoer Palvoelgyi

We study two decomposition problems in combinatorial geometry. The first part of the thesis deals with the decomposition of multiple coverings of the plane. We say that a planar set is cover-decomposable if there is a constant m such that any m-fold coveri ...

EPFL2010

Pruned Continuous Haar Transform of 2D Polygonal Patterns with Application to VLSI Layouts

Paul Hurley, Robin Scheibler, Amina Chebira

We introduce an algorithm for the efﬁcient computation of the continuous Haar transform of 2D patterns that can be described by polygons. These patterns are ubiquitous in VLSI processes where they are used to describe design and mask layouts. There speed i ...

2010

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