实平面奇异代数曲线的全局B样条逼近

提出了一种用k次B样条曲线全局逼近实平面k次代数曲线的算法,每个连通部分用一条B样条曲线逼近.它适合于任意亏格的不可约的实平面代数曲线(包括含奇异点的曲线).这种逼近建立在所提出的代数曲线胀开采样的基础上,这种胀开采样算法从本质上解决了奇异点周围采样难的问题.实验结果表明,该方法的逼近精度高于已有算法.

Global B-Spline Approximations of Singular Real Algebraic Plane Curves

This paper proposes an algorithm for globally approximating real algebraic plane curves of degree k with B-spline curves of the same degree. Each connected component is approximated with a B-spline curve. It is suitable for all irreducible real plane algebraic curves with arbitrary genus (including singular curves). This method is based on our blowup sampling method of algebraic curves, which solves the difficult problem of sampling around singular points in essence. The experimental results show that the algorithm achieves better accuracy than the existed methods.