相关论文: Testing the Existence of a Supporting Plane

This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…

We find an algorithm to compute the cohomology groups of spherical vector bundles on complex projective K3 surfaces, in terms of their Mukai vectors. In many good cases, we give significant simplifications of the algorithm. As an…

The implicit theory that a simulation represents is precisely not in the individual choices but rather in the 'envelope' of possible trajectories - what is important is the shape of the whole envelope. Typically a huge amount of computation…

We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. A straightforward approach to this problem consists of…

We present a method for finding correspondence between 3D models. From an initial set of feature correspondences, our method uses a fast voting scheme to separate the inliers from the outliers. The novelty of our method lies in the use of a…

Copi, Huterer, Starkman and Schwarz introduced multipole vectors in a tensor context and used them to demonstrate that the first-year WMAP quadrupole and octopole planes align at roughly the 99.9% confidence level. In the present article…

Congruence between two n-point sets in 4 dimension can be checked in O(n log n) time. On the way to establishing this result, we revisit several parts of 4-dimensional geometry, such as angles and distances between planes, Hopf fibrations,…

Let R and S be two vectors of real numbers whose entries have the same sum. In the transportation problems one wishes to find a matrix A with row sum vector R and column sum vector S. If, in addition, the two vectors only contain…

Reflection equation for the scattering of lines moving in half-plane is obtained. The corresponding geometric picture is related with configurations of half-planes touching the boundary plane in 2+1 dimensions. This equation can be obtained…

We propose a conservative algorithm to test the geometrical validity of simplicial (triangles, tetrahedra), tensor product (quadrilaterals, hexahedra), and mixed (prisms) elements of arbitrary polynomial order as they deform over a…

We present subquadratic algorithms in the algebraic decision-tree model for several \textsc{3Sum}-hard geometric problems, all of which can be reduced to the following question: Given two sets $A$, $B$, each consisting of $n$ pairwise…

Ocean wave energy is a source of renewable energy that has gained much attention for its potential to contribute significantly to meeting the global energy demand. In this research, we investigate the problem of maximising the energy…

We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of…

An integral equation is a way to encapsulate the relationships between a function and its integrals. We develop a systematic way of describing Volterra integral equations -- specifically an algorithm that reduces any separable Volterra…

We present an algorithm for reliably and systematically proving the existence of spectral gaps in Hamiltonians with quasicrystalline order, based on numerical calculations on finite domains. We apply this algorithm to prove that the…

This paper proposes a new numerical optimization algorithm inspired by the strawberry plant for solving complicated engineering problems. Plants like strawberry develop both runners and roots for propagation and search for water resources…

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…

A method for object classification that is based on distribution analysis is proposed. In addition, a method for finding relevant features and the unification of this algorithm with another classification algorithm is proposed. The…

This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…

We classify all sets of nonzero vectors in $\mathbb{R}^3$ such that the angle formed by each pair is a rational multiple of $\pi$. The special case of four-element subsets lets us classify all tetrahedra whose dihedral angles are multiples…