Estimation of the Bezout number for piecewise algebraic curve

2003 ◽  
Vol 46 (5) ◽  
pp. 710 ◽  
Author(s):  
Renhong WANG
Keyword(s):  
Algebraic Curve ◽  
Piecewise Algebraic Curve

scholarly journals Least Squares Fitting of Piecewise Algebraic Curves

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Chun-Gang Zhu ◽  
Ren-Hong Wang
Keyword(s):  
Least Squares ◽  
Algebraic Curve ◽  
Algebraic Curves ◽  
Scattered Data ◽  
Energy Term ◽  
Bivariate Spline ◽  
Piecewise Algebraic Curve ◽  
Piecewise Algebraic Curves ◽  
The Given

A piecewise algebraic curve is defined as the zero contour of a bivariate spline. In this paper, we present a new method for fittingC1piecewise algebraic curves of degree 2 over type-2 triangulation to the given scattered data. By simultaneously approximating points, associated normals and tangents, and points constraints, the energy term is also considered in the method. Moreover, some examples are presented.

scholarly journals Piecewise algebraic curve

2002 ◽  
Vol 144 (1-2) ◽  
pp. 277-289 ◽  
Author(s):  
Ren-Hong Wang ◽  
Yi-Sheng Lai
Keyword(s):  
Algebraic Curve ◽  
Piecewise Algebraic Curve

scholarly journals An Algorithm for Isolating the Real Solutions of Piecewise Algebraic Curves

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Jinming Wu ◽  
Xiaolei Zhang
Keyword(s):  
Iterative Algorithm ◽  
Algebraic Curve ◽  
Spline Function ◽  
Algebraic Curves ◽  
The Real ◽  
Real Solutions ◽  
Bivariate Spline ◽  
Piecewise Algebraic Curve ◽  
Piecewise Algebraic Curves

The piecewise algebraic curve, as the set of zeros of a bivariate spline function, is a generalization of the classical algebraic curve. In this paper, an algorithm is presented to compute the real solutions of two piecewise algebraic curves. It is primarily based on the Krawczyk-Moore iterative algorithm and good initial iterative interval searching algorithm. The proposed algorithm is relatively easy to implement.

scholarly journals An Upper Bound of the Bezout Number for Piecewise Algebraic Curves over a Rectangular Partition

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Feng-Gong Lang ◽  
Xiao-Ping Xu
Keyword(s):  
Upper Bound ◽  
Algebraic Curve ◽  
Algebraic Curves ◽  
Zero Set ◽  
Bivariate Spline ◽  
Common Intersection ◽  
Piecewise Algebraic Curve ◽  
Piecewise Algebraic Curves ◽  
The Common ◽  
Intersection Points

A piecewise algebraic curve is a curve defined by the zero set of a bivariate spline function. Given two bivariate spline spaces (Δ) over a domainDwith a partition Δ, the Bezout number BN(m,r;n,t;Δ) is defined as the maximum finite number of the common intersection points of two arbitrary piecewise algebraic curves (Δ). In this paper, an upper bound of the Bezout number for piecewise algebraic curves over a rectangular partition is obtained.

On multiple curves. II

1945 ◽  
Vol 41 (2) ◽  
pp. 117-126
Author(s):  
W. V. D. Hodge
Keyword(s):  
Algebraic Curve ◽  
Abelian Integrals

In this note I consider the Abelian integrals of the first kind on an algebraic curve Γ which is a normal multiple of a curve C, as defined in Note I*.

Super Real Algebraic Curve

2004 ◽  
pp. 396-396
Author(s):  
Yolanda Lozano ◽  
Steven Duplij ◽  
Malte Henkel ◽  
Malte Henkel ◽  
Euro Spallucci ◽  
...  
Keyword(s):  
Algebraic Curve ◽  
Real Algebraic Curve

Number of points of an algebraic curve

1983 ◽  
Vol 17 (1) ◽  
pp. 53-54 ◽  
Author(s):  
S. G. Vlâdut ◽  
V. G. Drinfel'd
Keyword(s):  
Algebraic Curve
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