摘要
为了提高平面二次曲线求交结果的精度和拓扑稳定性,提出一种基于二次曲线分类的二元二次方程组实根求解方法.首先将二元二次方程组的2个方程依照系数判断出其在x-y平面上的曲线类型,并根据不同的曲线类型分类情况,应用曲线的参数方程将原方程组转化为一元四次方程;然后求解出一元四次方程的解,并依此求出原二元二次方程组的解.实验结果表明,与吴消元法相比,该方法有效地提高了二元二次方程组求解的精度.
In order to improve accuracy and topological stability in calculating the intersection of planar quadratic curves, we present a real-root solving method for bivariate quadratic equation systems, which is based on the classification of the quadratic curves. Each equation is first classified to several types of quadratic curves in the x-y plane according to its coefficients. Then transform the equation system into a quartic equation via the parametric equation of an arbitrary quadratic curve. Solve the quartic equation, and finally obtain the roots of the bivariate quadratic equation system. The experiments illustrate that our method can improve the accuracy, compared with the method of Wu.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2014年第5期725-730,共6页
Journal of Computer-Aided Design & Computer Graphics
基金
国家"八六三"高技术研究发展计划(2012AA040902)
国家"九七三"重点基础研究发展计划项目(2010CB328001)
国家自然科学基金(61063029
61173077)
关键词
二元二次方程组
实根求解
几何分类
参数方程
二次曲线
bivariate quadratic equation system
real root solving
geometric classification
parametricequation
quadratic curve
