Related papers: Rational complex Bezier curves
In the first part of the paper Beilinson's theorem on the bounded derived category of coherent sheaves on P^n is extended to weighted projective spaces in a rather explicit form. To this purpose the usual category of coherent sheaves is…
First we solve the problem of finding minimal degree families on toric surfaces by reducing it to lattice geometry. Then we describe how to find minimal degree families on, more generally, rational complex projective surfaces.
The conchoid of a plane curve $C$ is constructed using a fixed circle $B$ in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves $B$ and $C$ in the projective plane. We present two…
We use twisted stable maps to compute the number of rational degree d plane curves having prescribed contacts to a smooth plane cubic.
This study aims on proposing a new structure for constructing Bernstein-like bases. The structure uses an auxiliary function and a shape parameter to construct a new family of bases from any family of blending functions. The new family of…
A polynomial transformation of the real plane $\Bbb R^2$ is a mapping $\Bbb R^2\to\Bbb R^2$ given by two polynomials of two variables. Such a transformation is called cubic if the degrees of its polynomials are not greater than three. It…
Cylindrical Algebraic Decomposition (CAD) has long been one of the most important algorithms within Symbolic Computation, as a tool to perform quantifier elimination in first order logic over the reals. More recently it is finding…
In this paper, we consider rational cuspidal plane curves having exactly two cusps whose complements have logarithmic Kodaira dimension two. We classify such curves with the property that the strict transforms of them via the minimal…
We study a particular plane curve over a finite field whose normalization is of genus 0. The number of rational points of this curve achieves the Aubry-Perret bound for rational curves. The configuration of its rational points and a…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
Computing occluding contours is a key building block of non-photorealistic rendering, but producing contours with consistent visibility has been notoriously challenging. This paper describes the first general-purpose smooth surface…
We formalize the quantum arithmetic, i.e. a relationship between number theory and operator algebras. Namely, it is proved that rational projective varieties are dual to the $C^*$-algebras with real multiplication. Our construction fits all…
The family of Euclidean triangles having some fixed perimeter and area can be identified with a subset of points on a nonsingular cubic plane curve, i.e., an elliptic curve; furthermore, if the perimeter and the square of the area are…
The construction of parametric curve and surface plays important role in computer aided geometric design (CAGD), computer aided design (CAD), and geometric modeling. In this paper, we define a new kind of blending functions associated with…
In this talk the main features of the operator formalism for the $b-c$ systems on general algebraic curves developed in refs. [1-2] are reviewed. The first part of the talk is an introduction to the language of algebraic curves. Some…
Consider a simple algebraic group G of adjoint type, and its wonderful compactification X. We show that X admits a unique family of minimal rational curves, and we explicitly describe the subfamily consisting of curves through a general…
We present a method for computing projective isomorphisms between rational surfaces that are given in terms of their parametrizations. The main idea is to reduce the computation of such projective isomorphisms to five base cases by…
First we construct a free resolution for the Milnor (or Jacobian) algebra $M(f)$ of a complex projective Chebyshev plane curve $\CC_d:f=0$ of degree $d$. In particular, this resolution implies that the dimensions of the graded components…
In this paper, we develop a new and efficient approach to the computation of envelope surfaces. We interpret one-parameter systems of surfaces as curves in the homogeneous spaces of suitable Lie groups. Using the formalism of Lie groups and…
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. Its existence is equivalent to the existence of a perfect cuboid with all…