Linear Systems of Rational Curves on Rational Surfaces
نویسندگان
چکیده
Given a curve C on a projective nonsingular rational surface S, over an algebraically closed field of characteristic zero, we are interested in the set ΩC of linear systems L on S satisfying C ∈ L, dimL > 1, and the general member of L is a rational curve. The main result of the paper gives a complete description of ΩC and, in particular, characterizes the curves C for which ΩC is non empty. 2000 Math. Subj. Class. Primary: 14C20, 14J26.
منابع مشابه
Exact Parameterization of Convolution Surfaces and Rational Surfaces with Linear Normals
It is shown that curves and surfaces with a linear field of normal vectors are dual to graphs of univariate and bivariate polynomials. We discuss the geometric properties of these curves and surfaces. In particular, it is shown that the convolution with general rational curves and surfaces yields again rational curves and surfaces.
متن کاملAutomatic parameterization of rational curves and surfaces III: Algebraic plane curves
We consider algorithms to compute the genus and rational parametric equations, for implicitly defined irreducible rational plane algebraic curves of arbitrary degree. Rational panuneterizations exist for all irreducible algebraic curves of genus O. The genus is compuled by a complete analysis of the singularities of plane algebraic curves, using affine quadratic transformations. The rational pa...
متن کاملRational surfaces with linear normals and their convolutions with rational surfaces
It is shown that polynomial (or rational) parametric surfaces with a linear field of normal vectors are dual to graphs bivariate polynomials (or rational functions). We discuss the geometric properties of these surfaces. In particular, using the dual representation it is shown that the convolution with general rational surfaces yields again rational surfaces. Similar results hold in the case of...
متن کاملVariational design of rational Bezier curves and surfaces
The design of curves and surfaces in C.A.D. systems has many applications in car, plane or ship industry. Because they offer more flexibility, rational functions are often prefered to polynomial functions to modelize curves and surfaces. In this work, several methods to generate rational Bezier curves and surfaces which minimize some functionals are proposed. The functionals measure a technical...
متن کاملComputing Rational Parametrizations of Canal Surfaces
Current CAD systems can represent curves and surfaces only in rational B-spline (NURBS) form ( .Farin, 1994; .Hoschek and Lasser, 1993). On the other hand, certain curves and surfaces that arise in practical applications such as offsets of rational curves or surfaces are in general not rational and therefore need to be approximated. This motivated .Farouki and Sakkalis (1990) to introduce the s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012