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On canonical representations of convex polyhedra

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Analytical calculation of the inertia matrices of convex spheropolyhedra

Lionel Pournin

Spheropolyhedra are bodies obtained as Minkowski sums of polyhedra with spheres. They are simple, yet flexible models of non-spherical particles for granular media simulated with the Distinct Element Method (DEM). We here give an analytical method for the ...

2008

Partial and approximate symmetry detection for 3D geometry

Mark Pauly

"Symmetry is a complexity-reducing concept [...]; seek it every-where." - Alan J. Perlis Many natural and man-made objects exhibit significant symmetries or contain repeated substructures. This paper presents a new algorithm that processes geometric models ...

2006

On canonical representation of convex polyhedra

Stefano Picozzi

Convex polyhedra are important objects in various areas of mathematics and other disciplines. A fundamental result, known as Minkowski-Weyl theorem, states that every polyhedron admits two types of representations, either as the solution set to a finite sy ...

EPFL2005

Toward a Multilevel Cognitive Probabilistic Representation of Space

Roland Siegwart, Adriana Tapus

This paper addresses the problem of perception and representation of space for a mobile agent. A probabilistic hierarchical framework is suggested as a solution to this problem. The method proposed is a combination of probabilistic belief with Object Grap ...

2005

On duality of canonical representations

Stefano Picozzi

Every convex polyhedron in

R^d

admits both H- and V-representations. In both cases, a representation is defined to be canonical if it is minimal and unique up to simple transformations. In general, canonical H- and V-representations are discussed separat ...

2004

Adaptive Hough transform for the detection of natural shapes under weak affine transformations

Jean-Philippe Thiran

This paper introduces a two-steps adaptive generalized Hough transform (GHT) for the detection of non-analytic objects undergoing weak affine transformations in images. The first step of our algorithm coarsely locates the region of interest with a GHT for ...

2004

The lexico-smallest representation of convex polyhedra

Stefano Picozzi

Every convex polyhedron in the Euclidean space

R^d

admits both H- and V-representation. For both formats, a representation is canonical if it is minimal and unique up to some elementary operations. In this paper, we extend the usual definition of canonic ...

2003

Representation of the weakly nonlinear propagation in air-filled pipes with Volterra series

Martin Hasler

This article the resolution of a boundary controlled nonlinear partial differential equation with Volterra series. The generalized Burger's equation which is investigated, accounts for the dominant effects of the acoustic propagation in cylindrical ducts i ...

2003

Wavelets on the 2-Sphere: A Group-Theoretical Approach

Pierre Vandergheynst

We present a purely group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S2, based on the construction of general coherent states associated to square integrable group representations. The parameter space X of our CWT is t ...

1999

Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron

Thomas Liebling, François Margot

In this paper, we investigate the applicability of backtrack technique to solve the vertex enumeration problem and the face enumeration problem for a convex polyhedron given by a system of linear inequalities. We show that there is a linear-time backtrack ...

1997

On duality of canonical representations

Stefano Picozzi

Every convex polyhedron in

R^d

2004

The lexico-smallest representation of convex polyhedra

Stefano Picozzi

Every convex polyhedron in the Euclidean space

R^d

2003