Related papers: Computing the intersection of two quadrics through…
We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…
In this paper, we present a method to determine if a lift-and-project cut for a mixed-integer linear program is irregular, in which case the cut is not equivalent to any intersection cut from the bases of the linear relaxation. This is an…
We give an accessible introduction and elaboration on the methods used in obtaining a geodesic, which is the curve of shortest length connecting two points lying on the surface of a function. This is found through computing what's known as…
We study the complexity of computing the projection of an arbitrary $d$-polytope along $k$ orthogonal vectors for various input and output forms. We show that if $d$ and $k$ are part of the input (i.e. not a constant) and we are interested…
We study algebraic and combinatorial aspects of (classical) projections of $m$-dimensional tropical varieties onto $(m+1)$-dimensional planes. Building upon the work of Sturmfels, Tevelev, and Yu on tropical elimination as well as the work…
The detection and classification of intersections between triangles are crucial tasks in a wide range of applications within Computer Graphics and Geometry Processing, including mesh Arrangements, mesh Booleans, and generic mesh processing…
The computation of the topology of a real algebraic plane curve is greatly simplified if there are no more than one critical point in each vertical line: the general position condition. When this condition is not satisfied, then a finite…
We propose a conic transformation method to solve the Perspective-Three-Point (P3P) problem. In contrast to the current state-of-the-art solvers, which formulate the P3P problem by intersecting two conics and constructing a degenerate conic…
Using the connection between hyperelliptic curves, Clifford algebras, and complete intersections $X$ of two quadrics, we describe Ulrich bundles on $X$ and construct some of minimal possible rank.
We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…
We use the cut and paste relation $[Y^{[2]}] = [Y][\mathbb{P}^m] + \mathbb{L}^2 [F(Y)]$ in $K_0(\text{Var}_k)$ of Galkin--Shinder for cubic hypersurfaces arising from projective geometry to characterize cubic hypersurfaces of sufficiently…
We approximately compute the correspondence degree (as defined by Lazarsfeld and Martin) between two unbalanced complete intersections. This is accomplished by showing that the procedure of taking a subvariety of a product $Y \times Y'$ and…
For affine algebraic plane curves we reduce a calculation of its invariants to calculation of the intersection of kernels of some derivations.
A $\textit{polygonal curve}$ is a collection of $m$ connected line segments specified as the linear interpolation of a list of points $\{p_0, p_1, \ldots, p_m\}$. These curves may be obtained by sampling points from an oriented curve in…
Given a finite set of non-collinear points in the plane, there exists a line that passes through exactly two points. Such a line is called an ordinary line. An efficient algorithm for computing such a line was proposed by Mukhopadhyay et…
We study rationality problems for smooth complete intersections of two quadrics. We focus on the three-dimensional case, with a view toward understanding the invariants governing the rationality of a geometrically rational threefold over a…
This paper proposed a method to judge whether the point is inside or outside of the simple convex polygon by the intersection of the vertical line. It determined the point to an area enclosed by two straight lines, then convert the problem…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
We classify completely the intersections of the Hermitian curve with parabolas in the affine plane. To obtain our results we employ well-known algebraic methods for finite fields and geometric properties of the curve automorphisms. In…
We address the problem of bounding from below the self-intersection of integral curves on the projective plane blown-up at general points. In particular, by applying classical deformation theory we obtain the expected bound in the case of…