Related papers: Simplifying triangulations of S^3
The goal of this paper is to establish the classification of all homogeneous surfaces of 3-sphere by using the moving frame method. We will show that such surfaces are 2-spheres and flat torus.
It is known that any two triangulations of a compact 3-manifold are related by finite sequences of certain local transformations. We prove here an upper bound for the length of a shortest transformation sequence relating any two…
In this work we count the number of satisfying states of triangulations of a convex n-gon using the transfer matrix method. We show an exponential (in n) lower bound. We also give the exact formula for the number of satisfying states of a…
Normal surface theory is a central tool in algorithmic three-dimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important algorithms. However, it is not well understood how the number…
We construct embeddings of simplicial complexes into a (surface of a) simplicial ball whose triangulation has bounded degrees and low volume. This construction can be used either to efficiently "simplify a complicated space" by realizing it…
In this paper we present an interesting gadget based on the chain pair simplification problem under the discrete Fr\'echet distance (CPS-3F), which allows the construction of arbitrarily long paths that must be chosen in the simplification…
It is conjectured that every cusped hyperbolic 3-manifold has a decomposition into positive volume ideal hyperbolic tetrahedra (a "geometric" triangulation of the manifold). Under a mild homology assumption on the manifold we construct…
Parametrized motion planning algorithms have high degree of flexibility and universality, they can work under a variety of external conditions, which are viewed as parameters and form part of the input of the algorithm. In this paper we…
A fiber-uniform bound on the complexity of an essential simplicial map $S^3\rightarrow S^2$ is proven, and the tightness of the bound is investigated. It follows that the triangulation of the Hopf map constructed by Madahar and Sarkaria is…
This paper introduces a new method for constructing approximate solutions to a class of Wiener--Hopf equations. This is particularly useful since exact solutions of this class of Wiener--Hopf equations, at the moment, cannot be obtained.…
In this paper we prove that any triangulation of a 2-dimensional sphere with a strict 4-coloring on its vertices can seen as the boundary of a triangulation of a 3-dimensional disk with the same vertices and preserving the 4-coloring.
An algorithm is presented for numerical computation of choreographies in the plane in a Newtonian potential and on the sphere in a cotangent potential. It is based on stereographic projection, approximation by trigonometric polynomials, and…
We develop an efficient numerical scheme for the 3D mean-field spherical dynamo equation. The scheme is based on a semi-implicit discretization in time and a spectral method in space based on the divergence-free spherical harmonic…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
In this paper, we describe geometrical constructions to obtain triangulations of connected sums of closed orientable triangulated 3-manifolds. Using these constructions, we show that it takes time polynomial in the number of tetrahedra to…
A new algorithm for line clipping against convex polyhedron is given. The suggested algorithm is faster for higher number of facets of the given polyhedron than the traditional Cyrus-Beck's and others algorithms with complexity O(N) . The…
In this paper we study the problem of hyperball (hypersphere) packings in $3$-dimensional hyperbolic space. We introduce a new definition of the non-compact saturated ball packings and describe to each saturated hyperball packing, a new…
Based on the work of Durhuus-J{\'o}nsson and Benedetti-Ziegler, we revisit the question of the number of triangulations of the 3-ball. We introduce a notion of nucleus (a triangulation of the 3-ball without internal nodes, and with each…
Spectral synthesis calculations based on three-dimensional stellar atmosphere models are limited by the affordable angular resolution of the radiation field. This hampers an accurate treatment of rotational line broadening. We aim to find a…
A completely well-centered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and…