Related papers: Characterization of Planar Cubic Alternative curve

In this paper we construct parameterizations of elliptic curves over the rationals which have many consecutive integral multiples. Using these parameterizations, we perform searches in GMP and Magma to find curves with points of small…

Two cubic equations and three auxiliary equations for edges and face diagonals of a rational perfect cuboid have been recently derived. They constitute a background for two inverse problems. The coefficients of cubic equations and the right…

Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By…

In this paper we consider plane quartics with to involutions. We compute the Dixmier invariants, the bitangents and the Matrix representation problem of these curves, showing that they have symbolic solutions for the last two questions.

We initiate the study of a class of real plane algebraic curves which we call expressive. These are the curves whose defining polynomial has the smallest number of critical points allowed by the topology of the set of real points of a…

Enumerative algebraic geometry deals with problems of counting geometric objects defined algebraically, An important class of enumerative problems is that of counting curves: given a class of curves in some projective variety defined by…

In 1640's, Blaise Pascal discovered a remarkable property of a hexagon inscribed in a conic - Pascal Theorem, which gave birth of the projective geometry. In this paper, a new geometric invariant of algebraic curves is discovered by a…

Let K be a field of characteristic different from 2 and C an elliptic curve over K given by a Weierstrass equation. To divide an element of the group C by 2, one must solve a certain quartic equation. We characterise the quartics arising…

Statistical problems often involve linear equality and inequality constraints on model parameters. Direct estimation of parameters restricted to general polyhedral cones, particularly when one is interested in estimating low dimensional…

A rational perfect cuboid is a rectangular parallelepiped whose edges and face diagonals are given by rational numbers and whose space diagonal is equal to unity. It is described by a system of four equations with respect to six variables.…

The conditions for cubic equations, to have 3 real roots and 2 of the roots lie in the closed interval $[-1, 1]$ are given. These conditions are visualized. This question arises in physics in e.g. the theory of tops.

Straight lines are common features in human made environments, which makes them a frequently explored feature for control applications. Many control schemes, like Visual Servoing, require the 3D parameters of the features to be estimated.…

We present a set of conditions which, if satisfied, provide for a complete asymptotic analysis of random matrices with source term containing two distinct eigenvalues. These conditions are shown to be equivalent to the existence of a…

Convex geometries are closure systems satisfying the anti-exchange axiom. Every finite convex geometry can be embedded into a convex geometry of finitely many points in an n-dimensional space equipped with a convex hull operator, by the…

This paper presents an algorithm for detecting and computing the cusp points in the joint space of 3-RPR planar parallel manipulators. In manipulator kinematics, cusp points are special points, which appear on the singular curves of the…

We present a conjecture for the power-law exponent in the asymptotic number of types of plane curves as the number of self-intersections goes to infinity. In view of the description of prime alternating links as flype equivalence classes of…

Solving point-wise feature correspondence in visual data is a fundamental problem in computer vision. A powerful model that addresses this challenge is to formulate it as graph matching, which entails solving a Quadratic Assignment Problem…

In this paper we present algorithms for computing the topology of planar and space rational curves defined by a parametrization. The algorithms given here work directly with the parametrization of the curve, and do not require to compute or…

We establish an exact formula for the average number of edges appearing on the boundary of the global convex hull of n independent Brownian paths in the plane. This requires the introduction of a counting criterion which amounts to "cutting…

A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This…