Related papers: Contact detection between an ellipsoid and a combi…
We characterize all possible relative positions between a hyperboloid of one sheet and a sphere through the roots of a characteristic polynomial associated to these quadrics. The classification is also suitable for a hyperboloid and a…
We classify all the relative positions between an ellipsoid and an elliptic paraboloid when the ellipsoid is small in comparison with the paraboloid ({\it small} meaning that the ellipsoid cannot be tangent to the paraboloid at two points…
The problem of determining whether a given quantum state is separable is known to be computationally difficult. We develop an approach to this problem based on approximations of convex polytopes in high dimensions. By showing that a convex…
We obtain the distance of closest approach of the surfaces of two arbitrary ellipsoids valid at any orientation and separation, measured along their inter-center vector. This directional distance is derived from the Elliptic Contact…
It has been shown that the edge structure of the characteristic imset polytope is closely connected to the question of causal discovery. The diameter of a polytope is an indicator of how connected the polytope is and moreover gives us a…
We study global solutions to the thin obstacle problem with at most quadratic growth at infinity. We show that every ellipsoid can be realized as the contact set of such a solution. On the other hand, if such a solution has a compact…
Configuration polynomials generalize the classical Kirchhoff polynomial defined by a graph. Their study sheds light on certain polynomials appearing in Feynman integrands. Contact equivalence provides a way to study the associated…
Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a…
This paper presents a method to estimate the 3D object position and occupancy given a set of object detections in multiple images and calibrated cameras. This problem is modelled as the estimation of a set of quadrics given 2D conics fit to…
Collision detection is a critical functionality for robotics. The degree to which objects collide cannot be represented as a continuously differentiable function for any shapes other than spheres. This paper proposes a framework for…
All the segments (or their continuations) of a billiard trajectory inside an ellipsoid of $\Rset^n$ are tangent to n-1 quadrics of the pencil of confocal quadrics determined by the ellipsoid. The quadrics associated to periodic billiard…
This paper studies the problem of passive grasp stability under an external disturbance, that is, the ability of a grasp to resist a disturbance through passive responses at the contacts. To obtain physically consistent results, such a…
Several characterizations of complex ellipsoids among convex bodies in Cn, in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms is an important tool.
This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The method is constructive and is easy to use. It is based upon the observation that…
A theorem of Meyer and Reisner characterizes ellipsoids by the collinearity of centroids of parallel sections: if $\Omega\subset\mathbb{R}^{n+1}$ is a convex body such that for every $n$-dimensional subspace $M\subset\mathbb{R}^{n+1}$ the…
One of the most important problems in Geometric Tomography is to establish properties of a given convex body if we know some properties over its sections or its projections. There are many interesting and deep results that provide…
Collision detection plays an important role in simulation, control, and learning for robotic systems. However, no existing method is differentiable with respect to the configurations of the objects, greatly limiting the sort of algorithms…
In this paper, we investigate some polynomial conditions that arise from Euclidean geometry. First we study polynomials related to quadrilaterals with supplementary angles, this includes convex cyclic quadrilaterals, as well as certain…
The characteristic polynomials of the adjacency matrix of line graphs of caterpillars and then the characteristic polynomials of their Laplacian or signless Laplacian matrices are characterized, using recursive formulas. Furthermore, the…
We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on the existence of a linear relationship between two…