【摘要】 在计算机动画、计算机图形学、计算机辅助设计、机器人等领域中,经常需要检测多个实体间的位置关系。我们基于广义特征多项式的方法,给出了判断平面上椭圆与抛物线,椭圆与双曲线所有位置关系(分离、外切、相交、内切、内含等)的代数条件。这些代数条件表示为由椭圆与抛物线,椭圆与双曲线确定的广义特征多项式的根的分布。判别方法简单实用。更多还原

【Abstract】 In many scientific areas such as computer animation, computer graphics, computer aided geometry design and robot, it is very common to detect the positional relationship of several entities. We derive an algebraic condition (based on the generalized characteristic polynomial) for detecting the positional relationship of a planar ellipse and a planar parabola (hyperbola) by considering all the cases: separation, exterior contact, intersection, interior contact and inclusion. The algebraic condition can be represented by the distribution of the roots of the generalized characteristic equation of the ellipse and parabola (hyperbola). The criterion is simple and effective, and easier than old methods.更多还原