Related papers: A resultant approach to detect intersecting curves…
The projection onto the intersection of sets generally does not allow for a closed form even when the individual projection operators have explicit descriptions. In this work, we systematically analyze the projection onto the intersection…
We investigate arcs on a pair of pants and present an algorithm to compute the self-intersection number of an arc. Additionally, we establish bounds for the self-intersection number in terms of the word length. We also prove that the…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…
We consider two mixed curve $C,C'\subset {\Bbb C}^2$ which are defined by mixed functions of two variables $\bf z=(z_1,z_2)$. We have shown in \cite{MC}, that they have canonical orientations. If $C$ and $C'$ are smooth and intersect…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
Previously, numerical evidence was presented of a self-intersecting Bezier curve having the unknot for its control polygon. This numerical demonstration resolved open questions in scientific visualization, but did not provide a formal proof…
For two closed curves on a plane (discrete version) and local criteria for similarity of points on the curves one gets a potential, which describes the similarity between curve points. This is the base for a global similarity measure of…
The arithmetic of elliptic curves, namely polynomial addition and scalar multiplication, can be described in terms of global sections of line bundles on $E\times E$ and $E$, respectively, with respect to a given projective embedding of $E$…
We obtain a sharp bound on the number of self-intersections of a closed planar curve with trigonometric parameterization. Moreover, we show that a generic curve of this form is normal in the sense of Whitney.
The problem of finding a point in the intersection of closed sets can be solved by the method of alternating projections and its variants. It was shown in earlier papers that for convex sets, the strategy of using quadratic programming (QP)…
In this paper we consider a generalization of a well known result by Veronese about rational normal curves. More precisely, given a collection of linear spaces in $\PP^n$ we study the existence of rational normal curves intersecting each…
We are introducing two methods for revealing the true inflection point of data that contains or not error. The starting point is a set of geometrical properties that follow the existence of an inflection point p for a smooth function. These…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
We bound the genus of a projective curve lying on a complete intersection surface in terms of its degree and the degrees of the defining equations of the surface on which it lies.
We present a simple sublinear time algorithm for testing the following geometric property. Let $P_1, ..., P_n$ be $n$ convex sets in $\mathbb{R}^d$ ($n \gg d$), such as polytopes, balls, etc. We assume that the complexity of each set…
A graph $G$ with vertex set $\{v_1,v_2,\ldots,v_n\}$ is an intersection graph of segments if there are segments $s_1,\ldots,s_n$ in the plane such that $s_i$ and $s_j$ have a common point if and only if $\{v_i,v_j\}$ is an edge of~$G$. In…
Consider two paths $f,g:[0;1]\to [0;1]^2$ on the unit square such that $f(0)=(0,0)$, $f(1)=(1,1)$, $g(0)=(0,1)$, $g(1)=(1,0)$, $f(0;1)\subseteq (0;1)^2$ and $g(0;1)\subseteq (0;1)^2$. By continuity of $f$ and $g$ there is a point of…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
Given a specific collection of curves on an oriented surface with punctures, we associate a power series by counting its intersections with multicurves. This paper presents a reciprocity formula on the power series when multicurves with no…
We introduce a method for efficiently computing the exact shortest path to the boundary of a mesh from a given internal point in the presence of self-intersections. We provide a formal definition of shortest boundary paths for…