Related papers: A resultant approach to detect intersecting curves…
In this paper we study the intersection theory on surfaces with abelian quotient singularities and we derive properties of quotients of weighted projective planes. We also use this theory to study weighted blow-ups in order to construct…
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…
The notion of an unexpected curve in the plane was introduced in 2018, and was quickly generalized in several directions in a flurry of mathematical activity by many authors. In this expository paper we first describe some of the main…
Given a set of objects $O$ in the plane, the corresponding intersection graph is defined as follows. Each object defines a vertex and an edge joins two vertices whenever the corresponding objects intersect. We study here the case of unit…
We solve the problem of characteristic numbers of elliptic curves in any dimensional projective space The answers are given in the form of effective recursions. Many numerical examples are provided. A C++ program implementing all the…
There is presented an algorithm for computing the topological degree for a large class of polynomial mappings. As an application there is given an effective algebraic formula for the intersection number of a polynomial immersion M --> R^2m,…
We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that are not defined by any explicit parameterization and is…
The task of establishing correspondences between two 3D shapes is a long-standing challenge in computer vision. While numerous studies address full-full and partial-full 3D shape matching, only a limited number of works have explored the…
This work provides a curve-based approach to Ulrich bundles on surfaces, establishing a correspondence that characterizes their existence, with a focus on applications to surfaces in $\mathbb{P}^3$.
Let S, T be surfaces in P3. Suppose that S intersect T is set-theoretically a smooth curve C of degree d and genus g. Suppose that S and T have no common singular points. Then if C is not a complete intersection, then deg(S), deg(T) < 2d^4.…
In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
We study the virtual intersection theory of Hyperquot schemes parameterizing sequences of quotient sheaves of a vector bundle on a smooth projective curve. Our results generalize the Vafa--Intriligator formula for Quot schemes and provide a…
We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and…
The order in which plane-filling curves visit points in the plane can be exploited to design efficient algorithms. Typically, the curves are useful because they preserve locality: points that are close to each other along the curve tend to…
For polyhedral convex cones in ${\mathbb R}^d$, we give a proof for the conic kinematic formula for conic curvature measures, which avoids the use of characterization theorems. For the random cones defined as typical cones of an isotropic…
We prove the famous Faber intersection number conjecture and other more general results by using a recursion formula of $n$-point functions for intersection numbers on moduli spaces of curves. We also present some vanishing properties of…
We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exists.
This paper presents a real-time solution for collision detection between objects based on the physics properties. Traditional approaches on collision detection often rely on the geometric relationships that computing the intersections…
Considering a finite intersection of balls and a finite union of other balls in an Euclidean space, we propose an exact method to test whether the intersection is covered by the union. We reformulate this problem into quadratic programming…