Related papers: Computing basepoints of linear series in the plane
The polygon retrieval problem on points is the problem of preprocessing a set of $n$ points on the plane, so that given a polygon query, the subset of points lying inside it can be reported efficiently. It is of great interest in areas such…
We study certain generic systems of real polynomial equations associated with triangulations of convex polytopes and investigate their number of real solutions. Our main focus is set on pairs of plane algebraic curves which form a so-called…
This paper is devoted to presenting a new approach to determine the intersection of two quadrics based on the detailed analysis of its projection in the plane (the so called cutcurve) allowing to perform the corresponding lifting correctly.…
In the point set embeddability problem, we are given a plane graph $G$ with $n$ vertices and a point set $S$ with $n$ points. Now the goal is to answer the question whether there exists a straight-line drawing of $G$ such that each vertex…
For a smooth plane cubic $B$, we count curves $C$ of degree $d$ such that the normalizations of $C\backslash B$ are isomorphic to $\Bbb A^1$, for $d\leq7$ (for $d=7$ under some assumption). We also count plane rational quartic curves…
In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
The aim of this paper is to investigate an attempt to build a binary classification algorithm using principles of geometry such as vectors, planes, and vector algebra. The basic idea behind the proposed algorithm is that a hyperplane can be…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We describe a practical algorithm to compute the (oriented) genus of a graph, give results of the program implementing this algorithm, and compare the performance to existing algorithms. The aim of this algorithm is to be fast enough for…
In this paper, we describe an algorithm for fitting an analytic and bandlimited closed or open curve to interpolate an arbitrary collection of points in $\mathbb{R}^{2}$. The main idea is to smooth the parametrization of the curve by…
We discuss the principle tools and results and state a few open problems concerning the classification and topology of plane sextics and trigonal curves in ruled surfaces.
We establish asymptotic formulas for counting rational points near finite type curves on the plane, generalizing Huang's result.
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…
In this paper we give several methods to construct curves over finite fields with many points and illustrate this with examples of the results.
Whether it is object detection, model reconstruction, laser odometry, or point cloud registration: Plane extraction is a vital component of many robotic systems. In this paper, we propose a strictly probabilistic method to detect finite…
We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.
Matching is a method of the design of experiments. If we had an even number of patients and wanted to form pairs of patients such that their ages, for example, in each pair be as close as possible, we would use nonbipartite matching. Not…
We present a new method for visualizing implicit real algebraic curves inside a bounding box in the $2$-D or $3$-D ambient space based on numerical continuation and critical point methods. The underlying techniques work also for tracing…
We present an alternative and simpler method for computing principal typings of flow networks. When limited to planar flow networks, the method can be made to run in fixed-parameter linear-time -- where the parameter not to be exceeded is…