In this paper we present a simple technique to approximate the volume enclosed by a given triangle mesh with a set of overlapping ellipsoids. This type of geometry representation allows us to approximately reconstruct 3D-shapes from a very small amount of information being transmitted. The two central questions that we address are: how can we compute optimal fitting ellipsoids that lie in the i...

Bounding hull, such as convex hull, concave hull, alpha shapes etc. has vast applications in different areas especially in computational geometry. Alpha shape and concave hull are generalizations of convex hull. Unlike the convex hull, they construct non-convex enclosure on a set of points. In this paper, we introduce another generalization of convex hull, named alpha-concave hull, and compare ...

A tiling of a surface is a decomposition of the surface into pieces, i.e. tiles, which cover it without gaps or overlaps. In this paper some special polygonal tiling of sphere, ellipsoid, cylinder, and torus as the most abundant shapes of fullerenes are investigated.

In this paper, we study the approximation and estimation of s-concave densities via Rényi divergence. We first show that the approximation of a probability measure Q by an s-concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [Ann. Statist.38 (2010) 2998-3027] if and only if Q admits full-dimensional support and a first moment. We also show c...

The history of polyhedra, linear inequalities, and linear programming has many diverse origins. Polyhedra have been around since the beginning of mathematics in ancient times. It appears that Fourier was the first to consider linear inequalities seriously. This was in the first half of the 19 century. He invented a method, today often called Fourier-Motzkin elimination, with which linear progra...

In this paper we propose a regularized relaxation based graph matching algorithm. The graph matching problem is formulated as a constrained convex quadratic program, by relaxing the permutation matrix to a doubly stochastic one. To gradually push the doubly stochastic matrix back to a permutation one, a simple weighted concave regular term is added to the convex objective function. The concave ...

In contemporary convex geometry, the rapidly developing Lp-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the Lp-affine surface area for convex bodies. Here, we introduce a functional form of this concept, for log concave and s-concave functions. We show that the new functional form is a generalization of the original Lp-affi...

A FORTRAN IV algorithm is given for determining the hydrodynamic parameters of a macromolecule in solution for any specified value ofthe two axial ratios (a/b, D/c) ofthe equivalent triaxial ellipsoid model of semi-axes a > b > c for its gross conformafion. Ellipsoid model Axial ratios Elliptic integrals Myoglobin I . I N T R O D U C T I O N The ellipsoid of revolution (i.e. an ellipsoid with t...

The Ellipsoid algorithm was developed by (formerly) Soviet mathematicians (Shor (1970), Yudin and Nemirovskii (1975)). Khachian (1979) proved that it provides a polynomial time algorithm for linear programming. The average behavior of the Ellipsoid algorithm is too slow, making it not competitive with the simplex algorithm. However, the theoretical implications of the algorithm are very importa...