Related papers: On the Intersection of Two Conics
This paper presents formulae for calculation the solid angle of intersecting spherical caps, conical surfaces and polyhedral cones.
By a numerical continuation method called a diagonal homotopy we can compute the intersection of two positive dimensional solution sets of polynomial systems. This paper proposes to use this diagonal homotopy as the key step in a procedure…
In these proceedings we will review recent progress in applying ideas from the mathematical framework of twisted cohomology to the study of canonical differential equations for Feynman integrals. Firstly, we will show how the intersection…
Reconstructing 3D point clouds into triangle meshes is a key problem in computational geometry and surface reconstruction. Point cloud triangulation solves this problem by providing edge information to the input points. Since no vertex…
We study the set of lines that meet a fixed line and are tangent to two spheres and classify the configurations consisting of a single line and three spheres for which there are infinitely many lines tangent to the three spheres that also…
Sub-diffraction-limit resolution, or super-resolution, had been successfully demonstrated by recent theoretical and experimental studies for two-point sources with ideal equal-brightness and strict incoherenceness. Unfortunately, practical…
The usual quantizer based on an n-dimensional lattice L maps a point x in R^n to a closest lattice point. Suppose L is the intersection of lattices L_1, ..., L_r. Then one may instead combine the information obtained by simultaneously…
Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the…
An iterative formula based on Newton Method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional Newton Method may fail to converge to the desired root. In addition, the method…
The Perspective-Three-Point Problem (P3P) is solved by first focusing on determining the directions of the lines through pairs of control points, relative to the camera, rather than the distances from the camera to the control points. The…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
We aim at estimating the fundamental matrix in two views from five correspondences of rotation invariant features obtained by e.g.\ the SIFT detector. The proposed minimal solver first estimates a homography from three correspondences…
For a polyhedron $P$ in $\mathbb{R}^d$, denote by $|P|$ its combinatorial complexity, i.e., the number of faces of all dimensions of the polyhedra. In this paper, we revisit the classic problem of preprocessing polyhedra independently so…
Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide…
Given a ternary homogeneous polynomial, the fixed points of the map from $\mathbb{P}^2$ to itself defined by its gradient are called its eigenpoints. We focus on cubic polynomials, and analyze configurations of eigenpoints that admit one or…
Eigensolvers involving complex moments can determine all the eigenvalues in a given region in the complex plane and the corresponding eigenvectors of a regular linear matrix pencil. The complex moment acts as a filter for extracting…
We present an approach to finding the implicit equation of a planar rational parametric cubic curve, by defining a new basis for the representation. The basis, which contains only four cubic bivariate polynomials, is defined in terms of the…
The conjugate locus of a point $p$ in a surface $\mathcal{S}$ will have a certain number of cusps. As the point $p$ is moved in the surface the conjugate locus may spontaneously gain or lose cusps. In this paper we explain this…
We consider the problem of computing the distance-dependent two-point function of general planar maps and hypermaps, i.e. the problem of counting such maps with two marked points at a prescribed distance. The maps considered here may have…
This paper develops an algorithm that identifies and decomposes a median graph of a triangulation of a 2-dimensional (2D) oriented bordered surface and in addition restores all corresponding triangulation whenever they exist. The algorithm…