Related papers: Reconstruction of Centrally Symmetrical Convex Bod…

The combinatorial Ricci curvature of Forman, which is defined at the edges of a CW complex, and which makes use of only the face relations of the cells in the complex, does not satisfy an analog of the Gauss-Bonnet Theorem, and does not…

In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel…

Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This…

High proved the following theorem. If the intersections of any two congruent copies of a plane convex body are centrally symmetric, then this body is a circle. In our paper we extend the theorem of High to spherical and hyperbolic planes.…

A flag $C_0 \subsetneq C_1 \cdots \subsetneq C_s \subsetneq {\mathbb F}_q^n $ of linear codes is said to be self-orthogonal if the duals of the codes in the flag satisfy $C_{i}^\perp=C_{s-i}$, and it is said to satisfy the isometry-dual…

We have derived long series expansions for the perimeter generating functions of the radius of gyration of various polygons with a convexity constraint. Using the series we numerically find simple (algebraic) exact solutions for the…

We investigate a duality relation between floating and illumination bodies. The definitions of these two bodies suggest that the polar of the floating body should be similar to the illumination body of the polar. We consider this question…

In the paper we consider convex cones in infinite-dimensional real vector spaces which are endowed with no topology. The main purpose is to study an internal geometric structure of convex cones and to obtain an analytical description of…

In the literature we see that after introducing a geometric structure by imposing some restrictions on Riemann-Christoffel curvature tensor, the same type structure given by imposing same restriction on other curvature tensors being…

For a compact convex set F in R^n, with the origin in its interior, we present a formula to compute the curvature at a fixed point on its boundary, in the direction of any tangent vector. This formula is equivalent to the existing ones, but…

In unilateral pelvic fracture reductions, surgeons attempt to reconstruct the bone fragments such that bilateral symmetry in the bony anatomy is restored. We propose to exploit this "structurally symmetric" nature of the pelvic bone, and…

In this work we prove the following result: Let $K$ be a strictly convex body in the Euclidean space $\mathbb{R}^n, n\geq 3$, and let $L$ be a hypersurface, which is the image of an embedding of the sphere $\mathbb{S}^{n-1}$, such that $K$…

Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…

We study the problem of reconstructing a signal from its projection on a subspace. The proposed signal reconstruction algorithms utilize a guiding subspace that represents desired properties of reconstructed signals. We show that optimal…

The purpose of this paper is to study the reflections of a convex body. In particular, we are interested in orthogonal reflections of its sections that can be extended to reflections of the whole body. For this reason, we need to study the…

Typical Structure-from-Motion (SfM) pipelines rely on finding correspondences across images, recovering the projective structure of the observed scene and upgrading it to a metric frame using camera self-calibration constraints. Solving…

Let $\Sigma$ be a $C^3$ compact symmetric convex hypersurface in $\mathbf{R}^{8}$. For some special cases, we prove that when $\Sigma$ carries exactly four geometrically distinct closed characteristics, then all of them must be symmetric.

We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…

We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.

The convergence of the projection algorithm for solving the convex feasibility problem for a family of closed convex sets, is in connection with the regularity properties of the family. In the paper [18] are pointed out four cases of such a…