In this paper, an algorithm that determines a real algebraic curve is outlined. Its basicstep is to divide the plane into subdomain1s that include only simple branches of the algebraic curvewithout singular points. Ea...In this paper, an algorithm that determines a real algebraic curve is outlined. Its basicstep is to divide the plane into subdomain1s that include only simple branches of the algebraic curvewithout singular points. Each of the branches is then stably and efficiently traced in the particularsubdomain. Except for tracing, the algorithm requires only a couple of simple operations on poly-nomials that ran be carried out exacrly if the coefficients are rational, and the determination of the real roots of several univariate polynomials.展开更多
In this note we prove that the corner cutting procedure preserves continuityproperties,i.e.,a sequence of polygons obtained in this way belongs to the Lipschitz classof the same constant and exponent.As a consequence ...In this note we prove that the corner cutting procedure preserves continuityproperties,i.e.,a sequence of polygons obtained in this way belongs to the Lipschitz classof the same constant and exponent.As a consequence this also holds for all functions orcurves obtained as the limit of this procedure, such as the Bernstein polynomials,Bezierand spline parametric curves,etc.展开更多
文摘In this paper, an algorithm that determines a real algebraic curve is outlined. Its basicstep is to divide the plane into subdomain1s that include only simple branches of the algebraic curvewithout singular points. Each of the branches is then stably and efficiently traced in the particularsubdomain. Except for tracing, the algorithm requires only a couple of simple operations on poly-nomials that ran be carried out exacrly if the coefficients are rational, and the determination of the real roots of several univariate polynomials.
文摘In this note we prove that the corner cutting procedure preserves continuityproperties,i.e.,a sequence of polygons obtained in this way belongs to the Lipschitz classof the same constant and exponent.As a consequence this also holds for all functions orcurves obtained as the limit of this procedure, such as the Bernstein polynomials,Bezierand spline parametric curves,etc.
